Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees...

15
Hindawi Publishing Corporation Mathematical Problems in Engineering Volume 2013, Article ID 293962, 14 pages http://dx.doi.org/10.1155/2013/293962 Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees in Multihop WiMAX Mesh Networks Chien-Yu Wu, 1 Hann-Jang Ho, 2 Sing-Ling Lee, 1 and Liang Lung Chen 1 1 Institute of Computer Science and Information Engineering, National Chung Cheng University, No. 168, Section 1, University Road, Min-Hsiung Township, Chia-yi County 62102, Taiwan 2 Department of Applied Digital Media, WuFeng University, No. 117, Section 2, Chiankuo Road, Min-Hsiung Township, Chia-yi County 62153, Taiwan Correspondence should be addressed to Hann-Jang Ho; [email protected] Received 17 September 2013; Accepted 9 October 2013 Academic Editor: Teen-Hang Meen Copyright © 2013 Chien-Yu Wu et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. e WiMAX technology has been defined to provide high throughput over long distance communications and support the quality of service (QoS) control applied on different applications. is paper studies the fairness time-slot allocation and scheduling problem for enhancing throughput and guaranteeing QoS in multihop WiMAX mesh networks. For allocating time slots to multiple subscribe stations (SSs), fairness is a key concern. e notion of max-min fairness is applied as our metric to define the QoS- based max-min fair scheduling problem for maximizing the minimum satisfaction ratio of each SS. We formulate an integer linear programming (ILP) model to provide an optimal solution on small-scale networks. For large-scale networks, several heuristic algorithms are proposed for better running time and scalability. e performance of heuristic algorithms is compared with previous methods in the literatures. Experimental results show that the proposed algorithms are better in terms of QoS satisfaction ratio and throughput. 1. Introduction In recent years, worldwide interoperability for microwave access (WiMAX), the broadband wireless access technology based on IEEE 802.16 standard [1], has received enormous attention in wireless communication networks. Based on IEEE 802.16, WiMAX system has been defined to provide high throughput over long distance and to support the quality of service (QoS) control applied on different applications. e IEEE 802.16 standard supports both the point-to-multipoint (PMP) mode and the mesh mode. In PMP mode, stations are organized as a cellular network, where subscriber stations (SSs) are directly connected to base stations (BSs). Such net- works require each SS to be within the communication range of its associated BS, thus greatly limiting the coverage range of the network. In the mesh mode, the mobile stations are connected as an ad hoc network. Moreover, the mobile stations send the packets to the neighbors; the neighbors relay the received packets to the base station. us, it is unnecessary to have a direct connection between each mobile station and the base station. In an IEEE 802.16 mesh network, transmissions can undergo a multihop manner. e standard specifies a cen- tralized scheduling mechanism for the BS to manage the network. Stations will form a routing tree rooted at the BS for the communication purpose. SSs in the network will send request messages containing their traffic demands to the BS to ask for resources. e BS then uses the topology information along with SSs’ requests to determine the routing tree and to allocate resources. All next generation cellu- lar wireless systems employ orthogonal frequency division multiple access (OFDMA) based multicarrier technology. An OFDMA frame consists of time slots in the time domain and subchannels in the frequency domain. A time-slot and sub- channel combination, referred to as a tile, is the minimum allocable unit. In the wireless transmission technology, the schedule for data transmission is a very important research issue. e main purpose of the schedule includes: (1) increasing the network throughput, (2) shorting the scheduled time, (3) pro- viding a guarantee QoS service, and (4) keeping transferring

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Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2013 Article ID 293962 14 pageshttpdxdoiorg1011552013293962

Research ArticleFairness Time-Slot Allocation and Scheduling with QoSGuarantees in Multihop WiMAX Mesh Networks

Chien-Yu Wu1 Hann-Jang Ho2 Sing-Ling Lee1 and Liang Lung Chen1

1 Institute of Computer Science and Information Engineering National Chung Cheng UniversityNo 168 Section 1 University Road Min-Hsiung Township Chia-yi County 62102 Taiwan

2Department of Applied Digital Media WuFeng University No 117 Section 2 Chiankuo RoadMin-Hsiung Township Chia-yi County 62153 Taiwan

Correspondence should be addressed to Hann-Jang Ho hannjanghogmailcom

Received 17 September 2013 Accepted 9 October 2013

Academic Editor Teen-Hang Meen

Copyright copy 2013 Chien-Yu Wu et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

TheWiMAX technology has been defined to provide high throughput over long distance communications and support the quality ofservice (QoS) control applied on different applicationsThis paper studies the fairness time-slot allocation and scheduling problemfor enhancing throughput and guaranteeing QoS in multihop WiMAX mesh networks For allocating time slots to multiplesubscribe stations (SSs) fairness is a key concern The notion of max-min fairness is applied as our metric to define the QoS-based max-min fair scheduling problem for maximizing the minimum satisfaction ratio of each SS We formulate an integer linearprogramming (ILP) model to provide an optimal solution on small-scale networks For large-scale networks several heuristicalgorithms are proposed for better running time and scalabilityThe performance of heuristic algorithms is compared with previousmethods in the literatures Experimental results show that the proposed algorithms are better in terms of QoS satisfaction ratio andthroughput

1 Introduction

In recent years worldwide interoperability for microwaveaccess (WiMAX) the broadband wireless access technologybased on IEEE 80216 standard [1] has received enormousattention in wireless communication networks Based onIEEE 80216 WiMAX system has been defined to providehigh throughput over long distance and to support the qualityof service (QoS) control applied on different applicationsTheIEEE 80216 standard supports both the point-to-multipoint(PMP) mode and the mesh mode In PMPmode stations areorganized as a cellular network where subscriber stations(SSs) are directly connected to base stations (BSs) Such net-works require each SS to be within the communicationrange of its associated BS thus greatly limiting the coveragerange of the network In the mesh mode the mobile stationsare connected as an ad hoc network Moreover the mobilestations send the packets to the neighbors the neighborsrelay the received packets to the base station Thus it isunnecessary to have a direct connection between eachmobilestation and the base station

In an IEEE 80216 mesh network transmissions canundergo a multihop manner The standard specifies a cen-tralized scheduling mechanism for the BS to manage thenetwork Stations will form a routing tree rooted at the BS forthe communication purpose SSs in the network will sendrequest messages containing their traffic demands to theBS to ask for resources The BS then uses the topologyinformation alongwith SSsrsquo requests to determine the routingtree and to allocate resources All next generation cellu-lar wireless systems employ orthogonal frequency divisionmultiple access (OFDMA) basedmulticarrier technology AnOFDMA frame consists of time slots in the time domain andsubchannels in the frequency domain A time-slot and sub-channel combination referred to as a tile is the minimumallocable unit

In the wireless transmission technology the schedule fordata transmission is a very important research issue Themain purpose of the schedule includes (1) increasing thenetwork throughput (2) shorting the scheduled time (3)pro-viding a guarantee QoS service and (4) keeping transferring

2 Mathematical Problems in Engineering

fairness in the networkTherefore it is very important to havea good scheduling algorithm in the wireless transmission

Since current wireless network systems usually use theOFDMA as communication technology they also plan toprovide various QoS services for a large number of usersThe high data transfer throughput and QoS assurance havebecome the main goal of the wireless network [2ndash4] To getmore efficient bandwidth usage and to provide better QoSservices to users of the wireless network dynamic resourceallocation method has been widely studied in [2 3] Whenwe consider the real-time service flows such as VoIP andwireless multimedia communications their quality of ser-vices (QoSs) should be satisfied The real-time connectionswill periodically transmit or receive a constant amount oftraffic

Recently several literatures discuss the schedulingscheme for multihop transmissions in WiMAX meshnetworks since the standard protocol usually does notspecify any particular scheduling scheme For example thethroughput and fairness issues have been studied in [5]However the previous literature does not guarantee the QoSwhile considering the fairness scheduling of SSs in real timeIt is worth exploring how the well-known fairness schemessuch as max-min max-flow absolute and proportionalfairness can be implemented in 80216j networks with theQoS constraint This paper concentrates on the time-slotallocation and scheduling for WiMAX mesh networks withOFDMAprotocolThe goal of this paper is to provide variousscheduling schemes which optimize both QoS and fairnessof resource allocations for the WiMAX mesh networksFrom the experimental results we show that our proposedschemes are better than the previous work in terms of QoSsatisfaction ratio

This paper applies the concept ofmax-min fair schedulingto enhance the minimum satisfaction ratio over the WiMAXmesh networks We propose an ILP model to solve the prob-lem and provide heuristicmethods to ensure theQoS priorityof scheduling to achieve better overall QoS satisfaction ratioand throughput

The main contributions of our work are listed below(1) Propose a heuristic algorithm that can optimize the

max-min fair and guarantee QoS In our proposedmethod QoS requirements are a primary consider-ation for allocating resources to various SSs If thereare remaining resources after stratifying the QoSrequirements we will then consider the max-min fairscheduling to improve the overall throughput andminimize the satisfaction ratio In IEEE 80216j meshnetworks the proposed algorithm can meet the QoSrequirements of various SSs in a frame and enhancethe network overall QoS satisfaction ratio

(2) Exploit spectral reuseThe spectral reuse is adopted byour heuristic algorithm to avoid the packets collisionsto improve the network throughput and QoS satisfac-tion ratio

(3) Construct the ILP model We construct an integer lin-ear programming model which constraints on theQoS requirements andmax-min fairness assignments

for solving the optimization problem in multihopWiMAX mesh networks

2 Network Model

21 MMR Infrastructure This paper focuses on the time-slotallocation and scheduling on the network system with IEEE80216j mobile multihop relay-based (MMR) infrastructureIn accordancewith the recommendation ofWiMAXstandard[6] BS is the root of the tree to assist the transmission ofWiMAXmesh networks The RSs are the intermediate nodesof the tree and the SSs are the leaf node of the tree

We mainly focus on the scheduling between the SSs andRSs Our goal is to find a scheduling method which can meetthe QoS requirements of each SS and achieve a fair allocationof network resourcesWe also study how to allocate subchan-nels and time slots according to the bandwidth requirementsof each SS in a frame We assign the transmission scheduleto maximize the minimum satisfaction ratio over all SSs toget the overall max-min fairness for the multihop relayedWiMAX mesh network

22MeshMode We focus on the 80216mesh networkwhichis composed by one BS and several SSs The BS is responsiblefor connecting the back-end network Each SS transfers datato neighboring SSs without the BSrsquos agreementThe data flowaway from the BS is called downlink data flow converselywhich toward the BS is called uplink data flow For meshnetworks most studies focus on topology design [7] In80216mesh networks some issues are studied for supportingQoS in [8 9] Shetiya and Sharma [8] studied theQoS routingproblem of Central Scheduling Hong and Pang [9] consid-ered the multihop scheduling problem with bandwidth anddelay constraints In these researches different approaches forestablishing the routing tree of mesh networks are analyzedand some issues of time-slot allocation are discussed

23 Spectral Reuse This paper applies spectral reuse to solvethe resource allocation problem for the 80216 mesh networkThe advantage of using spectral reuse is to improve the trans-mission capacity and the throughput of network Fu et al[10] proposed an algorithm tomaximize the usage of spectralreuse Chen et al [11] studied how to use the spectral reuse tosolve the problem of resource allocation

24 Interference Model Scheduling strategies must ensurethat transmissions in each time slot do not collide Thereare two types of collision situations in the wireless networkenvironment They are called Primary Interference and Sec-ondary Interference [12 13] Primary Interference occurs in asingle time slot of scheduling the SS cannot domore than onething In other words the SS can only transfer or receive datain a single time slot Secondary Interference occurs when theoriginally receiver119883 turns into the transfer but the user119883 isstill in the range of the transfer 119884 The user 119883 will affect thetransmission of the user 119884 There are some studies that focuson WiMAX mesh network interference problems [14 15]Wei et al [16] proposed an interference-aware multihop

Mathematical Problems in Engineering 3

Table 1 Parameters and variables table

Symbol Description119866 = (119881 119864) Mesh network topology G119881 The set of stations119864 The set of edges119879 The set of time slot in a frame119867 The set of subchannel in each time slotℎ The index parameter of subchannel forallℎ isin 119867S A set of all the SSs119904119894

A subscriber SS 119894 forall119904119894isin S

R Set of all relay stations119903119894

A relay node 119894 forall119903119894isin R

119888119897

The link capacity of each link 119897 forall119897 isin 119864hp119894

The set of hops from 119904119894to BS

br119894

Theminimum bandwidth requirement of the 119904119894for guaranteeing QoS

BR119894

Themaximum bandwidth requirement of the 119904119894

120582119894

The actual quantity of node 119894 upload the packet forall119894 isin S cupR

120590119894

The actual quantity of node 119894 upload the required tile forall119894 isin S cupR

119910119894

119904119894satisfaction ratio

tr119894

The tile requirement of 119904119894for transmitting packets from 119904

119894to BS during each hop

TR The set of tile requirement TR = tr119894| forall119904119894isin S

119868 (sdot) The subset of nodes which will interfere with node or link transceiving119868119894

The subset of nodes which will not interfere with 1199041015840119894119904 transceiving

pa (119894) The parent of node 119894 on the tree topologycd (119903) The set of children node SSs or RSs of 119903119891119897119905ℎ

A decision variable which is 1 if link 119897 is assigned with time slot 119905 and subchannel ℎ and 0 otherwiseOL119894 IL119894

The set of output and input links of node 119894 respectively

routing algorithm to maximize the degree of use of networkbandwidth to maximize the network throughput

25 Fairness Scheduling Nowadays the related works onWiMAX mesh networks through a network of relay stationsscheduling and resource allocation are concerned widely It iscommon to study the fairness in many wireless networks in[17ndash20] Sayenko et al [19] studied the proportional fairnessand considered the difference between frequency selectionswith multiuser scheduling problems Andrews and Zhang[20] proposed a round-robin based scheduling method forIEEE 80216 BS to ensure QoS requirements of the SS inuplink (UL) and downlink (DL) can be met But the networkbandwidth usage efficiently and bandwidth requirementswere not considered in [19 20]

In this paper we propose heuristic scheduling algorithmsthat identify each SS to maximize the minimum satisfactionratio in the network and meanwhile to meet the bandwidthrequirements for each SS We compare the QoS satisfactionratio throughput andmin satisfaction ratiowith the previousmethod proposed in [21] Experimental results show that ourmethod is better in terms of QoS satisfaction ratio

3 QoS-Based Max-Min Fair Scheduling

31 Problem Definition Based on theWiMAX standard [1] atree network topology119866 = (119881 119864) is given For readability thefollowing parameters and variables are listed in Table 1 A BSas the root a set of subscriber users S = 119904

1 1199042 119904

119899 as the

leaf nodes and a set of relay stationsR = 1199031 1199032 119903

119898 as the

intermediate nodes Let the parameter 119888119897be the link capacity

of each link 119897 forall119897 isin 119864 Let the parameter br119894be the minimum

bandwidth requirements of each SS 119904119894during a frame Let

the parameter BR119894be themaximum bandwidth requirements

of each SS 119904119894during a frame The problem is limited to the

following restrictions(1) no spectral reuse for any pair of links which interfere

with each other(2) an RS cannot transmit and receive data at the same

time(3) the total number of data delivered by an RS to BS

during a frame must be equal to the number of datareceived from its children node during one frame

(4) must satisfy the minimum bandwidth requirementsof each SS to guarantee QoS

4 Mathematical Problems in Engineering

Therefore the multihop fair scheduling with QoS con-trol problem is defined as to find a way to schedule thesubchannel-time slot (tile) for a scheduling frame After thetile scheduling the minimum satisfaction ratio 119910

119894of each 119904

119894

will be maximized and the bandwidth requirements of each119904119894will be satisfied to guarantee QoS

32 Integer Linear Programming for the Problem In [22] itwas proved that scheduling with channel capacity is NP-hardTherefore our scheduling problem with time-varying chan-nel will be NP-hard To find an optimal solution we providean Integer Linear Programming (ILP) for this problem

For each node 119894 isin S cup119877 pa(119894) denotes the parent of node119894 on the tree topology For each RS 119903 isin R the parameter cd(119903)is used to represent the set of children node (SSs or RSs) of 119903For each node 119894 in tree network 119866 the variable 119891119897

119905ℎdenotes

that whether the link 119897 = (119894 119895) is assigned with time-slot 119905and subchannel ℎ We refer to the method [23 24] to verifywhether there are interferences between these two edges 119868(119897)represents the interference link set of link 119897

Maximize 119910 (1)

sum

1198971015840isin119868(119897)

1198911198971015840

119905ℎ+ 119891119897

119905ℎle 1 forallℎ isin 119867 forall119905 isin 119879 forall119897 isin OL

119894

forall119894 isin S cupR

(2)

sumforallℎisin119867

sumforall119897isinOL

119903

119891119897

119905ℎ+ sumforallℎisin119867

sumforall119897isinIL

119903

119891119897

119905ℎle 1 forall119905 isin 119879

forall119903 isin R

(3)

sumforall119897isinIL

119903

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897

le sumforall119897isinOL

119903

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897 forall119903 isin R

(4)

sumforall119897isinOL

119894

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897ge br119894 forall119894 isin S (5)

119910 le 119910119894 forall119894 isin S (6)

where 119910119894=

1

BR119894

sumforall119897isinOL

119894

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897 forall119894 isin S (7)

119891119897

119905ℎ= 0 1 forall119905 isin 119879 forallℎ isin 119867 forall119897 isin 119864 (8)

The objective function of QoS-based max-min fairscheduling problem is shown as (1) The goal is to maximizethe minimum satisfaction ratio 119910 The satisfaction ratio 119910

119894is

calculated by (7) In (7) the parameter BR119894is the maximum

bandwidth requirement of 119904119894 the parameter 119888

119897is the capacity

of link 119897 and the decision variables 119891119897119905ℎ

are defined in (8) Ifthe time-slot (119905 ℎ) is allocated to link 119897 the value of decisionvariable 119891119897

119905ℎis 1 Otherwise the value of decision variable 119891119897

119905ℎ

is 0 The QoS-based max-min fair scheduling problem hasfour constraints as follows

(i) The spectral reuse constraints are shown as (2) For alllink 119897 in OL

119894 a tile can be used no more than once in

each pair of interference links 119868(119897) Where the OL119894is

the set of output links of all nodes 119894 isin S cupR

(ii) The single transceiver constraints are shown as (3)For all time-slot 119905 in119879 each RS 119903 in119877 cannot transmitand receive data in the same time slot

(iii) The flow constraints are shown as (4) All data that areaccepted byRS 119903 in a framewill be sent out in the sameframe Where the parameters OL

119903and IL

119903are the set

of output and input links of RS 119903

(iv) The minimum bandwidth requirement constraintsare shown as (5) The minimum bandwidth require-ments of each 119904

119894must be satisfied to guarantee QoS in

a frame

(v) The satisfaction ratio constraints are shown as (6)The satisfaction 119910

119894of each 119904119904

119894will be greater than the

variable 119910

33 Greedy Algorithm for QoS-Based Max-Min Fair Schedul-ing Though the ILP solution can be used to obtain optimalsolutions for small-sized problem but if the network scalegrows larger it has large time and space consumption forlarge-sized network The heuristics algorithm is needed forbetter running time in large-sized network In the followingwe designed a heuristic algorithm

331 Heuristic Algorithm The strategy of the proposedheuristic algorithm is smallest total bandwidth requirementfirst and then applying spectral reuse scheme to assignresource After QoS of all SSs is guaranteed the max-min fairscheduling scheme is used to enhance the overall throughputand satisfaction ratio The proposed heuristic algorithm hasfour steps as follows

Step 1 (allocate limited resources to meet the QoS require-ments of each SS) At first the total number of tile require-ments (tr

119894times hp119894) of each 119904

119894is estimated Then the resources

are allocated to all SSs by Algorithm 2 119876119900119878 119878119888ℎ119890119889119906119897119894119899119892()in increasing order of total tile requirements Until theresources are not enough allocated or the requirements ofall SSs are met the scheduler will terminate the process of119876119900119878 119878119888ℎ119890119889119906119897119894119899119892()

Step 2 (increase the number of meeting QoS requirements) Ifthe bandwidth requirements of 119904

119894are not satisfied the spectral

reuse mechanism is used to find available resource for eachunmet SS inAlgorithm 3 119876119900119878 119878119901119890119888119905119903119886119897 119877119890119906119904119890()The strategyof spectral reuse is to gain tiles from all allocated tiles of 119904

119895

there is no link between each 119904119895and the picked 119904

119894 Hence the

satisfaction rate has an opportunity to increase

Mathematical Problems in Engineering 5

Input 119866SR 119867 119879 brBROutput min satisfaction ratio QoS satisfaction ratio throughput

(1) Initialization 120582119894larr 0 120590

119894larr 0 forall119904

119894isin 119878119878

(2) for all 119878119878 node V119894on 119866 do

(3) tr119894larr lceil

BR119894

119888119894

rceil

(4) for all RS V119895on the path hp

119894from V

119894to BS do

(5) tr119894larr tr119894+ lceil

BR119894

119888119895

rceil

(6) endfor(7) endfor(8) Sort (TR)(9) 119860

119905larr |119867| forall119905 isin 119879

(10) Set all 119904119904119894119876119900119878119860119897119897119900119888119886119905119890119889 = false(11) QoS Scheduling (119866SR 119860 119879TR brBR)(12) QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)(13) Maxmin Scheduling (119866SR 119860 119879 119884BR)(14) Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868BR)

Algorithm 1 Heuristic Algorithm

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Step 2(3) 119894119899119889119890119909 larr 1

(4) for 119896 = 1 rarr |hp119894|

(5) 119903119890119902 larr lceilbr119894

119888119896

rceil

(6) for 119905 = 119894119899119889119890119909 rarr |119879|

(7) if 119860119905ge 119903119890119902

(8) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(9) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(10) else(11) if (|119879| minus 119905) lt (hp

119894minus 119896)

(12) free all tiles which allocated to 119904119894

(13) 119878119878 larr 119878119878 119904119894

(14) go to Step 1(15) else(16) 119860

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905 119894119899119889119890119909 larr 119905 119905 larr |119879|

(17) Step 3 if all hops of 119904119894are allocated successfully

(18) Slarr S 119904119894

(19) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120590119894times 119888119894

(20) for all RS 119903119904119895on the path from 119904

119894to BS do

(21) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120590119895times 119888119895

(22) endfor

(23) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(24) Step 4 if all SSs meet requirement or no sufficient resources can be allocated(25) terminate scheduling(26) else go to Step 1

Algorithm 2 QoS Scheduling (119866SR 119860 119879TR brBR)

6 Mathematical Problems in Engineering

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(3) Step 2(4) 119894119899119889119890119909 larr 1

(5) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(6) 119903119890119902 larr lceilbr119894

119888119896

rceil

(7) for 119905 = 119894119899119889119890119909 rarr |119879|

(8) if (119860119905+ 119877119905) gt 119903119890119902 then

(9) if 119860119905ge 119903119890119902

(10) 119860119905larr 119860119905minus 119903119890119902

(11) else(12) 119860

119905larr 0 119877

119905larr 119877119905minus (119903119890119902 minus 119860

119905)

(13) 119903119890119902 larr 0 119894119899119889119890119909 larr 119905 119905 larr |119879|

(14) else if (|119879| minus 119905) lt (hp119894minus 119896)

(15) free all tiles which allocated to 119904119894during this step

(16) 119878119878 larr 119878119878 119904119894

(17) go to Step 1(18) Step 3(19) if the resource is fully allocated successfully to all hops of 119904

119894 then

(20) Slarr S 119904119894

(21) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120582119894+ 120590119894times 119888119894

(22) for all RS 119903119904119895on the path from 119904

119894to BS do

(23) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120582119895+ 120590119895times 119888119895

(24) endfor

(25) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(26) Step 4 if all SSs meet QoS or no sufficient resources can be allocated then(27) Termination(28) else go to Step 1

Algorithm 3 QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)

Step 3 (remaining resources to do the max-min fair schedul-ing)When the first two steps are finished then some remain-ing resources are available Then the available tiles are allo-cated to the SSs that have lowest satisfaction and satisfactionratio is upgraded by Algorithm 4 119872119886119909119898119894119899 119878119888ℎ119890119889119906119897119894119899119892()

Step 4 (upgrade the min satisfaction ratio) FinallyAlgorithm 5 119872119886119909119898119894119899 119878119901119890119888119905119903119886119897 119877119890119906119904119890() finds out an 119904

119894

which has lowest satisfaction ratio among all SSs to increaseits satisfaction ratio Until all the SSs are allocated availabletiles by the spectral reuse mechanism or the satisfactionratio of 119904

119894are equal to 1 Then the procedure of scheduling

algorithm will be finished

332 Scheduling Algorithm Description with an Example Asshown in Figure 1 the networks are composed of one BSthree RSs = 119903

1 1199032 1199033 and six SSs = 119904

1 1199042 1199043 1199044 1199045 1199046 The

number of maximum bandwidth requirements of each SSsBR119894are 10 10 8 8 8 and 10 The bandwidth requirements

of SSs br119894are 7 2 4 5 6 and 3 for guaranteeing QoS The

capacity of each link 119888119897is set to 1 The number of time-slots

119905 is set to 7 The number of subchannels ℎ is set to 3 Theinterference of each RS and SS is defined as follows

119868 (1199031) = 119904

1 1199042 1199032 1199033 119868 (119903

2) = 119903

1 1199033 1199043 1199044

119868 (1199033)= 1199032 1199045 1199046 119868 (119904

1)= 1199042 1199031 119868 (119904

6)= 1199045 1199033

119868 (1199042) = 119904

1 1199031 1199043 119868 (119904

3) = 119904

2 1199034 1199044

119868 (1199044) = 119904

3 1199032 1199045 119868 (119904

5) = 119904

4 1199033 1199046

(9)

At first the value of tr119894(= lceilBR

119894119888119894rceil + sum

forall119895isinhp119894119904119894lceilBR119894119888119895rceil)

of each 119904119894is calculated at lines (2)ndash(7) in Algorithm 1 Then

the value of TR is sorted by increasing order at line (8) inAlgorithm 1 The value of parameter 119860

119905is initialized as |119867|

for all time-slot 119905The limited resources are allocated by Algorithm 2The 119904

119894

is selected with minimum total tile requirement tr119894at line

(1) of Algorithm 2 Then the resources are allocated atlines (2)ndash(16) of Algorithm 2 After resources allocation arecompleted the parameters and variables of the SS and RSwill be updated at lines (17)ndash(23) of Algorithm 2 At lines

Mathematical Problems in Engineering 7

Output 119884119860(1) Step 1(2) Choose a 119904

119894with the smallest satisfaction

(3) if 119910119894== 1 then terminate scheduling

(4) else go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(8) 119903119890119902 larr lceilBR119894

119888119896

rceil minus 120590119896

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else if 119860119905lt 119903119890119902

(14) 119860119905larr 0 119905119903

119894larr 119903119890119902 minus 119860

119905

(15) else if (|119879| minus 119905) lt (1003816100381610038161003816hp1198941003816100381610038161003816 minus 119896)

(16) free all tiles which allocated to 119904119894in Step 2

(17) 119878119878 larr 119878119878 119904119894

(18) go to Step 1(19) Step 3(20) if the resource is fully allocated successfully to all hops of 119904

119894 then

(21) Slarr S 119904119894

(22) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(23) for all RS 119903119904119895on the path from 119904

119894to BS do

(24) 120582119895larr 120582119895+ 119888119894

(25) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(26) Step 4(27) if 119910

119894= 1 or S is empty then

(28) terminate scheduling(29) else go to Step 1

Algorithm 4 Maxmin Scheduling (119866SR 119860 119879 119884BR)

(24)ndash(26) of Algorithm 2 if no available resources are ableto allocate to each SS the procedure goes back to the mainalgorithm Otherwise the scheduler continue to find the nextSSwhich can allocate resources tomeet theQoS requirementsof the SS In our example the total number of tiles is 21 InAlgorithm 2 the sequence of 119904

119894will be selected as 119904

2 1199046 1199043

The value of parameter tr119894is estimated as follows

tr1= lceil

BR1

1198881

rceil + sumforall119895isinhp

11199041

lceilBR1

119888119895

rceil = 14

tr2= lceil

BR2

1198882

rceil + sumforall119895isinhp

21199042

lceilBR2

119888119895

rceil = 4

tr3= lceil

BR3

1198883

rceil + sumforall119895isinhp

31199043

lceilBR3

119888119895

rceil = 8

tr4= lceil

BR4

1198884

rceil + sumforall119895isinhp

41199044

lceilBR4

119888119895

rceil = 10

tr5= lceil

BR5

1198885

rceil + sumforall119895isinhp

51199045

lceilBR5

119888119895

rceil = 12

tr6= lceil

BR6

1198886

rceil + sumforall119895isinhp

61199046

lceilBR6

119888119895

rceil = 6

(10)

The scheduling results of Algorithm 2 are shown inFigure 2

Moreover if the bandwidth requirements of some SSsare still unsatisfied the number of 119878119878 with QoS guaranteewill be raised by Algorithm 3 The bandwidth requirementunsatisfied 119904

119894will be found with the minimum tr

119894at line

(1) of Algorithm 3 All allocated tiles of 119904119895 forall119904119895isin 119868119894 are

recovered to set119877 at line (2) ofAlgorithm 3Then the spectralreuse strategy is used to maximize satisfaction ratio at lines(3)ndash(17) in Algorithm 3 for picked 119904

119894 If the available tiles

119860119905+ 119877119905can meet the requirement of 119904

119894at time slot 119905 for

119896th hop the required tiles are allocated at lines (8)ndash(13) ofAlgorithm 3 While the requirements of all hops are met theparameters and variables of the SS and RS will be updated at

8 Mathematical Problems in Engineering

Output 119884(1) Step 1 Choose a 119904

119894with the smallest satisfaction

(2) if 119910119894= 1 then terminate scheduling

(3) else Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(4) go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr hp119894

(8) 119903119890119902 larr tr119894

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902 then

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else(14) if (119860

119905+ 119877119905) ge 119903119890119902 then

(15) assign 119903119890119902 available tiles to 119896th hop of 119904119894

(16) else if (|119879| minus 119905) lt (hp119894minus 119896) then

(17) free all tiles which allocated to 119904119894in Step 2

(18) Slarr S 119904119894

(19) go to Step 1(20) else(21) 119860

119905larr 0 119877

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905

(22) Step 3 if all hops of 119904119894are fully allocated successfully then

(23) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(24) for all RS 119903119904119895on the path from 119904

119894to BS do

(25) 120582119895larr 120582119895+ 119888119894

(26) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(27) end for(28) Step 4(29) if 119910

119894= 1 or S is empty then

(30) terminate scheduling(31) else go to Step 1

Algorithm 5 Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868 119861119877)

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri7 2 4 5 6 3

h1

h2

h3t1 t2 t3 t4 t5 t6 t7

OFDMA frame

Figure 1 The network topology

Mathematical Problems in Engineering 9

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

5 6 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

7

hop1 hop2

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

Figure 2 The allocation of resources meets the QoS requirements of 1199042 1199043 and 119904

6

67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4 5 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA framehop1

s4s2

hop2

s3

s4s6 s3s3s3

r1

r1r2

r2

r2r2

r3

r3

r3

s4s6

s4s6

s2 s4

4 + 5

Figure 3 1199044performs the spectral reuse

lines (18)ndash(25) in Algorithm 3 Otherwise all acquired tilesof 119904119894are freed at line (15) of Algorithm 3 If the resources

allocation have not been finished the scheduler will findout the next one to meet the bandwidth requirements of 119904

119894

to guarantee QoS by the spectral reuse strategy Until theminimum bandwidth requirements of all SSs are satisfied orthe available tiles are not enough to allocate then this stepwillbe terminated The results of first hop of 119904

4are scheduled by

spectral reuse strategy of Algorithm 3 as shown in Figure 3Because the available tiles are insufficient at second hop 119904

4

cannot be assigned as shown in Figure 4 Hence all acquiredtiles of 119904

4need to be freed Due to the available tiles which are

not enough to assign this step is terminatedIf the remaining available tiles have not been allocated

completely then these remaining resources can increase thenetwork minimum satisfaction ratio by Algorithm 4 The SSwould be picked with lowest satisfaction ratio in sequence atline (2) of Algorithm 4 While the lowest satisfaction ratio isequal to 1 the scheduling of Algorithm 4 is terminated

Otherwise the scheduler will check whether there avail-able tiles can be assigned to the 119904

119894at lines (5)ndash(18) of

Algorithm 4 if the resources could be allocated to the SSAfter the parameters and variables of SS and RS are updatedat lines (19)ndash(26) of Algorithm 4 the scheduler continueto find out the lowest satisfaction ratio of SS and to assignavailable tiles to increase satisfaction ratio Until no availabletiles can be allocated or the requirements of all SSs are metthe scheduling procedure is terminated The max-min fairscheduling is performed with remaining tiles in Algorithm 4The satisfaction ratio of 119904

1 1199044 1199045 is 0 Because the second

hop has no enough available tiles the schedule fails for1199041 1199044 1199045 The scheduling results of Algorithm 4 are shown

in Figure 5Finally the spectral reuse strategy is operated on the

SS which has lowest satisfaction ratio for increasing theminimum satisfaction ratio in Algorithm 5 At line (1) ofAlgorithm 5 the scheduler pick a 119904

119894that has lowest satisfac-

tion ratio If the lowest satisfaction ratio equals to 1 at line (2)

10 Mathematical Problems in Engineering

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

bri

hop1 hop2

Figure 4 When lacking resources 1199044cannot perform spectral reuse

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

y1 = 0 y2 = 15 y3 = 12 y4 = 0 y5 = 0 y6 = 310

hop1 hop2

Figure 5 No remaining resources can be used to perform max-min fair scheduling

of Algorithm 5 the scheduling of Algorithm 5 is terminatedOtherwise all allocated tiles of 119904

119895are recovered to set119877 forall119904

119895isin

119868119894at line (3) of Algorithm 5 Then the spectral reuse strategy

is used to allocate tiles to 119904119894for maximizing satisfaction ratio

at lines (5)ndash(21) of Algorithm 5 When the available tiles set119860119905enough to assign to 119896th hop the tiles of 119860

119905set are firstly

allocated at lines (10)ndash(12) of Algorithm 5 When the set 119860119905

cannot fulfill the 119903119890119902 of 119904119894 both the set 119860

119905and 119877

119905are applied

to allocate at lines (13)ndash(21) of Algorithm 5 When both theset 119860119905and 119877

119905cannot satisfy the 119903119890119902 of 119904

119894at time slot 119905 at line

(21) of Algorithm 5 the difference of required tiles wouldbe found at next time slot If the requirement of all hopscannot be met all acquired tiles of 119904

119894have to be freed at

lines (16)ndash(19) of Algorithm 5 Then the scheduler continueto find out next SS until no resources can be allocated ByAlgorithm 4 the scheduled satisfaction ratio of 119904

1 1199044 1199045 is

0 Algorithm 5 enhances satisfaction ratio of 1199041 1199044 1199045 to

01 0125 0125 The scheduling results of Algorithm 5 areshown in Figure 6

Finally we get min satisfaction ratio = 01 QoS satisfac-tion ratio = 05 and throughput = 12 as shown in Figure 7

4 Simulation

In this section we implement our heuristic algorithms andthe algorithm proposed in [21] for performance comparisonWe compare three parameters in the experimental resultsnamely average minimum satisfaction ratio average QoSsatisfaction ratio and average throughput

41 Environmental Setup For experimental environmentsetting SS transmission range and interference range are

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

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Stochastic AnalysisInternational Journal of

Page 2: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

2 Mathematical Problems in Engineering

fairness in the networkTherefore it is very important to havea good scheduling algorithm in the wireless transmission

Since current wireless network systems usually use theOFDMA as communication technology they also plan toprovide various QoS services for a large number of usersThe high data transfer throughput and QoS assurance havebecome the main goal of the wireless network [2ndash4] To getmore efficient bandwidth usage and to provide better QoSservices to users of the wireless network dynamic resourceallocation method has been widely studied in [2 3] Whenwe consider the real-time service flows such as VoIP andwireless multimedia communications their quality of ser-vices (QoSs) should be satisfied The real-time connectionswill periodically transmit or receive a constant amount oftraffic

Recently several literatures discuss the schedulingscheme for multihop transmissions in WiMAX meshnetworks since the standard protocol usually does notspecify any particular scheduling scheme For example thethroughput and fairness issues have been studied in [5]However the previous literature does not guarantee the QoSwhile considering the fairness scheduling of SSs in real timeIt is worth exploring how the well-known fairness schemessuch as max-min max-flow absolute and proportionalfairness can be implemented in 80216j networks with theQoS constraint This paper concentrates on the time-slotallocation and scheduling for WiMAX mesh networks withOFDMAprotocolThe goal of this paper is to provide variousscheduling schemes which optimize both QoS and fairnessof resource allocations for the WiMAX mesh networksFrom the experimental results we show that our proposedschemes are better than the previous work in terms of QoSsatisfaction ratio

This paper applies the concept ofmax-min fair schedulingto enhance the minimum satisfaction ratio over the WiMAXmesh networks We propose an ILP model to solve the prob-lem and provide heuristicmethods to ensure theQoS priorityof scheduling to achieve better overall QoS satisfaction ratioand throughput

The main contributions of our work are listed below(1) Propose a heuristic algorithm that can optimize the

max-min fair and guarantee QoS In our proposedmethod QoS requirements are a primary consider-ation for allocating resources to various SSs If thereare remaining resources after stratifying the QoSrequirements we will then consider the max-min fairscheduling to improve the overall throughput andminimize the satisfaction ratio In IEEE 80216j meshnetworks the proposed algorithm can meet the QoSrequirements of various SSs in a frame and enhancethe network overall QoS satisfaction ratio

(2) Exploit spectral reuseThe spectral reuse is adopted byour heuristic algorithm to avoid the packets collisionsto improve the network throughput and QoS satisfac-tion ratio

(3) Construct the ILP model We construct an integer lin-ear programming model which constraints on theQoS requirements andmax-min fairness assignments

for solving the optimization problem in multihopWiMAX mesh networks

2 Network Model

21 MMR Infrastructure This paper focuses on the time-slotallocation and scheduling on the network system with IEEE80216j mobile multihop relay-based (MMR) infrastructureIn accordancewith the recommendation ofWiMAXstandard[6] BS is the root of the tree to assist the transmission ofWiMAXmesh networks The RSs are the intermediate nodesof the tree and the SSs are the leaf node of the tree

We mainly focus on the scheduling between the SSs andRSs Our goal is to find a scheduling method which can meetthe QoS requirements of each SS and achieve a fair allocationof network resourcesWe also study how to allocate subchan-nels and time slots according to the bandwidth requirementsof each SS in a frame We assign the transmission scheduleto maximize the minimum satisfaction ratio over all SSs toget the overall max-min fairness for the multihop relayedWiMAX mesh network

22MeshMode We focus on the 80216mesh networkwhichis composed by one BS and several SSs The BS is responsiblefor connecting the back-end network Each SS transfers datato neighboring SSs without the BSrsquos agreementThe data flowaway from the BS is called downlink data flow converselywhich toward the BS is called uplink data flow For meshnetworks most studies focus on topology design [7] In80216mesh networks some issues are studied for supportingQoS in [8 9] Shetiya and Sharma [8] studied theQoS routingproblem of Central Scheduling Hong and Pang [9] consid-ered the multihop scheduling problem with bandwidth anddelay constraints In these researches different approaches forestablishing the routing tree of mesh networks are analyzedand some issues of time-slot allocation are discussed

23 Spectral Reuse This paper applies spectral reuse to solvethe resource allocation problem for the 80216 mesh networkThe advantage of using spectral reuse is to improve the trans-mission capacity and the throughput of network Fu et al[10] proposed an algorithm tomaximize the usage of spectralreuse Chen et al [11] studied how to use the spectral reuse tosolve the problem of resource allocation

24 Interference Model Scheduling strategies must ensurethat transmissions in each time slot do not collide Thereare two types of collision situations in the wireless networkenvironment They are called Primary Interference and Sec-ondary Interference [12 13] Primary Interference occurs in asingle time slot of scheduling the SS cannot domore than onething In other words the SS can only transfer or receive datain a single time slot Secondary Interference occurs when theoriginally receiver119883 turns into the transfer but the user119883 isstill in the range of the transfer 119884 The user 119883 will affect thetransmission of the user 119884 There are some studies that focuson WiMAX mesh network interference problems [14 15]Wei et al [16] proposed an interference-aware multihop

Mathematical Problems in Engineering 3

Table 1 Parameters and variables table

Symbol Description119866 = (119881 119864) Mesh network topology G119881 The set of stations119864 The set of edges119879 The set of time slot in a frame119867 The set of subchannel in each time slotℎ The index parameter of subchannel forallℎ isin 119867S A set of all the SSs119904119894

A subscriber SS 119894 forall119904119894isin S

R Set of all relay stations119903119894

A relay node 119894 forall119903119894isin R

119888119897

The link capacity of each link 119897 forall119897 isin 119864hp119894

The set of hops from 119904119894to BS

br119894

Theminimum bandwidth requirement of the 119904119894for guaranteeing QoS

BR119894

Themaximum bandwidth requirement of the 119904119894

120582119894

The actual quantity of node 119894 upload the packet forall119894 isin S cupR

120590119894

The actual quantity of node 119894 upload the required tile forall119894 isin S cupR

119910119894

119904119894satisfaction ratio

tr119894

The tile requirement of 119904119894for transmitting packets from 119904

119894to BS during each hop

TR The set of tile requirement TR = tr119894| forall119904119894isin S

119868 (sdot) The subset of nodes which will interfere with node or link transceiving119868119894

The subset of nodes which will not interfere with 1199041015840119894119904 transceiving

pa (119894) The parent of node 119894 on the tree topologycd (119903) The set of children node SSs or RSs of 119903119891119897119905ℎ

A decision variable which is 1 if link 119897 is assigned with time slot 119905 and subchannel ℎ and 0 otherwiseOL119894 IL119894

The set of output and input links of node 119894 respectively

routing algorithm to maximize the degree of use of networkbandwidth to maximize the network throughput

25 Fairness Scheduling Nowadays the related works onWiMAX mesh networks through a network of relay stationsscheduling and resource allocation are concerned widely It iscommon to study the fairness in many wireless networks in[17ndash20] Sayenko et al [19] studied the proportional fairnessand considered the difference between frequency selectionswith multiuser scheduling problems Andrews and Zhang[20] proposed a round-robin based scheduling method forIEEE 80216 BS to ensure QoS requirements of the SS inuplink (UL) and downlink (DL) can be met But the networkbandwidth usage efficiently and bandwidth requirementswere not considered in [19 20]

In this paper we propose heuristic scheduling algorithmsthat identify each SS to maximize the minimum satisfactionratio in the network and meanwhile to meet the bandwidthrequirements for each SS We compare the QoS satisfactionratio throughput andmin satisfaction ratiowith the previousmethod proposed in [21] Experimental results show that ourmethod is better in terms of QoS satisfaction ratio

3 QoS-Based Max-Min Fair Scheduling

31 Problem Definition Based on theWiMAX standard [1] atree network topology119866 = (119881 119864) is given For readability thefollowing parameters and variables are listed in Table 1 A BSas the root a set of subscriber users S = 119904

1 1199042 119904

119899 as the

leaf nodes and a set of relay stationsR = 1199031 1199032 119903

119898 as the

intermediate nodes Let the parameter 119888119897be the link capacity

of each link 119897 forall119897 isin 119864 Let the parameter br119894be the minimum

bandwidth requirements of each SS 119904119894during a frame Let

the parameter BR119894be themaximum bandwidth requirements

of each SS 119904119894during a frame The problem is limited to the

following restrictions(1) no spectral reuse for any pair of links which interfere

with each other(2) an RS cannot transmit and receive data at the same

time(3) the total number of data delivered by an RS to BS

during a frame must be equal to the number of datareceived from its children node during one frame

(4) must satisfy the minimum bandwidth requirementsof each SS to guarantee QoS

4 Mathematical Problems in Engineering

Therefore the multihop fair scheduling with QoS con-trol problem is defined as to find a way to schedule thesubchannel-time slot (tile) for a scheduling frame After thetile scheduling the minimum satisfaction ratio 119910

119894of each 119904

119894

will be maximized and the bandwidth requirements of each119904119894will be satisfied to guarantee QoS

32 Integer Linear Programming for the Problem In [22] itwas proved that scheduling with channel capacity is NP-hardTherefore our scheduling problem with time-varying chan-nel will be NP-hard To find an optimal solution we providean Integer Linear Programming (ILP) for this problem

For each node 119894 isin S cup119877 pa(119894) denotes the parent of node119894 on the tree topology For each RS 119903 isin R the parameter cd(119903)is used to represent the set of children node (SSs or RSs) of 119903For each node 119894 in tree network 119866 the variable 119891119897

119905ℎdenotes

that whether the link 119897 = (119894 119895) is assigned with time-slot 119905and subchannel ℎ We refer to the method [23 24] to verifywhether there are interferences between these two edges 119868(119897)represents the interference link set of link 119897

Maximize 119910 (1)

sum

1198971015840isin119868(119897)

1198911198971015840

119905ℎ+ 119891119897

119905ℎle 1 forallℎ isin 119867 forall119905 isin 119879 forall119897 isin OL

119894

forall119894 isin S cupR

(2)

sumforallℎisin119867

sumforall119897isinOL

119903

119891119897

119905ℎ+ sumforallℎisin119867

sumforall119897isinIL

119903

119891119897

119905ℎle 1 forall119905 isin 119879

forall119903 isin R

(3)

sumforall119897isinIL

119903

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897

le sumforall119897isinOL

119903

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897 forall119903 isin R

(4)

sumforall119897isinOL

119894

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897ge br119894 forall119894 isin S (5)

119910 le 119910119894 forall119894 isin S (6)

where 119910119894=

1

BR119894

sumforall119897isinOL

119894

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897 forall119894 isin S (7)

119891119897

119905ℎ= 0 1 forall119905 isin 119879 forallℎ isin 119867 forall119897 isin 119864 (8)

The objective function of QoS-based max-min fairscheduling problem is shown as (1) The goal is to maximizethe minimum satisfaction ratio 119910 The satisfaction ratio 119910

119894is

calculated by (7) In (7) the parameter BR119894is the maximum

bandwidth requirement of 119904119894 the parameter 119888

119897is the capacity

of link 119897 and the decision variables 119891119897119905ℎ

are defined in (8) Ifthe time-slot (119905 ℎ) is allocated to link 119897 the value of decisionvariable 119891119897

119905ℎis 1 Otherwise the value of decision variable 119891119897

119905ℎ

is 0 The QoS-based max-min fair scheduling problem hasfour constraints as follows

(i) The spectral reuse constraints are shown as (2) For alllink 119897 in OL

119894 a tile can be used no more than once in

each pair of interference links 119868(119897) Where the OL119894is

the set of output links of all nodes 119894 isin S cupR

(ii) The single transceiver constraints are shown as (3)For all time-slot 119905 in119879 each RS 119903 in119877 cannot transmitand receive data in the same time slot

(iii) The flow constraints are shown as (4) All data that areaccepted byRS 119903 in a framewill be sent out in the sameframe Where the parameters OL

119903and IL

119903are the set

of output and input links of RS 119903

(iv) The minimum bandwidth requirement constraintsare shown as (5) The minimum bandwidth require-ments of each 119904

119894must be satisfied to guarantee QoS in

a frame

(v) The satisfaction ratio constraints are shown as (6)The satisfaction 119910

119894of each 119904119904

119894will be greater than the

variable 119910

33 Greedy Algorithm for QoS-Based Max-Min Fair Schedul-ing Though the ILP solution can be used to obtain optimalsolutions for small-sized problem but if the network scalegrows larger it has large time and space consumption forlarge-sized network The heuristics algorithm is needed forbetter running time in large-sized network In the followingwe designed a heuristic algorithm

331 Heuristic Algorithm The strategy of the proposedheuristic algorithm is smallest total bandwidth requirementfirst and then applying spectral reuse scheme to assignresource After QoS of all SSs is guaranteed the max-min fairscheduling scheme is used to enhance the overall throughputand satisfaction ratio The proposed heuristic algorithm hasfour steps as follows

Step 1 (allocate limited resources to meet the QoS require-ments of each SS) At first the total number of tile require-ments (tr

119894times hp119894) of each 119904

119894is estimated Then the resources

are allocated to all SSs by Algorithm 2 119876119900119878 119878119888ℎ119890119889119906119897119894119899119892()in increasing order of total tile requirements Until theresources are not enough allocated or the requirements ofall SSs are met the scheduler will terminate the process of119876119900119878 119878119888ℎ119890119889119906119897119894119899119892()

Step 2 (increase the number of meeting QoS requirements) Ifthe bandwidth requirements of 119904

119894are not satisfied the spectral

reuse mechanism is used to find available resource for eachunmet SS inAlgorithm 3 119876119900119878 119878119901119890119888119905119903119886119897 119877119890119906119904119890()The strategyof spectral reuse is to gain tiles from all allocated tiles of 119904

119895

there is no link between each 119904119895and the picked 119904

119894 Hence the

satisfaction rate has an opportunity to increase

Mathematical Problems in Engineering 5

Input 119866SR 119867 119879 brBROutput min satisfaction ratio QoS satisfaction ratio throughput

(1) Initialization 120582119894larr 0 120590

119894larr 0 forall119904

119894isin 119878119878

(2) for all 119878119878 node V119894on 119866 do

(3) tr119894larr lceil

BR119894

119888119894

rceil

(4) for all RS V119895on the path hp

119894from V

119894to BS do

(5) tr119894larr tr119894+ lceil

BR119894

119888119895

rceil

(6) endfor(7) endfor(8) Sort (TR)(9) 119860

119905larr |119867| forall119905 isin 119879

(10) Set all 119904119904119894119876119900119878119860119897119897119900119888119886119905119890119889 = false(11) QoS Scheduling (119866SR 119860 119879TR brBR)(12) QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)(13) Maxmin Scheduling (119866SR 119860 119879 119884BR)(14) Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868BR)

Algorithm 1 Heuristic Algorithm

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Step 2(3) 119894119899119889119890119909 larr 1

(4) for 119896 = 1 rarr |hp119894|

(5) 119903119890119902 larr lceilbr119894

119888119896

rceil

(6) for 119905 = 119894119899119889119890119909 rarr |119879|

(7) if 119860119905ge 119903119890119902

(8) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(9) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(10) else(11) if (|119879| minus 119905) lt (hp

119894minus 119896)

(12) free all tiles which allocated to 119904119894

(13) 119878119878 larr 119878119878 119904119894

(14) go to Step 1(15) else(16) 119860

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905 119894119899119889119890119909 larr 119905 119905 larr |119879|

(17) Step 3 if all hops of 119904119894are allocated successfully

(18) Slarr S 119904119894

(19) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120590119894times 119888119894

(20) for all RS 119903119904119895on the path from 119904

119894to BS do

(21) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120590119895times 119888119895

(22) endfor

(23) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(24) Step 4 if all SSs meet requirement or no sufficient resources can be allocated(25) terminate scheduling(26) else go to Step 1

Algorithm 2 QoS Scheduling (119866SR 119860 119879TR brBR)

6 Mathematical Problems in Engineering

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(3) Step 2(4) 119894119899119889119890119909 larr 1

(5) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(6) 119903119890119902 larr lceilbr119894

119888119896

rceil

(7) for 119905 = 119894119899119889119890119909 rarr |119879|

(8) if (119860119905+ 119877119905) gt 119903119890119902 then

(9) if 119860119905ge 119903119890119902

(10) 119860119905larr 119860119905minus 119903119890119902

(11) else(12) 119860

119905larr 0 119877

119905larr 119877119905minus (119903119890119902 minus 119860

119905)

(13) 119903119890119902 larr 0 119894119899119889119890119909 larr 119905 119905 larr |119879|

(14) else if (|119879| minus 119905) lt (hp119894minus 119896)

(15) free all tiles which allocated to 119904119894during this step

(16) 119878119878 larr 119878119878 119904119894

(17) go to Step 1(18) Step 3(19) if the resource is fully allocated successfully to all hops of 119904

119894 then

(20) Slarr S 119904119894

(21) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120582119894+ 120590119894times 119888119894

(22) for all RS 119903119904119895on the path from 119904

119894to BS do

(23) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120582119895+ 120590119895times 119888119895

(24) endfor

(25) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(26) Step 4 if all SSs meet QoS or no sufficient resources can be allocated then(27) Termination(28) else go to Step 1

Algorithm 3 QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)

Step 3 (remaining resources to do the max-min fair schedul-ing)When the first two steps are finished then some remain-ing resources are available Then the available tiles are allo-cated to the SSs that have lowest satisfaction and satisfactionratio is upgraded by Algorithm 4 119872119886119909119898119894119899 119878119888ℎ119890119889119906119897119894119899119892()

Step 4 (upgrade the min satisfaction ratio) FinallyAlgorithm 5 119872119886119909119898119894119899 119878119901119890119888119905119903119886119897 119877119890119906119904119890() finds out an 119904

119894

which has lowest satisfaction ratio among all SSs to increaseits satisfaction ratio Until all the SSs are allocated availabletiles by the spectral reuse mechanism or the satisfactionratio of 119904

119894are equal to 1 Then the procedure of scheduling

algorithm will be finished

332 Scheduling Algorithm Description with an Example Asshown in Figure 1 the networks are composed of one BSthree RSs = 119903

1 1199032 1199033 and six SSs = 119904

1 1199042 1199043 1199044 1199045 1199046 The

number of maximum bandwidth requirements of each SSsBR119894are 10 10 8 8 8 and 10 The bandwidth requirements

of SSs br119894are 7 2 4 5 6 and 3 for guaranteeing QoS The

capacity of each link 119888119897is set to 1 The number of time-slots

119905 is set to 7 The number of subchannels ℎ is set to 3 Theinterference of each RS and SS is defined as follows

119868 (1199031) = 119904

1 1199042 1199032 1199033 119868 (119903

2) = 119903

1 1199033 1199043 1199044

119868 (1199033)= 1199032 1199045 1199046 119868 (119904

1)= 1199042 1199031 119868 (119904

6)= 1199045 1199033

119868 (1199042) = 119904

1 1199031 1199043 119868 (119904

3) = 119904

2 1199034 1199044

119868 (1199044) = 119904

3 1199032 1199045 119868 (119904

5) = 119904

4 1199033 1199046

(9)

At first the value of tr119894(= lceilBR

119894119888119894rceil + sum

forall119895isinhp119894119904119894lceilBR119894119888119895rceil)

of each 119904119894is calculated at lines (2)ndash(7) in Algorithm 1 Then

the value of TR is sorted by increasing order at line (8) inAlgorithm 1 The value of parameter 119860

119905is initialized as |119867|

for all time-slot 119905The limited resources are allocated by Algorithm 2The 119904

119894

is selected with minimum total tile requirement tr119894at line

(1) of Algorithm 2 Then the resources are allocated atlines (2)ndash(16) of Algorithm 2 After resources allocation arecompleted the parameters and variables of the SS and RSwill be updated at lines (17)ndash(23) of Algorithm 2 At lines

Mathematical Problems in Engineering 7

Output 119884119860(1) Step 1(2) Choose a 119904

119894with the smallest satisfaction

(3) if 119910119894== 1 then terminate scheduling

(4) else go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(8) 119903119890119902 larr lceilBR119894

119888119896

rceil minus 120590119896

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else if 119860119905lt 119903119890119902

(14) 119860119905larr 0 119905119903

119894larr 119903119890119902 minus 119860

119905

(15) else if (|119879| minus 119905) lt (1003816100381610038161003816hp1198941003816100381610038161003816 minus 119896)

(16) free all tiles which allocated to 119904119894in Step 2

(17) 119878119878 larr 119878119878 119904119894

(18) go to Step 1(19) Step 3(20) if the resource is fully allocated successfully to all hops of 119904

119894 then

(21) Slarr S 119904119894

(22) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(23) for all RS 119903119904119895on the path from 119904

119894to BS do

(24) 120582119895larr 120582119895+ 119888119894

(25) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(26) Step 4(27) if 119910

119894= 1 or S is empty then

(28) terminate scheduling(29) else go to Step 1

Algorithm 4 Maxmin Scheduling (119866SR 119860 119879 119884BR)

(24)ndash(26) of Algorithm 2 if no available resources are ableto allocate to each SS the procedure goes back to the mainalgorithm Otherwise the scheduler continue to find the nextSSwhich can allocate resources tomeet theQoS requirementsof the SS In our example the total number of tiles is 21 InAlgorithm 2 the sequence of 119904

119894will be selected as 119904

2 1199046 1199043

The value of parameter tr119894is estimated as follows

tr1= lceil

BR1

1198881

rceil + sumforall119895isinhp

11199041

lceilBR1

119888119895

rceil = 14

tr2= lceil

BR2

1198882

rceil + sumforall119895isinhp

21199042

lceilBR2

119888119895

rceil = 4

tr3= lceil

BR3

1198883

rceil + sumforall119895isinhp

31199043

lceilBR3

119888119895

rceil = 8

tr4= lceil

BR4

1198884

rceil + sumforall119895isinhp

41199044

lceilBR4

119888119895

rceil = 10

tr5= lceil

BR5

1198885

rceil + sumforall119895isinhp

51199045

lceilBR5

119888119895

rceil = 12

tr6= lceil

BR6

1198886

rceil + sumforall119895isinhp

61199046

lceilBR6

119888119895

rceil = 6

(10)

The scheduling results of Algorithm 2 are shown inFigure 2

Moreover if the bandwidth requirements of some SSsare still unsatisfied the number of 119878119878 with QoS guaranteewill be raised by Algorithm 3 The bandwidth requirementunsatisfied 119904

119894will be found with the minimum tr

119894at line

(1) of Algorithm 3 All allocated tiles of 119904119895 forall119904119895isin 119868119894 are

recovered to set119877 at line (2) ofAlgorithm 3Then the spectralreuse strategy is used to maximize satisfaction ratio at lines(3)ndash(17) in Algorithm 3 for picked 119904

119894 If the available tiles

119860119905+ 119877119905can meet the requirement of 119904

119894at time slot 119905 for

119896th hop the required tiles are allocated at lines (8)ndash(13) ofAlgorithm 3 While the requirements of all hops are met theparameters and variables of the SS and RS will be updated at

8 Mathematical Problems in Engineering

Output 119884(1) Step 1 Choose a 119904

119894with the smallest satisfaction

(2) if 119910119894= 1 then terminate scheduling

(3) else Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(4) go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr hp119894

(8) 119903119890119902 larr tr119894

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902 then

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else(14) if (119860

119905+ 119877119905) ge 119903119890119902 then

(15) assign 119903119890119902 available tiles to 119896th hop of 119904119894

(16) else if (|119879| minus 119905) lt (hp119894minus 119896) then

(17) free all tiles which allocated to 119904119894in Step 2

(18) Slarr S 119904119894

(19) go to Step 1(20) else(21) 119860

119905larr 0 119877

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905

(22) Step 3 if all hops of 119904119894are fully allocated successfully then

(23) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(24) for all RS 119903119904119895on the path from 119904

119894to BS do

(25) 120582119895larr 120582119895+ 119888119894

(26) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(27) end for(28) Step 4(29) if 119910

119894= 1 or S is empty then

(30) terminate scheduling(31) else go to Step 1

Algorithm 5 Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868 119861119877)

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri7 2 4 5 6 3

h1

h2

h3t1 t2 t3 t4 t5 t6 t7

OFDMA frame

Figure 1 The network topology

Mathematical Problems in Engineering 9

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

5 6 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

7

hop1 hop2

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

Figure 2 The allocation of resources meets the QoS requirements of 1199042 1199043 and 119904

6

67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4 5 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA framehop1

s4s2

hop2

s3

s4s6 s3s3s3

r1

r1r2

r2

r2r2

r3

r3

r3

s4s6

s4s6

s2 s4

4 + 5

Figure 3 1199044performs the spectral reuse

lines (18)ndash(25) in Algorithm 3 Otherwise all acquired tilesof 119904119894are freed at line (15) of Algorithm 3 If the resources

allocation have not been finished the scheduler will findout the next one to meet the bandwidth requirements of 119904

119894

to guarantee QoS by the spectral reuse strategy Until theminimum bandwidth requirements of all SSs are satisfied orthe available tiles are not enough to allocate then this stepwillbe terminated The results of first hop of 119904

4are scheduled by

spectral reuse strategy of Algorithm 3 as shown in Figure 3Because the available tiles are insufficient at second hop 119904

4

cannot be assigned as shown in Figure 4 Hence all acquiredtiles of 119904

4need to be freed Due to the available tiles which are

not enough to assign this step is terminatedIf the remaining available tiles have not been allocated

completely then these remaining resources can increase thenetwork minimum satisfaction ratio by Algorithm 4 The SSwould be picked with lowest satisfaction ratio in sequence atline (2) of Algorithm 4 While the lowest satisfaction ratio isequal to 1 the scheduling of Algorithm 4 is terminated

Otherwise the scheduler will check whether there avail-able tiles can be assigned to the 119904

119894at lines (5)ndash(18) of

Algorithm 4 if the resources could be allocated to the SSAfter the parameters and variables of SS and RS are updatedat lines (19)ndash(26) of Algorithm 4 the scheduler continueto find out the lowest satisfaction ratio of SS and to assignavailable tiles to increase satisfaction ratio Until no availabletiles can be allocated or the requirements of all SSs are metthe scheduling procedure is terminated The max-min fairscheduling is performed with remaining tiles in Algorithm 4The satisfaction ratio of 119904

1 1199044 1199045 is 0 Because the second

hop has no enough available tiles the schedule fails for1199041 1199044 1199045 The scheduling results of Algorithm 4 are shown

in Figure 5Finally the spectral reuse strategy is operated on the

SS which has lowest satisfaction ratio for increasing theminimum satisfaction ratio in Algorithm 5 At line (1) ofAlgorithm 5 the scheduler pick a 119904

119894that has lowest satisfac-

tion ratio If the lowest satisfaction ratio equals to 1 at line (2)

10 Mathematical Problems in Engineering

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

bri

hop1 hop2

Figure 4 When lacking resources 1199044cannot perform spectral reuse

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

y1 = 0 y2 = 15 y3 = 12 y4 = 0 y5 = 0 y6 = 310

hop1 hop2

Figure 5 No remaining resources can be used to perform max-min fair scheduling

of Algorithm 5 the scheduling of Algorithm 5 is terminatedOtherwise all allocated tiles of 119904

119895are recovered to set119877 forall119904

119895isin

119868119894at line (3) of Algorithm 5 Then the spectral reuse strategy

is used to allocate tiles to 119904119894for maximizing satisfaction ratio

at lines (5)ndash(21) of Algorithm 5 When the available tiles set119860119905enough to assign to 119896th hop the tiles of 119860

119905set are firstly

allocated at lines (10)ndash(12) of Algorithm 5 When the set 119860119905

cannot fulfill the 119903119890119902 of 119904119894 both the set 119860

119905and 119877

119905are applied

to allocate at lines (13)ndash(21) of Algorithm 5 When both theset 119860119905and 119877

119905cannot satisfy the 119903119890119902 of 119904

119894at time slot 119905 at line

(21) of Algorithm 5 the difference of required tiles wouldbe found at next time slot If the requirement of all hopscannot be met all acquired tiles of 119904

119894have to be freed at

lines (16)ndash(19) of Algorithm 5 Then the scheduler continueto find out next SS until no resources can be allocated ByAlgorithm 4 the scheduled satisfaction ratio of 119904

1 1199044 1199045 is

0 Algorithm 5 enhances satisfaction ratio of 1199041 1199044 1199045 to

01 0125 0125 The scheduling results of Algorithm 5 areshown in Figure 6

Finally we get min satisfaction ratio = 01 QoS satisfac-tion ratio = 05 and throughput = 12 as shown in Figure 7

4 Simulation

In this section we implement our heuristic algorithms andthe algorithm proposed in [21] for performance comparisonWe compare three parameters in the experimental resultsnamely average minimum satisfaction ratio average QoSsatisfaction ratio and average throughput

41 Environmental Setup For experimental environmentsetting SS transmission range and interference range are

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

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Stochastic AnalysisInternational Journal of

Page 3: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

Mathematical Problems in Engineering 3

Table 1 Parameters and variables table

Symbol Description119866 = (119881 119864) Mesh network topology G119881 The set of stations119864 The set of edges119879 The set of time slot in a frame119867 The set of subchannel in each time slotℎ The index parameter of subchannel forallℎ isin 119867S A set of all the SSs119904119894

A subscriber SS 119894 forall119904119894isin S

R Set of all relay stations119903119894

A relay node 119894 forall119903119894isin R

119888119897

The link capacity of each link 119897 forall119897 isin 119864hp119894

The set of hops from 119904119894to BS

br119894

Theminimum bandwidth requirement of the 119904119894for guaranteeing QoS

BR119894

Themaximum bandwidth requirement of the 119904119894

120582119894

The actual quantity of node 119894 upload the packet forall119894 isin S cupR

120590119894

The actual quantity of node 119894 upload the required tile forall119894 isin S cupR

119910119894

119904119894satisfaction ratio

tr119894

The tile requirement of 119904119894for transmitting packets from 119904

119894to BS during each hop

TR The set of tile requirement TR = tr119894| forall119904119894isin S

119868 (sdot) The subset of nodes which will interfere with node or link transceiving119868119894

The subset of nodes which will not interfere with 1199041015840119894119904 transceiving

pa (119894) The parent of node 119894 on the tree topologycd (119903) The set of children node SSs or RSs of 119903119891119897119905ℎ

A decision variable which is 1 if link 119897 is assigned with time slot 119905 and subchannel ℎ and 0 otherwiseOL119894 IL119894

The set of output and input links of node 119894 respectively

routing algorithm to maximize the degree of use of networkbandwidth to maximize the network throughput

25 Fairness Scheduling Nowadays the related works onWiMAX mesh networks through a network of relay stationsscheduling and resource allocation are concerned widely It iscommon to study the fairness in many wireless networks in[17ndash20] Sayenko et al [19] studied the proportional fairnessand considered the difference between frequency selectionswith multiuser scheduling problems Andrews and Zhang[20] proposed a round-robin based scheduling method forIEEE 80216 BS to ensure QoS requirements of the SS inuplink (UL) and downlink (DL) can be met But the networkbandwidth usage efficiently and bandwidth requirementswere not considered in [19 20]

In this paper we propose heuristic scheduling algorithmsthat identify each SS to maximize the minimum satisfactionratio in the network and meanwhile to meet the bandwidthrequirements for each SS We compare the QoS satisfactionratio throughput andmin satisfaction ratiowith the previousmethod proposed in [21] Experimental results show that ourmethod is better in terms of QoS satisfaction ratio

3 QoS-Based Max-Min Fair Scheduling

31 Problem Definition Based on theWiMAX standard [1] atree network topology119866 = (119881 119864) is given For readability thefollowing parameters and variables are listed in Table 1 A BSas the root a set of subscriber users S = 119904

1 1199042 119904

119899 as the

leaf nodes and a set of relay stationsR = 1199031 1199032 119903

119898 as the

intermediate nodes Let the parameter 119888119897be the link capacity

of each link 119897 forall119897 isin 119864 Let the parameter br119894be the minimum

bandwidth requirements of each SS 119904119894during a frame Let

the parameter BR119894be themaximum bandwidth requirements

of each SS 119904119894during a frame The problem is limited to the

following restrictions(1) no spectral reuse for any pair of links which interfere

with each other(2) an RS cannot transmit and receive data at the same

time(3) the total number of data delivered by an RS to BS

during a frame must be equal to the number of datareceived from its children node during one frame

(4) must satisfy the minimum bandwidth requirementsof each SS to guarantee QoS

4 Mathematical Problems in Engineering

Therefore the multihop fair scheduling with QoS con-trol problem is defined as to find a way to schedule thesubchannel-time slot (tile) for a scheduling frame After thetile scheduling the minimum satisfaction ratio 119910

119894of each 119904

119894

will be maximized and the bandwidth requirements of each119904119894will be satisfied to guarantee QoS

32 Integer Linear Programming for the Problem In [22] itwas proved that scheduling with channel capacity is NP-hardTherefore our scheduling problem with time-varying chan-nel will be NP-hard To find an optimal solution we providean Integer Linear Programming (ILP) for this problem

For each node 119894 isin S cup119877 pa(119894) denotes the parent of node119894 on the tree topology For each RS 119903 isin R the parameter cd(119903)is used to represent the set of children node (SSs or RSs) of 119903For each node 119894 in tree network 119866 the variable 119891119897

119905ℎdenotes

that whether the link 119897 = (119894 119895) is assigned with time-slot 119905and subchannel ℎ We refer to the method [23 24] to verifywhether there are interferences between these two edges 119868(119897)represents the interference link set of link 119897

Maximize 119910 (1)

sum

1198971015840isin119868(119897)

1198911198971015840

119905ℎ+ 119891119897

119905ℎle 1 forallℎ isin 119867 forall119905 isin 119879 forall119897 isin OL

119894

forall119894 isin S cupR

(2)

sumforallℎisin119867

sumforall119897isinOL

119903

119891119897

119905ℎ+ sumforallℎisin119867

sumforall119897isinIL

119903

119891119897

119905ℎle 1 forall119905 isin 119879

forall119903 isin R

(3)

sumforall119897isinIL

119903

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897

le sumforall119897isinOL

119903

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897 forall119903 isin R

(4)

sumforall119897isinOL

119894

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897ge br119894 forall119894 isin S (5)

119910 le 119910119894 forall119894 isin S (6)

where 119910119894=

1

BR119894

sumforall119897isinOL

119894

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897 forall119894 isin S (7)

119891119897

119905ℎ= 0 1 forall119905 isin 119879 forallℎ isin 119867 forall119897 isin 119864 (8)

The objective function of QoS-based max-min fairscheduling problem is shown as (1) The goal is to maximizethe minimum satisfaction ratio 119910 The satisfaction ratio 119910

119894is

calculated by (7) In (7) the parameter BR119894is the maximum

bandwidth requirement of 119904119894 the parameter 119888

119897is the capacity

of link 119897 and the decision variables 119891119897119905ℎ

are defined in (8) Ifthe time-slot (119905 ℎ) is allocated to link 119897 the value of decisionvariable 119891119897

119905ℎis 1 Otherwise the value of decision variable 119891119897

119905ℎ

is 0 The QoS-based max-min fair scheduling problem hasfour constraints as follows

(i) The spectral reuse constraints are shown as (2) For alllink 119897 in OL

119894 a tile can be used no more than once in

each pair of interference links 119868(119897) Where the OL119894is

the set of output links of all nodes 119894 isin S cupR

(ii) The single transceiver constraints are shown as (3)For all time-slot 119905 in119879 each RS 119903 in119877 cannot transmitand receive data in the same time slot

(iii) The flow constraints are shown as (4) All data that areaccepted byRS 119903 in a framewill be sent out in the sameframe Where the parameters OL

119903and IL

119903are the set

of output and input links of RS 119903

(iv) The minimum bandwidth requirement constraintsare shown as (5) The minimum bandwidth require-ments of each 119904

119894must be satisfied to guarantee QoS in

a frame

(v) The satisfaction ratio constraints are shown as (6)The satisfaction 119910

119894of each 119904119904

119894will be greater than the

variable 119910

33 Greedy Algorithm for QoS-Based Max-Min Fair Schedul-ing Though the ILP solution can be used to obtain optimalsolutions for small-sized problem but if the network scalegrows larger it has large time and space consumption forlarge-sized network The heuristics algorithm is needed forbetter running time in large-sized network In the followingwe designed a heuristic algorithm

331 Heuristic Algorithm The strategy of the proposedheuristic algorithm is smallest total bandwidth requirementfirst and then applying spectral reuse scheme to assignresource After QoS of all SSs is guaranteed the max-min fairscheduling scheme is used to enhance the overall throughputand satisfaction ratio The proposed heuristic algorithm hasfour steps as follows

Step 1 (allocate limited resources to meet the QoS require-ments of each SS) At first the total number of tile require-ments (tr

119894times hp119894) of each 119904

119894is estimated Then the resources

are allocated to all SSs by Algorithm 2 119876119900119878 119878119888ℎ119890119889119906119897119894119899119892()in increasing order of total tile requirements Until theresources are not enough allocated or the requirements ofall SSs are met the scheduler will terminate the process of119876119900119878 119878119888ℎ119890119889119906119897119894119899119892()

Step 2 (increase the number of meeting QoS requirements) Ifthe bandwidth requirements of 119904

119894are not satisfied the spectral

reuse mechanism is used to find available resource for eachunmet SS inAlgorithm 3 119876119900119878 119878119901119890119888119905119903119886119897 119877119890119906119904119890()The strategyof spectral reuse is to gain tiles from all allocated tiles of 119904

119895

there is no link between each 119904119895and the picked 119904

119894 Hence the

satisfaction rate has an opportunity to increase

Mathematical Problems in Engineering 5

Input 119866SR 119867 119879 brBROutput min satisfaction ratio QoS satisfaction ratio throughput

(1) Initialization 120582119894larr 0 120590

119894larr 0 forall119904

119894isin 119878119878

(2) for all 119878119878 node V119894on 119866 do

(3) tr119894larr lceil

BR119894

119888119894

rceil

(4) for all RS V119895on the path hp

119894from V

119894to BS do

(5) tr119894larr tr119894+ lceil

BR119894

119888119895

rceil

(6) endfor(7) endfor(8) Sort (TR)(9) 119860

119905larr |119867| forall119905 isin 119879

(10) Set all 119904119904119894119876119900119878119860119897119897119900119888119886119905119890119889 = false(11) QoS Scheduling (119866SR 119860 119879TR brBR)(12) QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)(13) Maxmin Scheduling (119866SR 119860 119879 119884BR)(14) Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868BR)

Algorithm 1 Heuristic Algorithm

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Step 2(3) 119894119899119889119890119909 larr 1

(4) for 119896 = 1 rarr |hp119894|

(5) 119903119890119902 larr lceilbr119894

119888119896

rceil

(6) for 119905 = 119894119899119889119890119909 rarr |119879|

(7) if 119860119905ge 119903119890119902

(8) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(9) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(10) else(11) if (|119879| minus 119905) lt (hp

119894minus 119896)

(12) free all tiles which allocated to 119904119894

(13) 119878119878 larr 119878119878 119904119894

(14) go to Step 1(15) else(16) 119860

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905 119894119899119889119890119909 larr 119905 119905 larr |119879|

(17) Step 3 if all hops of 119904119894are allocated successfully

(18) Slarr S 119904119894

(19) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120590119894times 119888119894

(20) for all RS 119903119904119895on the path from 119904

119894to BS do

(21) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120590119895times 119888119895

(22) endfor

(23) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(24) Step 4 if all SSs meet requirement or no sufficient resources can be allocated(25) terminate scheduling(26) else go to Step 1

Algorithm 2 QoS Scheduling (119866SR 119860 119879TR brBR)

6 Mathematical Problems in Engineering

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(3) Step 2(4) 119894119899119889119890119909 larr 1

(5) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(6) 119903119890119902 larr lceilbr119894

119888119896

rceil

(7) for 119905 = 119894119899119889119890119909 rarr |119879|

(8) if (119860119905+ 119877119905) gt 119903119890119902 then

(9) if 119860119905ge 119903119890119902

(10) 119860119905larr 119860119905minus 119903119890119902

(11) else(12) 119860

119905larr 0 119877

119905larr 119877119905minus (119903119890119902 minus 119860

119905)

(13) 119903119890119902 larr 0 119894119899119889119890119909 larr 119905 119905 larr |119879|

(14) else if (|119879| minus 119905) lt (hp119894minus 119896)

(15) free all tiles which allocated to 119904119894during this step

(16) 119878119878 larr 119878119878 119904119894

(17) go to Step 1(18) Step 3(19) if the resource is fully allocated successfully to all hops of 119904

119894 then

(20) Slarr S 119904119894

(21) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120582119894+ 120590119894times 119888119894

(22) for all RS 119903119904119895on the path from 119904

119894to BS do

(23) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120582119895+ 120590119895times 119888119895

(24) endfor

(25) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(26) Step 4 if all SSs meet QoS or no sufficient resources can be allocated then(27) Termination(28) else go to Step 1

Algorithm 3 QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)

Step 3 (remaining resources to do the max-min fair schedul-ing)When the first two steps are finished then some remain-ing resources are available Then the available tiles are allo-cated to the SSs that have lowest satisfaction and satisfactionratio is upgraded by Algorithm 4 119872119886119909119898119894119899 119878119888ℎ119890119889119906119897119894119899119892()

Step 4 (upgrade the min satisfaction ratio) FinallyAlgorithm 5 119872119886119909119898119894119899 119878119901119890119888119905119903119886119897 119877119890119906119904119890() finds out an 119904

119894

which has lowest satisfaction ratio among all SSs to increaseits satisfaction ratio Until all the SSs are allocated availabletiles by the spectral reuse mechanism or the satisfactionratio of 119904

119894are equal to 1 Then the procedure of scheduling

algorithm will be finished

332 Scheduling Algorithm Description with an Example Asshown in Figure 1 the networks are composed of one BSthree RSs = 119903

1 1199032 1199033 and six SSs = 119904

1 1199042 1199043 1199044 1199045 1199046 The

number of maximum bandwidth requirements of each SSsBR119894are 10 10 8 8 8 and 10 The bandwidth requirements

of SSs br119894are 7 2 4 5 6 and 3 for guaranteeing QoS The

capacity of each link 119888119897is set to 1 The number of time-slots

119905 is set to 7 The number of subchannels ℎ is set to 3 Theinterference of each RS and SS is defined as follows

119868 (1199031) = 119904

1 1199042 1199032 1199033 119868 (119903

2) = 119903

1 1199033 1199043 1199044

119868 (1199033)= 1199032 1199045 1199046 119868 (119904

1)= 1199042 1199031 119868 (119904

6)= 1199045 1199033

119868 (1199042) = 119904

1 1199031 1199043 119868 (119904

3) = 119904

2 1199034 1199044

119868 (1199044) = 119904

3 1199032 1199045 119868 (119904

5) = 119904

4 1199033 1199046

(9)

At first the value of tr119894(= lceilBR

119894119888119894rceil + sum

forall119895isinhp119894119904119894lceilBR119894119888119895rceil)

of each 119904119894is calculated at lines (2)ndash(7) in Algorithm 1 Then

the value of TR is sorted by increasing order at line (8) inAlgorithm 1 The value of parameter 119860

119905is initialized as |119867|

for all time-slot 119905The limited resources are allocated by Algorithm 2The 119904

119894

is selected with minimum total tile requirement tr119894at line

(1) of Algorithm 2 Then the resources are allocated atlines (2)ndash(16) of Algorithm 2 After resources allocation arecompleted the parameters and variables of the SS and RSwill be updated at lines (17)ndash(23) of Algorithm 2 At lines

Mathematical Problems in Engineering 7

Output 119884119860(1) Step 1(2) Choose a 119904

119894with the smallest satisfaction

(3) if 119910119894== 1 then terminate scheduling

(4) else go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(8) 119903119890119902 larr lceilBR119894

119888119896

rceil minus 120590119896

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else if 119860119905lt 119903119890119902

(14) 119860119905larr 0 119905119903

119894larr 119903119890119902 minus 119860

119905

(15) else if (|119879| minus 119905) lt (1003816100381610038161003816hp1198941003816100381610038161003816 minus 119896)

(16) free all tiles which allocated to 119904119894in Step 2

(17) 119878119878 larr 119878119878 119904119894

(18) go to Step 1(19) Step 3(20) if the resource is fully allocated successfully to all hops of 119904

119894 then

(21) Slarr S 119904119894

(22) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(23) for all RS 119903119904119895on the path from 119904

119894to BS do

(24) 120582119895larr 120582119895+ 119888119894

(25) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(26) Step 4(27) if 119910

119894= 1 or S is empty then

(28) terminate scheduling(29) else go to Step 1

Algorithm 4 Maxmin Scheduling (119866SR 119860 119879 119884BR)

(24)ndash(26) of Algorithm 2 if no available resources are ableto allocate to each SS the procedure goes back to the mainalgorithm Otherwise the scheduler continue to find the nextSSwhich can allocate resources tomeet theQoS requirementsof the SS In our example the total number of tiles is 21 InAlgorithm 2 the sequence of 119904

119894will be selected as 119904

2 1199046 1199043

The value of parameter tr119894is estimated as follows

tr1= lceil

BR1

1198881

rceil + sumforall119895isinhp

11199041

lceilBR1

119888119895

rceil = 14

tr2= lceil

BR2

1198882

rceil + sumforall119895isinhp

21199042

lceilBR2

119888119895

rceil = 4

tr3= lceil

BR3

1198883

rceil + sumforall119895isinhp

31199043

lceilBR3

119888119895

rceil = 8

tr4= lceil

BR4

1198884

rceil + sumforall119895isinhp

41199044

lceilBR4

119888119895

rceil = 10

tr5= lceil

BR5

1198885

rceil + sumforall119895isinhp

51199045

lceilBR5

119888119895

rceil = 12

tr6= lceil

BR6

1198886

rceil + sumforall119895isinhp

61199046

lceilBR6

119888119895

rceil = 6

(10)

The scheduling results of Algorithm 2 are shown inFigure 2

Moreover if the bandwidth requirements of some SSsare still unsatisfied the number of 119878119878 with QoS guaranteewill be raised by Algorithm 3 The bandwidth requirementunsatisfied 119904

119894will be found with the minimum tr

119894at line

(1) of Algorithm 3 All allocated tiles of 119904119895 forall119904119895isin 119868119894 are

recovered to set119877 at line (2) ofAlgorithm 3Then the spectralreuse strategy is used to maximize satisfaction ratio at lines(3)ndash(17) in Algorithm 3 for picked 119904

119894 If the available tiles

119860119905+ 119877119905can meet the requirement of 119904

119894at time slot 119905 for

119896th hop the required tiles are allocated at lines (8)ndash(13) ofAlgorithm 3 While the requirements of all hops are met theparameters and variables of the SS and RS will be updated at

8 Mathematical Problems in Engineering

Output 119884(1) Step 1 Choose a 119904

119894with the smallest satisfaction

(2) if 119910119894= 1 then terminate scheduling

(3) else Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(4) go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr hp119894

(8) 119903119890119902 larr tr119894

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902 then

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else(14) if (119860

119905+ 119877119905) ge 119903119890119902 then

(15) assign 119903119890119902 available tiles to 119896th hop of 119904119894

(16) else if (|119879| minus 119905) lt (hp119894minus 119896) then

(17) free all tiles which allocated to 119904119894in Step 2

(18) Slarr S 119904119894

(19) go to Step 1(20) else(21) 119860

119905larr 0 119877

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905

(22) Step 3 if all hops of 119904119894are fully allocated successfully then

(23) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(24) for all RS 119903119904119895on the path from 119904

119894to BS do

(25) 120582119895larr 120582119895+ 119888119894

(26) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(27) end for(28) Step 4(29) if 119910

119894= 1 or S is empty then

(30) terminate scheduling(31) else go to Step 1

Algorithm 5 Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868 119861119877)

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri7 2 4 5 6 3

h1

h2

h3t1 t2 t3 t4 t5 t6 t7

OFDMA frame

Figure 1 The network topology

Mathematical Problems in Engineering 9

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

5 6 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

7

hop1 hop2

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

Figure 2 The allocation of resources meets the QoS requirements of 1199042 1199043 and 119904

6

67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4 5 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA framehop1

s4s2

hop2

s3

s4s6 s3s3s3

r1

r1r2

r2

r2r2

r3

r3

r3

s4s6

s4s6

s2 s4

4 + 5

Figure 3 1199044performs the spectral reuse

lines (18)ndash(25) in Algorithm 3 Otherwise all acquired tilesof 119904119894are freed at line (15) of Algorithm 3 If the resources

allocation have not been finished the scheduler will findout the next one to meet the bandwidth requirements of 119904

119894

to guarantee QoS by the spectral reuse strategy Until theminimum bandwidth requirements of all SSs are satisfied orthe available tiles are not enough to allocate then this stepwillbe terminated The results of first hop of 119904

4are scheduled by

spectral reuse strategy of Algorithm 3 as shown in Figure 3Because the available tiles are insufficient at second hop 119904

4

cannot be assigned as shown in Figure 4 Hence all acquiredtiles of 119904

4need to be freed Due to the available tiles which are

not enough to assign this step is terminatedIf the remaining available tiles have not been allocated

completely then these remaining resources can increase thenetwork minimum satisfaction ratio by Algorithm 4 The SSwould be picked with lowest satisfaction ratio in sequence atline (2) of Algorithm 4 While the lowest satisfaction ratio isequal to 1 the scheduling of Algorithm 4 is terminated

Otherwise the scheduler will check whether there avail-able tiles can be assigned to the 119904

119894at lines (5)ndash(18) of

Algorithm 4 if the resources could be allocated to the SSAfter the parameters and variables of SS and RS are updatedat lines (19)ndash(26) of Algorithm 4 the scheduler continueto find out the lowest satisfaction ratio of SS and to assignavailable tiles to increase satisfaction ratio Until no availabletiles can be allocated or the requirements of all SSs are metthe scheduling procedure is terminated The max-min fairscheduling is performed with remaining tiles in Algorithm 4The satisfaction ratio of 119904

1 1199044 1199045 is 0 Because the second

hop has no enough available tiles the schedule fails for1199041 1199044 1199045 The scheduling results of Algorithm 4 are shown

in Figure 5Finally the spectral reuse strategy is operated on the

SS which has lowest satisfaction ratio for increasing theminimum satisfaction ratio in Algorithm 5 At line (1) ofAlgorithm 5 the scheduler pick a 119904

119894that has lowest satisfac-

tion ratio If the lowest satisfaction ratio equals to 1 at line (2)

10 Mathematical Problems in Engineering

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

bri

hop1 hop2

Figure 4 When lacking resources 1199044cannot perform spectral reuse

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

y1 = 0 y2 = 15 y3 = 12 y4 = 0 y5 = 0 y6 = 310

hop1 hop2

Figure 5 No remaining resources can be used to perform max-min fair scheduling

of Algorithm 5 the scheduling of Algorithm 5 is terminatedOtherwise all allocated tiles of 119904

119895are recovered to set119877 forall119904

119895isin

119868119894at line (3) of Algorithm 5 Then the spectral reuse strategy

is used to allocate tiles to 119904119894for maximizing satisfaction ratio

at lines (5)ndash(21) of Algorithm 5 When the available tiles set119860119905enough to assign to 119896th hop the tiles of 119860

119905set are firstly

allocated at lines (10)ndash(12) of Algorithm 5 When the set 119860119905

cannot fulfill the 119903119890119902 of 119904119894 both the set 119860

119905and 119877

119905are applied

to allocate at lines (13)ndash(21) of Algorithm 5 When both theset 119860119905and 119877

119905cannot satisfy the 119903119890119902 of 119904

119894at time slot 119905 at line

(21) of Algorithm 5 the difference of required tiles wouldbe found at next time slot If the requirement of all hopscannot be met all acquired tiles of 119904

119894have to be freed at

lines (16)ndash(19) of Algorithm 5 Then the scheduler continueto find out next SS until no resources can be allocated ByAlgorithm 4 the scheduled satisfaction ratio of 119904

1 1199044 1199045 is

0 Algorithm 5 enhances satisfaction ratio of 1199041 1199044 1199045 to

01 0125 0125 The scheduling results of Algorithm 5 areshown in Figure 6

Finally we get min satisfaction ratio = 01 QoS satisfac-tion ratio = 05 and throughput = 12 as shown in Figure 7

4 Simulation

In this section we implement our heuristic algorithms andthe algorithm proposed in [21] for performance comparisonWe compare three parameters in the experimental resultsnamely average minimum satisfaction ratio average QoSsatisfaction ratio and average throughput

41 Environmental Setup For experimental environmentsetting SS transmission range and interference range are

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

Submit your manuscripts athttpwwwhindawicom

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 4: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

4 Mathematical Problems in Engineering

Therefore the multihop fair scheduling with QoS con-trol problem is defined as to find a way to schedule thesubchannel-time slot (tile) for a scheduling frame After thetile scheduling the minimum satisfaction ratio 119910

119894of each 119904

119894

will be maximized and the bandwidth requirements of each119904119894will be satisfied to guarantee QoS

32 Integer Linear Programming for the Problem In [22] itwas proved that scheduling with channel capacity is NP-hardTherefore our scheduling problem with time-varying chan-nel will be NP-hard To find an optimal solution we providean Integer Linear Programming (ILP) for this problem

For each node 119894 isin S cup119877 pa(119894) denotes the parent of node119894 on the tree topology For each RS 119903 isin R the parameter cd(119903)is used to represent the set of children node (SSs or RSs) of 119903For each node 119894 in tree network 119866 the variable 119891119897

119905ℎdenotes

that whether the link 119897 = (119894 119895) is assigned with time-slot 119905and subchannel ℎ We refer to the method [23 24] to verifywhether there are interferences between these two edges 119868(119897)represents the interference link set of link 119897

Maximize 119910 (1)

sum

1198971015840isin119868(119897)

1198911198971015840

119905ℎ+ 119891119897

119905ℎle 1 forallℎ isin 119867 forall119905 isin 119879 forall119897 isin OL

119894

forall119894 isin S cupR

(2)

sumforallℎisin119867

sumforall119897isinOL

119903

119891119897

119905ℎ+ sumforallℎisin119867

sumforall119897isinIL

119903

119891119897

119905ℎle 1 forall119905 isin 119879

forall119903 isin R

(3)

sumforall119897isinIL

119903

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897

le sumforall119897isinOL

119903

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897 forall119903 isin R

(4)

sumforall119897isinOL

119894

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897ge br119894 forall119894 isin S (5)

119910 le 119910119894 forall119894 isin S (6)

where 119910119894=

1

BR119894

sumforall119897isinOL

119894

( sumforallℎisin119867

sumforall119905isin119879

119891119897

119905ℎ) times 119888119897 forall119894 isin S (7)

119891119897

119905ℎ= 0 1 forall119905 isin 119879 forallℎ isin 119867 forall119897 isin 119864 (8)

The objective function of QoS-based max-min fairscheduling problem is shown as (1) The goal is to maximizethe minimum satisfaction ratio 119910 The satisfaction ratio 119910

119894is

calculated by (7) In (7) the parameter BR119894is the maximum

bandwidth requirement of 119904119894 the parameter 119888

119897is the capacity

of link 119897 and the decision variables 119891119897119905ℎ

are defined in (8) Ifthe time-slot (119905 ℎ) is allocated to link 119897 the value of decisionvariable 119891119897

119905ℎis 1 Otherwise the value of decision variable 119891119897

119905ℎ

is 0 The QoS-based max-min fair scheduling problem hasfour constraints as follows

(i) The spectral reuse constraints are shown as (2) For alllink 119897 in OL

119894 a tile can be used no more than once in

each pair of interference links 119868(119897) Where the OL119894is

the set of output links of all nodes 119894 isin S cupR

(ii) The single transceiver constraints are shown as (3)For all time-slot 119905 in119879 each RS 119903 in119877 cannot transmitand receive data in the same time slot

(iii) The flow constraints are shown as (4) All data that areaccepted byRS 119903 in a framewill be sent out in the sameframe Where the parameters OL

119903and IL

119903are the set

of output and input links of RS 119903

(iv) The minimum bandwidth requirement constraintsare shown as (5) The minimum bandwidth require-ments of each 119904

119894must be satisfied to guarantee QoS in

a frame

(v) The satisfaction ratio constraints are shown as (6)The satisfaction 119910

119894of each 119904119904

119894will be greater than the

variable 119910

33 Greedy Algorithm for QoS-Based Max-Min Fair Schedul-ing Though the ILP solution can be used to obtain optimalsolutions for small-sized problem but if the network scalegrows larger it has large time and space consumption forlarge-sized network The heuristics algorithm is needed forbetter running time in large-sized network In the followingwe designed a heuristic algorithm

331 Heuristic Algorithm The strategy of the proposedheuristic algorithm is smallest total bandwidth requirementfirst and then applying spectral reuse scheme to assignresource After QoS of all SSs is guaranteed the max-min fairscheduling scheme is used to enhance the overall throughputand satisfaction ratio The proposed heuristic algorithm hasfour steps as follows

Step 1 (allocate limited resources to meet the QoS require-ments of each SS) At first the total number of tile require-ments (tr

119894times hp119894) of each 119904

119894is estimated Then the resources

are allocated to all SSs by Algorithm 2 119876119900119878 119878119888ℎ119890119889119906119897119894119899119892()in increasing order of total tile requirements Until theresources are not enough allocated or the requirements ofall SSs are met the scheduler will terminate the process of119876119900119878 119878119888ℎ119890119889119906119897119894119899119892()

Step 2 (increase the number of meeting QoS requirements) Ifthe bandwidth requirements of 119904

119894are not satisfied the spectral

reuse mechanism is used to find available resource for eachunmet SS inAlgorithm 3 119876119900119878 119878119901119890119888119905119903119886119897 119877119890119906119904119890()The strategyof spectral reuse is to gain tiles from all allocated tiles of 119904

119895

there is no link between each 119904119895and the picked 119904

119894 Hence the

satisfaction rate has an opportunity to increase

Mathematical Problems in Engineering 5

Input 119866SR 119867 119879 brBROutput min satisfaction ratio QoS satisfaction ratio throughput

(1) Initialization 120582119894larr 0 120590

119894larr 0 forall119904

119894isin 119878119878

(2) for all 119878119878 node V119894on 119866 do

(3) tr119894larr lceil

BR119894

119888119894

rceil

(4) for all RS V119895on the path hp

119894from V

119894to BS do

(5) tr119894larr tr119894+ lceil

BR119894

119888119895

rceil

(6) endfor(7) endfor(8) Sort (TR)(9) 119860

119905larr |119867| forall119905 isin 119879

(10) Set all 119904119904119894119876119900119878119860119897119897119900119888119886119905119890119889 = false(11) QoS Scheduling (119866SR 119860 119879TR brBR)(12) QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)(13) Maxmin Scheduling (119866SR 119860 119879 119884BR)(14) Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868BR)

Algorithm 1 Heuristic Algorithm

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Step 2(3) 119894119899119889119890119909 larr 1

(4) for 119896 = 1 rarr |hp119894|

(5) 119903119890119902 larr lceilbr119894

119888119896

rceil

(6) for 119905 = 119894119899119889119890119909 rarr |119879|

(7) if 119860119905ge 119903119890119902

(8) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(9) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(10) else(11) if (|119879| minus 119905) lt (hp

119894minus 119896)

(12) free all tiles which allocated to 119904119894

(13) 119878119878 larr 119878119878 119904119894

(14) go to Step 1(15) else(16) 119860

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905 119894119899119889119890119909 larr 119905 119905 larr |119879|

(17) Step 3 if all hops of 119904119894are allocated successfully

(18) Slarr S 119904119894

(19) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120590119894times 119888119894

(20) for all RS 119903119904119895on the path from 119904

119894to BS do

(21) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120590119895times 119888119895

(22) endfor

(23) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(24) Step 4 if all SSs meet requirement or no sufficient resources can be allocated(25) terminate scheduling(26) else go to Step 1

Algorithm 2 QoS Scheduling (119866SR 119860 119879TR brBR)

6 Mathematical Problems in Engineering

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(3) Step 2(4) 119894119899119889119890119909 larr 1

(5) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(6) 119903119890119902 larr lceilbr119894

119888119896

rceil

(7) for 119905 = 119894119899119889119890119909 rarr |119879|

(8) if (119860119905+ 119877119905) gt 119903119890119902 then

(9) if 119860119905ge 119903119890119902

(10) 119860119905larr 119860119905minus 119903119890119902

(11) else(12) 119860

119905larr 0 119877

119905larr 119877119905minus (119903119890119902 minus 119860

119905)

(13) 119903119890119902 larr 0 119894119899119889119890119909 larr 119905 119905 larr |119879|

(14) else if (|119879| minus 119905) lt (hp119894minus 119896)

(15) free all tiles which allocated to 119904119894during this step

(16) 119878119878 larr 119878119878 119904119894

(17) go to Step 1(18) Step 3(19) if the resource is fully allocated successfully to all hops of 119904

119894 then

(20) Slarr S 119904119894

(21) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120582119894+ 120590119894times 119888119894

(22) for all RS 119903119904119895on the path from 119904

119894to BS do

(23) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120582119895+ 120590119895times 119888119895

(24) endfor

(25) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(26) Step 4 if all SSs meet QoS or no sufficient resources can be allocated then(27) Termination(28) else go to Step 1

Algorithm 3 QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)

Step 3 (remaining resources to do the max-min fair schedul-ing)When the first two steps are finished then some remain-ing resources are available Then the available tiles are allo-cated to the SSs that have lowest satisfaction and satisfactionratio is upgraded by Algorithm 4 119872119886119909119898119894119899 119878119888ℎ119890119889119906119897119894119899119892()

Step 4 (upgrade the min satisfaction ratio) FinallyAlgorithm 5 119872119886119909119898119894119899 119878119901119890119888119905119903119886119897 119877119890119906119904119890() finds out an 119904

119894

which has lowest satisfaction ratio among all SSs to increaseits satisfaction ratio Until all the SSs are allocated availabletiles by the spectral reuse mechanism or the satisfactionratio of 119904

119894are equal to 1 Then the procedure of scheduling

algorithm will be finished

332 Scheduling Algorithm Description with an Example Asshown in Figure 1 the networks are composed of one BSthree RSs = 119903

1 1199032 1199033 and six SSs = 119904

1 1199042 1199043 1199044 1199045 1199046 The

number of maximum bandwidth requirements of each SSsBR119894are 10 10 8 8 8 and 10 The bandwidth requirements

of SSs br119894are 7 2 4 5 6 and 3 for guaranteeing QoS The

capacity of each link 119888119897is set to 1 The number of time-slots

119905 is set to 7 The number of subchannels ℎ is set to 3 Theinterference of each RS and SS is defined as follows

119868 (1199031) = 119904

1 1199042 1199032 1199033 119868 (119903

2) = 119903

1 1199033 1199043 1199044

119868 (1199033)= 1199032 1199045 1199046 119868 (119904

1)= 1199042 1199031 119868 (119904

6)= 1199045 1199033

119868 (1199042) = 119904

1 1199031 1199043 119868 (119904

3) = 119904

2 1199034 1199044

119868 (1199044) = 119904

3 1199032 1199045 119868 (119904

5) = 119904

4 1199033 1199046

(9)

At first the value of tr119894(= lceilBR

119894119888119894rceil + sum

forall119895isinhp119894119904119894lceilBR119894119888119895rceil)

of each 119904119894is calculated at lines (2)ndash(7) in Algorithm 1 Then

the value of TR is sorted by increasing order at line (8) inAlgorithm 1 The value of parameter 119860

119905is initialized as |119867|

for all time-slot 119905The limited resources are allocated by Algorithm 2The 119904

119894

is selected with minimum total tile requirement tr119894at line

(1) of Algorithm 2 Then the resources are allocated atlines (2)ndash(16) of Algorithm 2 After resources allocation arecompleted the parameters and variables of the SS and RSwill be updated at lines (17)ndash(23) of Algorithm 2 At lines

Mathematical Problems in Engineering 7

Output 119884119860(1) Step 1(2) Choose a 119904

119894with the smallest satisfaction

(3) if 119910119894== 1 then terminate scheduling

(4) else go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(8) 119903119890119902 larr lceilBR119894

119888119896

rceil minus 120590119896

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else if 119860119905lt 119903119890119902

(14) 119860119905larr 0 119905119903

119894larr 119903119890119902 minus 119860

119905

(15) else if (|119879| minus 119905) lt (1003816100381610038161003816hp1198941003816100381610038161003816 minus 119896)

(16) free all tiles which allocated to 119904119894in Step 2

(17) 119878119878 larr 119878119878 119904119894

(18) go to Step 1(19) Step 3(20) if the resource is fully allocated successfully to all hops of 119904

119894 then

(21) Slarr S 119904119894

(22) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(23) for all RS 119903119904119895on the path from 119904

119894to BS do

(24) 120582119895larr 120582119895+ 119888119894

(25) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(26) Step 4(27) if 119910

119894= 1 or S is empty then

(28) terminate scheduling(29) else go to Step 1

Algorithm 4 Maxmin Scheduling (119866SR 119860 119879 119884BR)

(24)ndash(26) of Algorithm 2 if no available resources are ableto allocate to each SS the procedure goes back to the mainalgorithm Otherwise the scheduler continue to find the nextSSwhich can allocate resources tomeet theQoS requirementsof the SS In our example the total number of tiles is 21 InAlgorithm 2 the sequence of 119904

119894will be selected as 119904

2 1199046 1199043

The value of parameter tr119894is estimated as follows

tr1= lceil

BR1

1198881

rceil + sumforall119895isinhp

11199041

lceilBR1

119888119895

rceil = 14

tr2= lceil

BR2

1198882

rceil + sumforall119895isinhp

21199042

lceilBR2

119888119895

rceil = 4

tr3= lceil

BR3

1198883

rceil + sumforall119895isinhp

31199043

lceilBR3

119888119895

rceil = 8

tr4= lceil

BR4

1198884

rceil + sumforall119895isinhp

41199044

lceilBR4

119888119895

rceil = 10

tr5= lceil

BR5

1198885

rceil + sumforall119895isinhp

51199045

lceilBR5

119888119895

rceil = 12

tr6= lceil

BR6

1198886

rceil + sumforall119895isinhp

61199046

lceilBR6

119888119895

rceil = 6

(10)

The scheduling results of Algorithm 2 are shown inFigure 2

Moreover if the bandwidth requirements of some SSsare still unsatisfied the number of 119878119878 with QoS guaranteewill be raised by Algorithm 3 The bandwidth requirementunsatisfied 119904

119894will be found with the minimum tr

119894at line

(1) of Algorithm 3 All allocated tiles of 119904119895 forall119904119895isin 119868119894 are

recovered to set119877 at line (2) ofAlgorithm 3Then the spectralreuse strategy is used to maximize satisfaction ratio at lines(3)ndash(17) in Algorithm 3 for picked 119904

119894 If the available tiles

119860119905+ 119877119905can meet the requirement of 119904

119894at time slot 119905 for

119896th hop the required tiles are allocated at lines (8)ndash(13) ofAlgorithm 3 While the requirements of all hops are met theparameters and variables of the SS and RS will be updated at

8 Mathematical Problems in Engineering

Output 119884(1) Step 1 Choose a 119904

119894with the smallest satisfaction

(2) if 119910119894= 1 then terminate scheduling

(3) else Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(4) go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr hp119894

(8) 119903119890119902 larr tr119894

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902 then

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else(14) if (119860

119905+ 119877119905) ge 119903119890119902 then

(15) assign 119903119890119902 available tiles to 119896th hop of 119904119894

(16) else if (|119879| minus 119905) lt (hp119894minus 119896) then

(17) free all tiles which allocated to 119904119894in Step 2

(18) Slarr S 119904119894

(19) go to Step 1(20) else(21) 119860

119905larr 0 119877

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905

(22) Step 3 if all hops of 119904119894are fully allocated successfully then

(23) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(24) for all RS 119903119904119895on the path from 119904

119894to BS do

(25) 120582119895larr 120582119895+ 119888119894

(26) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(27) end for(28) Step 4(29) if 119910

119894= 1 or S is empty then

(30) terminate scheduling(31) else go to Step 1

Algorithm 5 Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868 119861119877)

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri7 2 4 5 6 3

h1

h2

h3t1 t2 t3 t4 t5 t6 t7

OFDMA frame

Figure 1 The network topology

Mathematical Problems in Engineering 9

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

5 6 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

7

hop1 hop2

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

Figure 2 The allocation of resources meets the QoS requirements of 1199042 1199043 and 119904

6

67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4 5 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA framehop1

s4s2

hop2

s3

s4s6 s3s3s3

r1

r1r2

r2

r2r2

r3

r3

r3

s4s6

s4s6

s2 s4

4 + 5

Figure 3 1199044performs the spectral reuse

lines (18)ndash(25) in Algorithm 3 Otherwise all acquired tilesof 119904119894are freed at line (15) of Algorithm 3 If the resources

allocation have not been finished the scheduler will findout the next one to meet the bandwidth requirements of 119904

119894

to guarantee QoS by the spectral reuse strategy Until theminimum bandwidth requirements of all SSs are satisfied orthe available tiles are not enough to allocate then this stepwillbe terminated The results of first hop of 119904

4are scheduled by

spectral reuse strategy of Algorithm 3 as shown in Figure 3Because the available tiles are insufficient at second hop 119904

4

cannot be assigned as shown in Figure 4 Hence all acquiredtiles of 119904

4need to be freed Due to the available tiles which are

not enough to assign this step is terminatedIf the remaining available tiles have not been allocated

completely then these remaining resources can increase thenetwork minimum satisfaction ratio by Algorithm 4 The SSwould be picked with lowest satisfaction ratio in sequence atline (2) of Algorithm 4 While the lowest satisfaction ratio isequal to 1 the scheduling of Algorithm 4 is terminated

Otherwise the scheduler will check whether there avail-able tiles can be assigned to the 119904

119894at lines (5)ndash(18) of

Algorithm 4 if the resources could be allocated to the SSAfter the parameters and variables of SS and RS are updatedat lines (19)ndash(26) of Algorithm 4 the scheduler continueto find out the lowest satisfaction ratio of SS and to assignavailable tiles to increase satisfaction ratio Until no availabletiles can be allocated or the requirements of all SSs are metthe scheduling procedure is terminated The max-min fairscheduling is performed with remaining tiles in Algorithm 4The satisfaction ratio of 119904

1 1199044 1199045 is 0 Because the second

hop has no enough available tiles the schedule fails for1199041 1199044 1199045 The scheduling results of Algorithm 4 are shown

in Figure 5Finally the spectral reuse strategy is operated on the

SS which has lowest satisfaction ratio for increasing theminimum satisfaction ratio in Algorithm 5 At line (1) ofAlgorithm 5 the scheduler pick a 119904

119894that has lowest satisfac-

tion ratio If the lowest satisfaction ratio equals to 1 at line (2)

10 Mathematical Problems in Engineering

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

bri

hop1 hop2

Figure 4 When lacking resources 1199044cannot perform spectral reuse

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

y1 = 0 y2 = 15 y3 = 12 y4 = 0 y5 = 0 y6 = 310

hop1 hop2

Figure 5 No remaining resources can be used to perform max-min fair scheduling

of Algorithm 5 the scheduling of Algorithm 5 is terminatedOtherwise all allocated tiles of 119904

119895are recovered to set119877 forall119904

119895isin

119868119894at line (3) of Algorithm 5 Then the spectral reuse strategy

is used to allocate tiles to 119904119894for maximizing satisfaction ratio

at lines (5)ndash(21) of Algorithm 5 When the available tiles set119860119905enough to assign to 119896th hop the tiles of 119860

119905set are firstly

allocated at lines (10)ndash(12) of Algorithm 5 When the set 119860119905

cannot fulfill the 119903119890119902 of 119904119894 both the set 119860

119905and 119877

119905are applied

to allocate at lines (13)ndash(21) of Algorithm 5 When both theset 119860119905and 119877

119905cannot satisfy the 119903119890119902 of 119904

119894at time slot 119905 at line

(21) of Algorithm 5 the difference of required tiles wouldbe found at next time slot If the requirement of all hopscannot be met all acquired tiles of 119904

119894have to be freed at

lines (16)ndash(19) of Algorithm 5 Then the scheduler continueto find out next SS until no resources can be allocated ByAlgorithm 4 the scheduled satisfaction ratio of 119904

1 1199044 1199045 is

0 Algorithm 5 enhances satisfaction ratio of 1199041 1199044 1199045 to

01 0125 0125 The scheduling results of Algorithm 5 areshown in Figure 6

Finally we get min satisfaction ratio = 01 QoS satisfac-tion ratio = 05 and throughput = 12 as shown in Figure 7

4 Simulation

In this section we implement our heuristic algorithms andthe algorithm proposed in [21] for performance comparisonWe compare three parameters in the experimental resultsnamely average minimum satisfaction ratio average QoSsatisfaction ratio and average throughput

41 Environmental Setup For experimental environmentsetting SS transmission range and interference range are

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

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Mathematical Problems in Engineering

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 5: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

Mathematical Problems in Engineering 5

Input 119866SR 119867 119879 brBROutput min satisfaction ratio QoS satisfaction ratio throughput

(1) Initialization 120582119894larr 0 120590

119894larr 0 forall119904

119894isin 119878119878

(2) for all 119878119878 node V119894on 119866 do

(3) tr119894larr lceil

BR119894

119888119894

rceil

(4) for all RS V119895on the path hp

119894from V

119894to BS do

(5) tr119894larr tr119894+ lceil

BR119894

119888119895

rceil

(6) endfor(7) endfor(8) Sort (TR)(9) 119860

119905larr |119867| forall119905 isin 119879

(10) Set all 119904119904119894119876119900119878119860119897119897119900119888119886119905119890119889 = false(11) QoS Scheduling (119866SR 119860 119879TR brBR)(12) QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)(13) Maxmin Scheduling (119866SR 119860 119879 119884BR)(14) Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868BR)

Algorithm 1 Heuristic Algorithm

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Step 2(3) 119894119899119889119890119909 larr 1

(4) for 119896 = 1 rarr |hp119894|

(5) 119903119890119902 larr lceilbr119894

119888119896

rceil

(6) for 119905 = 119894119899119889119890119909 rarr |119879|

(7) if 119860119905ge 119903119890119902

(8) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(9) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(10) else(11) if (|119879| minus 119905) lt (hp

119894minus 119896)

(12) free all tiles which allocated to 119904119894

(13) 119878119878 larr 119878119878 119904119894

(14) go to Step 1(15) else(16) 119860

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905 119894119899119889119890119909 larr 119905 119905 larr |119879|

(17) Step 3 if all hops of 119904119894are allocated successfully

(18) Slarr S 119904119894

(19) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120590119894times 119888119894

(20) for all RS 119903119904119895on the path from 119904

119894to BS do

(21) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120590119895times 119888119895

(22) endfor

(23) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(24) Step 4 if all SSs meet requirement or no sufficient resources can be allocated(25) terminate scheduling(26) else go to Step 1

Algorithm 2 QoS Scheduling (119866SR 119860 119879TR brBR)

6 Mathematical Problems in Engineering

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(3) Step 2(4) 119894119899119889119890119909 larr 1

(5) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(6) 119903119890119902 larr lceilbr119894

119888119896

rceil

(7) for 119905 = 119894119899119889119890119909 rarr |119879|

(8) if (119860119905+ 119877119905) gt 119903119890119902 then

(9) if 119860119905ge 119903119890119902

(10) 119860119905larr 119860119905minus 119903119890119902

(11) else(12) 119860

119905larr 0 119877

119905larr 119877119905minus (119903119890119902 minus 119860

119905)

(13) 119903119890119902 larr 0 119894119899119889119890119909 larr 119905 119905 larr |119879|

(14) else if (|119879| minus 119905) lt (hp119894minus 119896)

(15) free all tiles which allocated to 119904119894during this step

(16) 119878119878 larr 119878119878 119904119894

(17) go to Step 1(18) Step 3(19) if the resource is fully allocated successfully to all hops of 119904

119894 then

(20) Slarr S 119904119894

(21) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120582119894+ 120590119894times 119888119894

(22) for all RS 119903119904119895on the path from 119904

119894to BS do

(23) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120582119895+ 120590119895times 119888119895

(24) endfor

(25) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(26) Step 4 if all SSs meet QoS or no sufficient resources can be allocated then(27) Termination(28) else go to Step 1

Algorithm 3 QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)

Step 3 (remaining resources to do the max-min fair schedul-ing)When the first two steps are finished then some remain-ing resources are available Then the available tiles are allo-cated to the SSs that have lowest satisfaction and satisfactionratio is upgraded by Algorithm 4 119872119886119909119898119894119899 119878119888ℎ119890119889119906119897119894119899119892()

Step 4 (upgrade the min satisfaction ratio) FinallyAlgorithm 5 119872119886119909119898119894119899 119878119901119890119888119905119903119886119897 119877119890119906119904119890() finds out an 119904

119894

which has lowest satisfaction ratio among all SSs to increaseits satisfaction ratio Until all the SSs are allocated availabletiles by the spectral reuse mechanism or the satisfactionratio of 119904

119894are equal to 1 Then the procedure of scheduling

algorithm will be finished

332 Scheduling Algorithm Description with an Example Asshown in Figure 1 the networks are composed of one BSthree RSs = 119903

1 1199032 1199033 and six SSs = 119904

1 1199042 1199043 1199044 1199045 1199046 The

number of maximum bandwidth requirements of each SSsBR119894are 10 10 8 8 8 and 10 The bandwidth requirements

of SSs br119894are 7 2 4 5 6 and 3 for guaranteeing QoS The

capacity of each link 119888119897is set to 1 The number of time-slots

119905 is set to 7 The number of subchannels ℎ is set to 3 Theinterference of each RS and SS is defined as follows

119868 (1199031) = 119904

1 1199042 1199032 1199033 119868 (119903

2) = 119903

1 1199033 1199043 1199044

119868 (1199033)= 1199032 1199045 1199046 119868 (119904

1)= 1199042 1199031 119868 (119904

6)= 1199045 1199033

119868 (1199042) = 119904

1 1199031 1199043 119868 (119904

3) = 119904

2 1199034 1199044

119868 (1199044) = 119904

3 1199032 1199045 119868 (119904

5) = 119904

4 1199033 1199046

(9)

At first the value of tr119894(= lceilBR

119894119888119894rceil + sum

forall119895isinhp119894119904119894lceilBR119894119888119895rceil)

of each 119904119894is calculated at lines (2)ndash(7) in Algorithm 1 Then

the value of TR is sorted by increasing order at line (8) inAlgorithm 1 The value of parameter 119860

119905is initialized as |119867|

for all time-slot 119905The limited resources are allocated by Algorithm 2The 119904

119894

is selected with minimum total tile requirement tr119894at line

(1) of Algorithm 2 Then the resources are allocated atlines (2)ndash(16) of Algorithm 2 After resources allocation arecompleted the parameters and variables of the SS and RSwill be updated at lines (17)ndash(23) of Algorithm 2 At lines

Mathematical Problems in Engineering 7

Output 119884119860(1) Step 1(2) Choose a 119904

119894with the smallest satisfaction

(3) if 119910119894== 1 then terminate scheduling

(4) else go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(8) 119903119890119902 larr lceilBR119894

119888119896

rceil minus 120590119896

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else if 119860119905lt 119903119890119902

(14) 119860119905larr 0 119905119903

119894larr 119903119890119902 minus 119860

119905

(15) else if (|119879| minus 119905) lt (1003816100381610038161003816hp1198941003816100381610038161003816 minus 119896)

(16) free all tiles which allocated to 119904119894in Step 2

(17) 119878119878 larr 119878119878 119904119894

(18) go to Step 1(19) Step 3(20) if the resource is fully allocated successfully to all hops of 119904

119894 then

(21) Slarr S 119904119894

(22) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(23) for all RS 119903119904119895on the path from 119904

119894to BS do

(24) 120582119895larr 120582119895+ 119888119894

(25) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(26) Step 4(27) if 119910

119894= 1 or S is empty then

(28) terminate scheduling(29) else go to Step 1

Algorithm 4 Maxmin Scheduling (119866SR 119860 119879 119884BR)

(24)ndash(26) of Algorithm 2 if no available resources are ableto allocate to each SS the procedure goes back to the mainalgorithm Otherwise the scheduler continue to find the nextSSwhich can allocate resources tomeet theQoS requirementsof the SS In our example the total number of tiles is 21 InAlgorithm 2 the sequence of 119904

119894will be selected as 119904

2 1199046 1199043

The value of parameter tr119894is estimated as follows

tr1= lceil

BR1

1198881

rceil + sumforall119895isinhp

11199041

lceilBR1

119888119895

rceil = 14

tr2= lceil

BR2

1198882

rceil + sumforall119895isinhp

21199042

lceilBR2

119888119895

rceil = 4

tr3= lceil

BR3

1198883

rceil + sumforall119895isinhp

31199043

lceilBR3

119888119895

rceil = 8

tr4= lceil

BR4

1198884

rceil + sumforall119895isinhp

41199044

lceilBR4

119888119895

rceil = 10

tr5= lceil

BR5

1198885

rceil + sumforall119895isinhp

51199045

lceilBR5

119888119895

rceil = 12

tr6= lceil

BR6

1198886

rceil + sumforall119895isinhp

61199046

lceilBR6

119888119895

rceil = 6

(10)

The scheduling results of Algorithm 2 are shown inFigure 2

Moreover if the bandwidth requirements of some SSsare still unsatisfied the number of 119878119878 with QoS guaranteewill be raised by Algorithm 3 The bandwidth requirementunsatisfied 119904

119894will be found with the minimum tr

119894at line

(1) of Algorithm 3 All allocated tiles of 119904119895 forall119904119895isin 119868119894 are

recovered to set119877 at line (2) ofAlgorithm 3Then the spectralreuse strategy is used to maximize satisfaction ratio at lines(3)ndash(17) in Algorithm 3 for picked 119904

119894 If the available tiles

119860119905+ 119877119905can meet the requirement of 119904

119894at time slot 119905 for

119896th hop the required tiles are allocated at lines (8)ndash(13) ofAlgorithm 3 While the requirements of all hops are met theparameters and variables of the SS and RS will be updated at

8 Mathematical Problems in Engineering

Output 119884(1) Step 1 Choose a 119904

119894with the smallest satisfaction

(2) if 119910119894= 1 then terminate scheduling

(3) else Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(4) go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr hp119894

(8) 119903119890119902 larr tr119894

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902 then

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else(14) if (119860

119905+ 119877119905) ge 119903119890119902 then

(15) assign 119903119890119902 available tiles to 119896th hop of 119904119894

(16) else if (|119879| minus 119905) lt (hp119894minus 119896) then

(17) free all tiles which allocated to 119904119894in Step 2

(18) Slarr S 119904119894

(19) go to Step 1(20) else(21) 119860

119905larr 0 119877

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905

(22) Step 3 if all hops of 119904119894are fully allocated successfully then

(23) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(24) for all RS 119903119904119895on the path from 119904

119894to BS do

(25) 120582119895larr 120582119895+ 119888119894

(26) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(27) end for(28) Step 4(29) if 119910

119894= 1 or S is empty then

(30) terminate scheduling(31) else go to Step 1

Algorithm 5 Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868 119861119877)

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri7 2 4 5 6 3

h1

h2

h3t1 t2 t3 t4 t5 t6 t7

OFDMA frame

Figure 1 The network topology

Mathematical Problems in Engineering 9

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

5 6 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

7

hop1 hop2

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

Figure 2 The allocation of resources meets the QoS requirements of 1199042 1199043 and 119904

6

67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4 5 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA framehop1

s4s2

hop2

s3

s4s6 s3s3s3

r1

r1r2

r2

r2r2

r3

r3

r3

s4s6

s4s6

s2 s4

4 + 5

Figure 3 1199044performs the spectral reuse

lines (18)ndash(25) in Algorithm 3 Otherwise all acquired tilesof 119904119894are freed at line (15) of Algorithm 3 If the resources

allocation have not been finished the scheduler will findout the next one to meet the bandwidth requirements of 119904

119894

to guarantee QoS by the spectral reuse strategy Until theminimum bandwidth requirements of all SSs are satisfied orthe available tiles are not enough to allocate then this stepwillbe terminated The results of first hop of 119904

4are scheduled by

spectral reuse strategy of Algorithm 3 as shown in Figure 3Because the available tiles are insufficient at second hop 119904

4

cannot be assigned as shown in Figure 4 Hence all acquiredtiles of 119904

4need to be freed Due to the available tiles which are

not enough to assign this step is terminatedIf the remaining available tiles have not been allocated

completely then these remaining resources can increase thenetwork minimum satisfaction ratio by Algorithm 4 The SSwould be picked with lowest satisfaction ratio in sequence atline (2) of Algorithm 4 While the lowest satisfaction ratio isequal to 1 the scheduling of Algorithm 4 is terminated

Otherwise the scheduler will check whether there avail-able tiles can be assigned to the 119904

119894at lines (5)ndash(18) of

Algorithm 4 if the resources could be allocated to the SSAfter the parameters and variables of SS and RS are updatedat lines (19)ndash(26) of Algorithm 4 the scheduler continueto find out the lowest satisfaction ratio of SS and to assignavailable tiles to increase satisfaction ratio Until no availabletiles can be allocated or the requirements of all SSs are metthe scheduling procedure is terminated The max-min fairscheduling is performed with remaining tiles in Algorithm 4The satisfaction ratio of 119904

1 1199044 1199045 is 0 Because the second

hop has no enough available tiles the schedule fails for1199041 1199044 1199045 The scheduling results of Algorithm 4 are shown

in Figure 5Finally the spectral reuse strategy is operated on the

SS which has lowest satisfaction ratio for increasing theminimum satisfaction ratio in Algorithm 5 At line (1) ofAlgorithm 5 the scheduler pick a 119904

119894that has lowest satisfac-

tion ratio If the lowest satisfaction ratio equals to 1 at line (2)

10 Mathematical Problems in Engineering

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

bri

hop1 hop2

Figure 4 When lacking resources 1199044cannot perform spectral reuse

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

y1 = 0 y2 = 15 y3 = 12 y4 = 0 y5 = 0 y6 = 310

hop1 hop2

Figure 5 No remaining resources can be used to perform max-min fair scheduling

of Algorithm 5 the scheduling of Algorithm 5 is terminatedOtherwise all allocated tiles of 119904

119895are recovered to set119877 forall119904

119895isin

119868119894at line (3) of Algorithm 5 Then the spectral reuse strategy

is used to allocate tiles to 119904119894for maximizing satisfaction ratio

at lines (5)ndash(21) of Algorithm 5 When the available tiles set119860119905enough to assign to 119896th hop the tiles of 119860

119905set are firstly

allocated at lines (10)ndash(12) of Algorithm 5 When the set 119860119905

cannot fulfill the 119903119890119902 of 119904119894 both the set 119860

119905and 119877

119905are applied

to allocate at lines (13)ndash(21) of Algorithm 5 When both theset 119860119905and 119877

119905cannot satisfy the 119903119890119902 of 119904

119894at time slot 119905 at line

(21) of Algorithm 5 the difference of required tiles wouldbe found at next time slot If the requirement of all hopscannot be met all acquired tiles of 119904

119894have to be freed at

lines (16)ndash(19) of Algorithm 5 Then the scheduler continueto find out next SS until no resources can be allocated ByAlgorithm 4 the scheduled satisfaction ratio of 119904

1 1199044 1199045 is

0 Algorithm 5 enhances satisfaction ratio of 1199041 1199044 1199045 to

01 0125 0125 The scheduling results of Algorithm 5 areshown in Figure 6

Finally we get min satisfaction ratio = 01 QoS satisfac-tion ratio = 05 and throughput = 12 as shown in Figure 7

4 Simulation

In this section we implement our heuristic algorithms andthe algorithm proposed in [21] for performance comparisonWe compare three parameters in the experimental resultsnamely average minimum satisfaction ratio average QoSsatisfaction ratio and average throughput

41 Environmental Setup For experimental environmentsetting SS transmission range and interference range are

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

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Page 6: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

6 Mathematical Problems in Engineering

Output 119884119860(1) Step 1 Choose a 119904

119894from 119878119878 set with the minimal total tile requirement tr

119894

(2) Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(3) Step 2(4) 119894119899119889119890119909 larr 1

(5) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(6) 119903119890119902 larr lceilbr119894

119888119896

rceil

(7) for 119905 = 119894119899119889119890119909 rarr |119879|

(8) if (119860119905+ 119877119905) gt 119903119890119902 then

(9) if 119860119905ge 119903119890119902

(10) 119860119905larr 119860119905minus 119903119890119902

(11) else(12) 119860

119905larr 0 119877

119905larr 119877119905minus (119903119890119902 minus 119860

119905)

(13) 119903119890119902 larr 0 119894119899119889119890119909 larr 119905 119905 larr |119879|

(14) else if (|119879| minus 119905) lt (hp119894minus 119896)

(15) free all tiles which allocated to 119904119894during this step

(16) 119878119878 larr 119878119878 119904119894

(17) go to Step 1(18) Step 3(19) if the resource is fully allocated successfully to all hops of 119904

119894 then

(20) Slarr S 119904119894

(21) 120590119894larr lceil

br119894

119888119894

rceil 120582119894larr 120582119894+ 120590119894times 119888119894

(22) for all RS 119903119904119895on the path from 119904

119894to BS do

(23) 120590119895larr lceil

br119894

119888119895

rceil 120582119895larr 120582119895+ 120590119895times 119888119895

(24) endfor

(25) 119910119894larr120582119894+ sumforall119903119904119895isinhp119894

120582119895

BR119894times |hp119894|

(26) Step 4 if all SSs meet QoS or no sufficient resources can be allocated then(27) Termination(28) else go to Step 1

Algorithm 3 QoS Spectral Reuse (119866SR 119860 119879TR 119868 brBR)

Step 3 (remaining resources to do the max-min fair schedul-ing)When the first two steps are finished then some remain-ing resources are available Then the available tiles are allo-cated to the SSs that have lowest satisfaction and satisfactionratio is upgraded by Algorithm 4 119872119886119909119898119894119899 119878119888ℎ119890119889119906119897119894119899119892()

Step 4 (upgrade the min satisfaction ratio) FinallyAlgorithm 5 119872119886119909119898119894119899 119878119901119890119888119905119903119886119897 119877119890119906119904119890() finds out an 119904

119894

which has lowest satisfaction ratio among all SSs to increaseits satisfaction ratio Until all the SSs are allocated availabletiles by the spectral reuse mechanism or the satisfactionratio of 119904

119894are equal to 1 Then the procedure of scheduling

algorithm will be finished

332 Scheduling Algorithm Description with an Example Asshown in Figure 1 the networks are composed of one BSthree RSs = 119903

1 1199032 1199033 and six SSs = 119904

1 1199042 1199043 1199044 1199045 1199046 The

number of maximum bandwidth requirements of each SSsBR119894are 10 10 8 8 8 and 10 The bandwidth requirements

of SSs br119894are 7 2 4 5 6 and 3 for guaranteeing QoS The

capacity of each link 119888119897is set to 1 The number of time-slots

119905 is set to 7 The number of subchannels ℎ is set to 3 Theinterference of each RS and SS is defined as follows

119868 (1199031) = 119904

1 1199042 1199032 1199033 119868 (119903

2) = 119903

1 1199033 1199043 1199044

119868 (1199033)= 1199032 1199045 1199046 119868 (119904

1)= 1199042 1199031 119868 (119904

6)= 1199045 1199033

119868 (1199042) = 119904

1 1199031 1199043 119868 (119904

3) = 119904

2 1199034 1199044

119868 (1199044) = 119904

3 1199032 1199045 119868 (119904

5) = 119904

4 1199033 1199046

(9)

At first the value of tr119894(= lceilBR

119894119888119894rceil + sum

forall119895isinhp119894119904119894lceilBR119894119888119895rceil)

of each 119904119894is calculated at lines (2)ndash(7) in Algorithm 1 Then

the value of TR is sorted by increasing order at line (8) inAlgorithm 1 The value of parameter 119860

119905is initialized as |119867|

for all time-slot 119905The limited resources are allocated by Algorithm 2The 119904

119894

is selected with minimum total tile requirement tr119894at line

(1) of Algorithm 2 Then the resources are allocated atlines (2)ndash(16) of Algorithm 2 After resources allocation arecompleted the parameters and variables of the SS and RSwill be updated at lines (17)ndash(23) of Algorithm 2 At lines

Mathematical Problems in Engineering 7

Output 119884119860(1) Step 1(2) Choose a 119904

119894with the smallest satisfaction

(3) if 119910119894== 1 then terminate scheduling

(4) else go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(8) 119903119890119902 larr lceilBR119894

119888119896

rceil minus 120590119896

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else if 119860119905lt 119903119890119902

(14) 119860119905larr 0 119905119903

119894larr 119903119890119902 minus 119860

119905

(15) else if (|119879| minus 119905) lt (1003816100381610038161003816hp1198941003816100381610038161003816 minus 119896)

(16) free all tiles which allocated to 119904119894in Step 2

(17) 119878119878 larr 119878119878 119904119894

(18) go to Step 1(19) Step 3(20) if the resource is fully allocated successfully to all hops of 119904

119894 then

(21) Slarr S 119904119894

(22) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(23) for all RS 119903119904119895on the path from 119904

119894to BS do

(24) 120582119895larr 120582119895+ 119888119894

(25) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(26) Step 4(27) if 119910

119894= 1 or S is empty then

(28) terminate scheduling(29) else go to Step 1

Algorithm 4 Maxmin Scheduling (119866SR 119860 119879 119884BR)

(24)ndash(26) of Algorithm 2 if no available resources are ableto allocate to each SS the procedure goes back to the mainalgorithm Otherwise the scheduler continue to find the nextSSwhich can allocate resources tomeet theQoS requirementsof the SS In our example the total number of tiles is 21 InAlgorithm 2 the sequence of 119904

119894will be selected as 119904

2 1199046 1199043

The value of parameter tr119894is estimated as follows

tr1= lceil

BR1

1198881

rceil + sumforall119895isinhp

11199041

lceilBR1

119888119895

rceil = 14

tr2= lceil

BR2

1198882

rceil + sumforall119895isinhp

21199042

lceilBR2

119888119895

rceil = 4

tr3= lceil

BR3

1198883

rceil + sumforall119895isinhp

31199043

lceilBR3

119888119895

rceil = 8

tr4= lceil

BR4

1198884

rceil + sumforall119895isinhp

41199044

lceilBR4

119888119895

rceil = 10

tr5= lceil

BR5

1198885

rceil + sumforall119895isinhp

51199045

lceilBR5

119888119895

rceil = 12

tr6= lceil

BR6

1198886

rceil + sumforall119895isinhp

61199046

lceilBR6

119888119895

rceil = 6

(10)

The scheduling results of Algorithm 2 are shown inFigure 2

Moreover if the bandwidth requirements of some SSsare still unsatisfied the number of 119878119878 with QoS guaranteewill be raised by Algorithm 3 The bandwidth requirementunsatisfied 119904

119894will be found with the minimum tr

119894at line

(1) of Algorithm 3 All allocated tiles of 119904119895 forall119904119895isin 119868119894 are

recovered to set119877 at line (2) ofAlgorithm 3Then the spectralreuse strategy is used to maximize satisfaction ratio at lines(3)ndash(17) in Algorithm 3 for picked 119904

119894 If the available tiles

119860119905+ 119877119905can meet the requirement of 119904

119894at time slot 119905 for

119896th hop the required tiles are allocated at lines (8)ndash(13) ofAlgorithm 3 While the requirements of all hops are met theparameters and variables of the SS and RS will be updated at

8 Mathematical Problems in Engineering

Output 119884(1) Step 1 Choose a 119904

119894with the smallest satisfaction

(2) if 119910119894= 1 then terminate scheduling

(3) else Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(4) go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr hp119894

(8) 119903119890119902 larr tr119894

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902 then

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else(14) if (119860

119905+ 119877119905) ge 119903119890119902 then

(15) assign 119903119890119902 available tiles to 119896th hop of 119904119894

(16) else if (|119879| minus 119905) lt (hp119894minus 119896) then

(17) free all tiles which allocated to 119904119894in Step 2

(18) Slarr S 119904119894

(19) go to Step 1(20) else(21) 119860

119905larr 0 119877

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905

(22) Step 3 if all hops of 119904119894are fully allocated successfully then

(23) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(24) for all RS 119903119904119895on the path from 119904

119894to BS do

(25) 120582119895larr 120582119895+ 119888119894

(26) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(27) end for(28) Step 4(29) if 119910

119894= 1 or S is empty then

(30) terminate scheduling(31) else go to Step 1

Algorithm 5 Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868 119861119877)

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri7 2 4 5 6 3

h1

h2

h3t1 t2 t3 t4 t5 t6 t7

OFDMA frame

Figure 1 The network topology

Mathematical Problems in Engineering 9

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

5 6 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

7

hop1 hop2

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

Figure 2 The allocation of resources meets the QoS requirements of 1199042 1199043 and 119904

6

67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4 5 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA framehop1

s4s2

hop2

s3

s4s6 s3s3s3

r1

r1r2

r2

r2r2

r3

r3

r3

s4s6

s4s6

s2 s4

4 + 5

Figure 3 1199044performs the spectral reuse

lines (18)ndash(25) in Algorithm 3 Otherwise all acquired tilesof 119904119894are freed at line (15) of Algorithm 3 If the resources

allocation have not been finished the scheduler will findout the next one to meet the bandwidth requirements of 119904

119894

to guarantee QoS by the spectral reuse strategy Until theminimum bandwidth requirements of all SSs are satisfied orthe available tiles are not enough to allocate then this stepwillbe terminated The results of first hop of 119904

4are scheduled by

spectral reuse strategy of Algorithm 3 as shown in Figure 3Because the available tiles are insufficient at second hop 119904

4

cannot be assigned as shown in Figure 4 Hence all acquiredtiles of 119904

4need to be freed Due to the available tiles which are

not enough to assign this step is terminatedIf the remaining available tiles have not been allocated

completely then these remaining resources can increase thenetwork minimum satisfaction ratio by Algorithm 4 The SSwould be picked with lowest satisfaction ratio in sequence atline (2) of Algorithm 4 While the lowest satisfaction ratio isequal to 1 the scheduling of Algorithm 4 is terminated

Otherwise the scheduler will check whether there avail-able tiles can be assigned to the 119904

119894at lines (5)ndash(18) of

Algorithm 4 if the resources could be allocated to the SSAfter the parameters and variables of SS and RS are updatedat lines (19)ndash(26) of Algorithm 4 the scheduler continueto find out the lowest satisfaction ratio of SS and to assignavailable tiles to increase satisfaction ratio Until no availabletiles can be allocated or the requirements of all SSs are metthe scheduling procedure is terminated The max-min fairscheduling is performed with remaining tiles in Algorithm 4The satisfaction ratio of 119904

1 1199044 1199045 is 0 Because the second

hop has no enough available tiles the schedule fails for1199041 1199044 1199045 The scheduling results of Algorithm 4 are shown

in Figure 5Finally the spectral reuse strategy is operated on the

SS which has lowest satisfaction ratio for increasing theminimum satisfaction ratio in Algorithm 5 At line (1) ofAlgorithm 5 the scheduler pick a 119904

119894that has lowest satisfac-

tion ratio If the lowest satisfaction ratio equals to 1 at line (2)

10 Mathematical Problems in Engineering

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

bri

hop1 hop2

Figure 4 When lacking resources 1199044cannot perform spectral reuse

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

y1 = 0 y2 = 15 y3 = 12 y4 = 0 y5 = 0 y6 = 310

hop1 hop2

Figure 5 No remaining resources can be used to perform max-min fair scheduling

of Algorithm 5 the scheduling of Algorithm 5 is terminatedOtherwise all allocated tiles of 119904

119895are recovered to set119877 forall119904

119895isin

119868119894at line (3) of Algorithm 5 Then the spectral reuse strategy

is used to allocate tiles to 119904119894for maximizing satisfaction ratio

at lines (5)ndash(21) of Algorithm 5 When the available tiles set119860119905enough to assign to 119896th hop the tiles of 119860

119905set are firstly

allocated at lines (10)ndash(12) of Algorithm 5 When the set 119860119905

cannot fulfill the 119903119890119902 of 119904119894 both the set 119860

119905and 119877

119905are applied

to allocate at lines (13)ndash(21) of Algorithm 5 When both theset 119860119905and 119877

119905cannot satisfy the 119903119890119902 of 119904

119894at time slot 119905 at line

(21) of Algorithm 5 the difference of required tiles wouldbe found at next time slot If the requirement of all hopscannot be met all acquired tiles of 119904

119894have to be freed at

lines (16)ndash(19) of Algorithm 5 Then the scheduler continueto find out next SS until no resources can be allocated ByAlgorithm 4 the scheduled satisfaction ratio of 119904

1 1199044 1199045 is

0 Algorithm 5 enhances satisfaction ratio of 1199041 1199044 1199045 to

01 0125 0125 The scheduling results of Algorithm 5 areshown in Figure 6

Finally we get min satisfaction ratio = 01 QoS satisfac-tion ratio = 05 and throughput = 12 as shown in Figure 7

4 Simulation

In this section we implement our heuristic algorithms andthe algorithm proposed in [21] for performance comparisonWe compare three parameters in the experimental resultsnamely average minimum satisfaction ratio average QoSsatisfaction ratio and average throughput

41 Environmental Setup For experimental environmentsetting SS transmission range and interference range are

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

Submit your manuscripts athttpwwwhindawicom

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Stochastic AnalysisInternational Journal of

Page 7: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

Mathematical Problems in Engineering 7

Output 119884119860(1) Step 1(2) Choose a 119904

119894with the smallest satisfaction

(3) if 119910119894== 1 then terminate scheduling

(4) else go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr 1003816100381610038161003816hp1198941003816100381610038161003816

(8) 119903119890119902 larr lceilBR119894

119888119896

rceil minus 120590119896

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else if 119860119905lt 119903119890119902

(14) 119860119905larr 0 119905119903

119894larr 119903119890119902 minus 119860

119905

(15) else if (|119879| minus 119905) lt (1003816100381610038161003816hp1198941003816100381610038161003816 minus 119896)

(16) free all tiles which allocated to 119904119894in Step 2

(17) 119878119878 larr 119878119878 119904119894

(18) go to Step 1(19) Step 3(20) if the resource is fully allocated successfully to all hops of 119904

119894 then

(21) Slarr S 119904119894

(22) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(23) for all RS 119903119904119895on the path from 119904

119894to BS do

(24) 120582119895larr 120582119895+ 119888119894

(25) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(26) Step 4(27) if 119910

119894= 1 or S is empty then

(28) terminate scheduling(29) else go to Step 1

Algorithm 4 Maxmin Scheduling (119866SR 119860 119879 119884BR)

(24)ndash(26) of Algorithm 2 if no available resources are ableto allocate to each SS the procedure goes back to the mainalgorithm Otherwise the scheduler continue to find the nextSSwhich can allocate resources tomeet theQoS requirementsof the SS In our example the total number of tiles is 21 InAlgorithm 2 the sequence of 119904

119894will be selected as 119904

2 1199046 1199043

The value of parameter tr119894is estimated as follows

tr1= lceil

BR1

1198881

rceil + sumforall119895isinhp

11199041

lceilBR1

119888119895

rceil = 14

tr2= lceil

BR2

1198882

rceil + sumforall119895isinhp

21199042

lceilBR2

119888119895

rceil = 4

tr3= lceil

BR3

1198883

rceil + sumforall119895isinhp

31199043

lceilBR3

119888119895

rceil = 8

tr4= lceil

BR4

1198884

rceil + sumforall119895isinhp

41199044

lceilBR4

119888119895

rceil = 10

tr5= lceil

BR5

1198885

rceil + sumforall119895isinhp

51199045

lceilBR5

119888119895

rceil = 12

tr6= lceil

BR6

1198886

rceil + sumforall119895isinhp

61199046

lceilBR6

119888119895

rceil = 6

(10)

The scheduling results of Algorithm 2 are shown inFigure 2

Moreover if the bandwidth requirements of some SSsare still unsatisfied the number of 119878119878 with QoS guaranteewill be raised by Algorithm 3 The bandwidth requirementunsatisfied 119904

119894will be found with the minimum tr

119894at line

(1) of Algorithm 3 All allocated tiles of 119904119895 forall119904119895isin 119868119894 are

recovered to set119877 at line (2) ofAlgorithm 3Then the spectralreuse strategy is used to maximize satisfaction ratio at lines(3)ndash(17) in Algorithm 3 for picked 119904

119894 If the available tiles

119860119905+ 119877119905can meet the requirement of 119904

119894at time slot 119905 for

119896th hop the required tiles are allocated at lines (8)ndash(13) ofAlgorithm 3 While the requirements of all hops are met theparameters and variables of the SS and RS will be updated at

8 Mathematical Problems in Engineering

Output 119884(1) Step 1 Choose a 119904

119894with the smallest satisfaction

(2) if 119910119894= 1 then terminate scheduling

(3) else Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(4) go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr hp119894

(8) 119903119890119902 larr tr119894

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902 then

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else(14) if (119860

119905+ 119877119905) ge 119903119890119902 then

(15) assign 119903119890119902 available tiles to 119896th hop of 119904119894

(16) else if (|119879| minus 119905) lt (hp119894minus 119896) then

(17) free all tiles which allocated to 119904119894in Step 2

(18) Slarr S 119904119894

(19) go to Step 1(20) else(21) 119860

119905larr 0 119877

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905

(22) Step 3 if all hops of 119904119894are fully allocated successfully then

(23) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(24) for all RS 119903119904119895on the path from 119904

119894to BS do

(25) 120582119895larr 120582119895+ 119888119894

(26) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(27) end for(28) Step 4(29) if 119910

119894= 1 or S is empty then

(30) terminate scheduling(31) else go to Step 1

Algorithm 5 Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868 119861119877)

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri7 2 4 5 6 3

h1

h2

h3t1 t2 t3 t4 t5 t6 t7

OFDMA frame

Figure 1 The network topology

Mathematical Problems in Engineering 9

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

5 6 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

7

hop1 hop2

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

Figure 2 The allocation of resources meets the QoS requirements of 1199042 1199043 and 119904

6

67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4 5 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA framehop1

s4s2

hop2

s3

s4s6 s3s3s3

r1

r1r2

r2

r2r2

r3

r3

r3

s4s6

s4s6

s2 s4

4 + 5

Figure 3 1199044performs the spectral reuse

lines (18)ndash(25) in Algorithm 3 Otherwise all acquired tilesof 119904119894are freed at line (15) of Algorithm 3 If the resources

allocation have not been finished the scheduler will findout the next one to meet the bandwidth requirements of 119904

119894

to guarantee QoS by the spectral reuse strategy Until theminimum bandwidth requirements of all SSs are satisfied orthe available tiles are not enough to allocate then this stepwillbe terminated The results of first hop of 119904

4are scheduled by

spectral reuse strategy of Algorithm 3 as shown in Figure 3Because the available tiles are insufficient at second hop 119904

4

cannot be assigned as shown in Figure 4 Hence all acquiredtiles of 119904

4need to be freed Due to the available tiles which are

not enough to assign this step is terminatedIf the remaining available tiles have not been allocated

completely then these remaining resources can increase thenetwork minimum satisfaction ratio by Algorithm 4 The SSwould be picked with lowest satisfaction ratio in sequence atline (2) of Algorithm 4 While the lowest satisfaction ratio isequal to 1 the scheduling of Algorithm 4 is terminated

Otherwise the scheduler will check whether there avail-able tiles can be assigned to the 119904

119894at lines (5)ndash(18) of

Algorithm 4 if the resources could be allocated to the SSAfter the parameters and variables of SS and RS are updatedat lines (19)ndash(26) of Algorithm 4 the scheduler continueto find out the lowest satisfaction ratio of SS and to assignavailable tiles to increase satisfaction ratio Until no availabletiles can be allocated or the requirements of all SSs are metthe scheduling procedure is terminated The max-min fairscheduling is performed with remaining tiles in Algorithm 4The satisfaction ratio of 119904

1 1199044 1199045 is 0 Because the second

hop has no enough available tiles the schedule fails for1199041 1199044 1199045 The scheduling results of Algorithm 4 are shown

in Figure 5Finally the spectral reuse strategy is operated on the

SS which has lowest satisfaction ratio for increasing theminimum satisfaction ratio in Algorithm 5 At line (1) ofAlgorithm 5 the scheduler pick a 119904

119894that has lowest satisfac-

tion ratio If the lowest satisfaction ratio equals to 1 at line (2)

10 Mathematical Problems in Engineering

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

bri

hop1 hop2

Figure 4 When lacking resources 1199044cannot perform spectral reuse

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

y1 = 0 y2 = 15 y3 = 12 y4 = 0 y5 = 0 y6 = 310

hop1 hop2

Figure 5 No remaining resources can be used to perform max-min fair scheduling

of Algorithm 5 the scheduling of Algorithm 5 is terminatedOtherwise all allocated tiles of 119904

119895are recovered to set119877 forall119904

119895isin

119868119894at line (3) of Algorithm 5 Then the spectral reuse strategy

is used to allocate tiles to 119904119894for maximizing satisfaction ratio

at lines (5)ndash(21) of Algorithm 5 When the available tiles set119860119905enough to assign to 119896th hop the tiles of 119860

119905set are firstly

allocated at lines (10)ndash(12) of Algorithm 5 When the set 119860119905

cannot fulfill the 119903119890119902 of 119904119894 both the set 119860

119905and 119877

119905are applied

to allocate at lines (13)ndash(21) of Algorithm 5 When both theset 119860119905and 119877

119905cannot satisfy the 119903119890119902 of 119904

119894at time slot 119905 at line

(21) of Algorithm 5 the difference of required tiles wouldbe found at next time slot If the requirement of all hopscannot be met all acquired tiles of 119904

119894have to be freed at

lines (16)ndash(19) of Algorithm 5 Then the scheduler continueto find out next SS until no resources can be allocated ByAlgorithm 4 the scheduled satisfaction ratio of 119904

1 1199044 1199045 is

0 Algorithm 5 enhances satisfaction ratio of 1199041 1199044 1199045 to

01 0125 0125 The scheduling results of Algorithm 5 areshown in Figure 6

Finally we get min satisfaction ratio = 01 QoS satisfac-tion ratio = 05 and throughput = 12 as shown in Figure 7

4 Simulation

In this section we implement our heuristic algorithms andthe algorithm proposed in [21] for performance comparisonWe compare three parameters in the experimental resultsnamely average minimum satisfaction ratio average QoSsatisfaction ratio and average throughput

41 Environmental Setup For experimental environmentsetting SS transmission range and interference range are

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 8: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

8 Mathematical Problems in Engineering

Output 119884(1) Step 1 Choose a 119904

119894with the smallest satisfaction

(2) if 119910119894= 1 then terminate scheduling

(3) else Recover all allocated tiles of 119904119895to set 119877 forall119904

119895isin 119868119894

(4) go to Step 2(5) Step 2(6) 119894119899119889119890119909 larr 1

(7) for 119896 = 1 rarr hp119894

(8) 119903119890119902 larr tr119894

(9) for 119905 = 119894119899119889119890119909 rarr |119879|

(10) if 119860119905ge 119903119890119902 then

(11) 119860119905larr 119860119905minus 119903119890119902 119903119890119902 larr 0 119896 larr 119896 + 1

(12) 119894119899119889119890119909 larr 119905 119905 larr |119879|

(13) else(14) if (119860

119905+ 119877119905) ge 119903119890119902 then

(15) assign 119903119890119902 available tiles to 119896th hop of 119904119894

(16) else if (|119879| minus 119905) lt (hp119894minus 119896) then

(17) free all tiles which allocated to 119904119894in Step 2

(18) Slarr S 119904119894

(19) go to Step 1(20) else(21) 119860

119905larr 0 119877

119905larr 0 119903119890119902 larr 119903119890119902 minus 119860

119905

(22) Step 3 if all hops of 119904119894are fully allocated successfully then

(23) 120590119894larr 120590119894+ 1 120582

119894larr 120582119894+ 119888119894 119910119894larr

120582119894

BR119894

(24) for all RS 119903119904119895on the path from 119904

119894to BS do

(25) 120582119895larr 120582119895+ 119888119894

(26) 120590119895larr 120590119895+ lceil

120582119895

119888119895

rceil

(27) end for(28) Step 4(29) if 119910

119894= 1 or S is empty then

(30) terminate scheduling(31) else go to Step 1

Algorithm 5 Maxmin Spectral Reuse (119866SR 119860 119879 119884 119868 119861119877)

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri7 2 4 5 6 3

h1

h2

h3t1 t2 t3 t4 t5 t6 t7

OFDMA frame

Figure 1 The network topology

Mathematical Problems in Engineering 9

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

5 6 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

7

hop1 hop2

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

Figure 2 The allocation of resources meets the QoS requirements of 1199042 1199043 and 119904

6

67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4 5 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA framehop1

s4s2

hop2

s3

s4s6 s3s3s3

r1

r1r2

r2

r2r2

r3

r3

r3

s4s6

s4s6

s2 s4

4 + 5

Figure 3 1199044performs the spectral reuse

lines (18)ndash(25) in Algorithm 3 Otherwise all acquired tilesof 119904119894are freed at line (15) of Algorithm 3 If the resources

allocation have not been finished the scheduler will findout the next one to meet the bandwidth requirements of 119904

119894

to guarantee QoS by the spectral reuse strategy Until theminimum bandwidth requirements of all SSs are satisfied orthe available tiles are not enough to allocate then this stepwillbe terminated The results of first hop of 119904

4are scheduled by

spectral reuse strategy of Algorithm 3 as shown in Figure 3Because the available tiles are insufficient at second hop 119904

4

cannot be assigned as shown in Figure 4 Hence all acquiredtiles of 119904

4need to be freed Due to the available tiles which are

not enough to assign this step is terminatedIf the remaining available tiles have not been allocated

completely then these remaining resources can increase thenetwork minimum satisfaction ratio by Algorithm 4 The SSwould be picked with lowest satisfaction ratio in sequence atline (2) of Algorithm 4 While the lowest satisfaction ratio isequal to 1 the scheduling of Algorithm 4 is terminated

Otherwise the scheduler will check whether there avail-able tiles can be assigned to the 119904

119894at lines (5)ndash(18) of

Algorithm 4 if the resources could be allocated to the SSAfter the parameters and variables of SS and RS are updatedat lines (19)ndash(26) of Algorithm 4 the scheduler continueto find out the lowest satisfaction ratio of SS and to assignavailable tiles to increase satisfaction ratio Until no availabletiles can be allocated or the requirements of all SSs are metthe scheduling procedure is terminated The max-min fairscheduling is performed with remaining tiles in Algorithm 4The satisfaction ratio of 119904

1 1199044 1199045 is 0 Because the second

hop has no enough available tiles the schedule fails for1199041 1199044 1199045 The scheduling results of Algorithm 4 are shown

in Figure 5Finally the spectral reuse strategy is operated on the

SS which has lowest satisfaction ratio for increasing theminimum satisfaction ratio in Algorithm 5 At line (1) ofAlgorithm 5 the scheduler pick a 119904

119894that has lowest satisfac-

tion ratio If the lowest satisfaction ratio equals to 1 at line (2)

10 Mathematical Problems in Engineering

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

bri

hop1 hop2

Figure 4 When lacking resources 1199044cannot perform spectral reuse

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

y1 = 0 y2 = 15 y3 = 12 y4 = 0 y5 = 0 y6 = 310

hop1 hop2

Figure 5 No remaining resources can be used to perform max-min fair scheduling

of Algorithm 5 the scheduling of Algorithm 5 is terminatedOtherwise all allocated tiles of 119904

119895are recovered to set119877 forall119904

119895isin

119868119894at line (3) of Algorithm 5 Then the spectral reuse strategy

is used to allocate tiles to 119904119894for maximizing satisfaction ratio

at lines (5)ndash(21) of Algorithm 5 When the available tiles set119860119905enough to assign to 119896th hop the tiles of 119860

119905set are firstly

allocated at lines (10)ndash(12) of Algorithm 5 When the set 119860119905

cannot fulfill the 119903119890119902 of 119904119894 both the set 119860

119905and 119877

119905are applied

to allocate at lines (13)ndash(21) of Algorithm 5 When both theset 119860119905and 119877

119905cannot satisfy the 119903119890119902 of 119904

119894at time slot 119905 at line

(21) of Algorithm 5 the difference of required tiles wouldbe found at next time slot If the requirement of all hopscannot be met all acquired tiles of 119904

119894have to be freed at

lines (16)ndash(19) of Algorithm 5 Then the scheduler continueto find out next SS until no resources can be allocated ByAlgorithm 4 the scheduled satisfaction ratio of 119904

1 1199044 1199045 is

0 Algorithm 5 enhances satisfaction ratio of 1199041 1199044 1199045 to

01 0125 0125 The scheduling results of Algorithm 5 areshown in Figure 6

Finally we get min satisfaction ratio = 01 QoS satisfac-tion ratio = 05 and throughput = 12 as shown in Figure 7

4 Simulation

In this section we implement our heuristic algorithms andthe algorithm proposed in [21] for performance comparisonWe compare three parameters in the experimental resultsnamely average minimum satisfaction ratio average QoSsatisfaction ratio and average throughput

41 Environmental Setup For experimental environmentsetting SS transmission range and interference range are

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 9: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

Mathematical Problems in Engineering 9

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

5 6 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

7

hop1 hop2

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

Figure 2 The allocation of resources meets the QoS requirements of 1199042 1199043 and 119904

6

67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4 5 3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA framehop1

s4s2

hop2

s3

s4s6 s3s3s3

r1

r1r2

r2

r2r2

r3

r3

r3

s4s6

s4s6

s2 s4

4 + 5

Figure 3 1199044performs the spectral reuse

lines (18)ndash(25) in Algorithm 3 Otherwise all acquired tilesof 119904119894are freed at line (15) of Algorithm 3 If the resources

allocation have not been finished the scheduler will findout the next one to meet the bandwidth requirements of 119904

119894

to guarantee QoS by the spectral reuse strategy Until theminimum bandwidth requirements of all SSs are satisfied orthe available tiles are not enough to allocate then this stepwillbe terminated The results of first hop of 119904

4are scheduled by

spectral reuse strategy of Algorithm 3 as shown in Figure 3Because the available tiles are insufficient at second hop 119904

4

cannot be assigned as shown in Figure 4 Hence all acquiredtiles of 119904

4need to be freed Due to the available tiles which are

not enough to assign this step is terminatedIf the remaining available tiles have not been allocated

completely then these remaining resources can increase thenetwork minimum satisfaction ratio by Algorithm 4 The SSwould be picked with lowest satisfaction ratio in sequence atline (2) of Algorithm 4 While the lowest satisfaction ratio isequal to 1 the scheduling of Algorithm 4 is terminated

Otherwise the scheduler will check whether there avail-able tiles can be assigned to the 119904

119894at lines (5)ndash(18) of

Algorithm 4 if the resources could be allocated to the SSAfter the parameters and variables of SS and RS are updatedat lines (19)ndash(26) of Algorithm 4 the scheduler continueto find out the lowest satisfaction ratio of SS and to assignavailable tiles to increase satisfaction ratio Until no availabletiles can be allocated or the requirements of all SSs are metthe scheduling procedure is terminated The max-min fairscheduling is performed with remaining tiles in Algorithm 4The satisfaction ratio of 119904

1 1199044 1199045 is 0 Because the second

hop has no enough available tiles the schedule fails for1199041 1199044 1199045 The scheduling results of Algorithm 4 are shown

in Figure 5Finally the spectral reuse strategy is operated on the

SS which has lowest satisfaction ratio for increasing theminimum satisfaction ratio in Algorithm 5 At line (1) ofAlgorithm 5 the scheduler pick a 119904

119894that has lowest satisfac-

tion ratio If the lowest satisfaction ratio equals to 1 at line (2)

10 Mathematical Problems in Engineering

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

bri

hop1 hop2

Figure 4 When lacking resources 1199044cannot perform spectral reuse

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

y1 = 0 y2 = 15 y3 = 12 y4 = 0 y5 = 0 y6 = 310

hop1 hop2

Figure 5 No remaining resources can be used to perform max-min fair scheduling

of Algorithm 5 the scheduling of Algorithm 5 is terminatedOtherwise all allocated tiles of 119904

119895are recovered to set119877 forall119904

119895isin

119868119894at line (3) of Algorithm 5 Then the spectral reuse strategy

is used to allocate tiles to 119904119894for maximizing satisfaction ratio

at lines (5)ndash(21) of Algorithm 5 When the available tiles set119860119905enough to assign to 119896th hop the tiles of 119860

119905set are firstly

allocated at lines (10)ndash(12) of Algorithm 5 When the set 119860119905

cannot fulfill the 119903119890119902 of 119904119894 both the set 119860

119905and 119877

119905are applied

to allocate at lines (13)ndash(21) of Algorithm 5 When both theset 119860119905and 119877

119905cannot satisfy the 119903119890119902 of 119904

119894at time slot 119905 at line

(21) of Algorithm 5 the difference of required tiles wouldbe found at next time slot If the requirement of all hopscannot be met all acquired tiles of 119904

119894have to be freed at

lines (16)ndash(19) of Algorithm 5 Then the scheduler continueto find out next SS until no resources can be allocated ByAlgorithm 4 the scheduled satisfaction ratio of 119904

1 1199044 1199045 is

0 Algorithm 5 enhances satisfaction ratio of 1199041 1199044 1199045 to

01 0125 0125 The scheduling results of Algorithm 5 areshown in Figure 6

Finally we get min satisfaction ratio = 01 QoS satisfac-tion ratio = 05 and throughput = 12 as shown in Figure 7

4 Simulation

In this section we implement our heuristic algorithms andthe algorithm proposed in [21] for performance comparisonWe compare three parameters in the experimental resultsnamely average minimum satisfaction ratio average QoSsatisfaction ratio and average throughput

41 Environmental Setup For experimental environmentsetting SS transmission range and interference range are

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Mathematical Problems in Engineering

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Differential EquationsInternational Journal of

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 10: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

10 Mathematical Problems in Engineering

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

bri

hop1 hop2

Figure 4 When lacking resources 1199044cannot perform spectral reuse

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2

2

4

4

3

3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

y1 = 0 y2 = 15 y3 = 12 y4 = 0 y5 = 0 y6 = 310

hop1 hop2

Figure 5 No remaining resources can be used to perform max-min fair scheduling

of Algorithm 5 the scheduling of Algorithm 5 is terminatedOtherwise all allocated tiles of 119904

119895are recovered to set119877 forall119904

119895isin

119868119894at line (3) of Algorithm 5 Then the spectral reuse strategy

is used to allocate tiles to 119904119894for maximizing satisfaction ratio

at lines (5)ndash(21) of Algorithm 5 When the available tiles set119860119905enough to assign to 119896th hop the tiles of 119860

119905set are firstly

allocated at lines (10)ndash(12) of Algorithm 5 When the set 119860119905

cannot fulfill the 119903119890119902 of 119904119894 both the set 119860

119905and 119877

119905are applied

to allocate at lines (13)ndash(21) of Algorithm 5 When both theset 119860119905and 119877

119905cannot satisfy the 119903119890119902 of 119904

119894at time slot 119905 at line

(21) of Algorithm 5 the difference of required tiles wouldbe found at next time slot If the requirement of all hopscannot be met all acquired tiles of 119904

119894have to be freed at

lines (16)ndash(19) of Algorithm 5 Then the scheduler continueto find out next SS until no resources can be allocated ByAlgorithm 4 the scheduled satisfaction ratio of 119904

1 1199044 1199045 is

0 Algorithm 5 enhances satisfaction ratio of 1199041 1199044 1199045 to

01 0125 0125 The scheduling results of Algorithm 5 areshown in Figure 6

Finally we get min satisfaction ratio = 01 QoS satisfac-tion ratio = 05 and throughput = 12 as shown in Figure 7

4 Simulation

In this section we implement our heuristic algorithms andthe algorithm proposed in [21] for performance comparisonWe compare three parameters in the experimental resultsnamely average minimum satisfaction ratio average QoSsatisfaction ratio and average throughput

41 Environmental Setup For experimental environmentsetting SS transmission range and interference range are

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 11: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

Mathematical Problems in Engineering 11

5 67

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

bri2 4 3

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2s2

s3

s6s6

s6

s3s3

s3

r1

r1r2

r2

r2r2

r3

r3

r3

10 10 8 8 8 10 BRi

s4

s1

s5

r1

r2r3

4 + 1 3 + 12 + 1

hop1 hop2

y2 = 15 y3 = 12 y6 = 310y1 = 110 y4 = 18 y5 = 18

Figure 6 Using spectral reuse to perform max-min fair scheduling

BS

r1 r2 r3

s1 s2 s3 s4 s5 s6

h1

h2

h3

t1 t2 t3 t4 t5 t6 t7

OFDMA frame

s2 s6s6

s6

s3s3

s3

r1r1

r2

r2r2

r2

r3r3

r3

y2 = 15 y3 = 12 y6 = 310

s4

s3 s1

s2 s5

r1r2

r3

hop1 hop2

y1 = 110 y4 = 18 y5 = 18

3 5 4

Figure 7 The result of example

set 1000 and 1000 RS and the BS transmission range andinterference range are set 1000 and 2000 BS was deployedat the center of the field Multihop shortest path routing wasadopted to obtain the network topology SS is distributed inthe field by random each data packet requirement and QoSrequirement of SS are set randomly among 2 to 8 and theQoSrequirements of each SSmust be less than or equal to the datapacket requirement

In the beginning we use our heuristic algorithm andscheduling method of [21] in 1500 times 1500 square units anddeployed 4 RSs to compare with three goalsThese three goalsare minimum satisfaction ratio QoS satisfaction ratio andthroughput For OFDMA setting the number of time slotsand subchannels are 12 and 5 in a frame Then we consideranother large scale network which has 3000 times 3000 squareunits and deploy 16 RSs For OFDMA setting time-slots andsubchannels number are 48 and 5 in a frame

42 Experiment Results Then we compare heuristic methodwith [21] on the experimental results of these two methodsby three goals The three goals are the ratio of averageminimum satisfaction average QoS satisfaction ratio andaverage throughput

When the number of SSs is increasing in Figure 8(a) itwill lead to insufficient resources to allocate for all SSs thenmake min satisfaction ratio decrease Our method allocatesthe resources to the proposed QoS requirements of SS at firstpriority and does the max-min fair allocation scheduling onthe remaining resources We find that the method of [21] isbetter than our method in terms of average min satisfactionratio

When the field changed to 3000 times 3000 then 16 RSs areplaced for experiment and the number of SSs increased from10 to 100 We can find that the number of SSs increased and

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 12: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

12 Mathematical Problems in Engineering

0

02

04

06

08

1

12

5 10 15 20 25

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age m

in sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 8 Average min satisfaction ratio comparison

091

093

095

097

099

101

5 10 15 20 25

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

02

04

06

08

1

12

10 20 30 40 50 60 70 80 90 100

Aver

age Q

oS sa

tisfa

ctio

n ra

tio

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 9 Average QoS satisfaction ratio comparison

the number of hops increased in Figure 8(b) then the overallaverage min satisfaction ratio will decline obviously

In Figure 9 our heuristic algorithm will be higher thanthe method of [21] when comparing with average QoS satis-faction ratio In order to arrange the QoS requirements inincreasing order and allocate resources in increasing orderour heuristic algorithm is better than [21] in terms of QoSsatisfaction ratio

From Figure 10 we can find that the average throughputof the two methods is almost equal When the number of

hops increase the average throughput of two methods is alsoalmost equal

5 Conclusion

In this paper we study the multihop fairness schedulingproblem with QoS control for enhancing throughput andguaranteeing QoS in WiMAX mesh networks For allocatingresource tomultiple SSs fairness is a key concernThe notionof max-min fairness is applied as our metric to define the

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 13: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

Mathematical Problems in Engineering 13

0

20

40

60

80

100

120

5 10 15 20 25

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(a) Field 1500 times 1500 4 RS

0

50

100

150

200

250

300

350

10 20 30 40 50 60 70 80 90 100

Aver

age

thro

ughp

ut

The number of SSs

Max-min fair schedulingSmallest requirement first

(b) Field 3000 times 3000 16 RS

Figure 10 Average network throughput comparison

QoS-basedmax-min fair scheduling problem formaximizingthe minimum satisfaction ratio of each SS We formulate aninteger linear programming (ILP) model to provide anoptimal solution on small-scale networks Although the ILPsolution can be used to obtain optimal solutions for small-scale network it has high operation time and space consump-tion for large-scale networks

Therefore in the paper several heuristic scheduling algo-rithms are proposed tomaximize both theminimum satisfac-tion ratio and the QoS satisfaction ratio based onOrthogonalFrequency-DivisionMultiple Access (OFDMA)model in thenetworks The strategy of proposed heuristic algorithm issmallest total bandwidth requirement first and then applyingspectral reuse scheme to assign resource After QoS of allSSs is guaranteed the max-min fair scheduling scheme isused to enhance the overall throughput and satisfactionratio Experimental results show that our method is betterthan previous work in terms of QoS satisfaction ratio andthroughput

Acknowledgments

This work was supported in part by Taiwan NSC under Grantnos NSC 102-2221-E-274-004 and NSC 102-2221-E-194-054The authors would like to thank the reviewers for theirinsightful comments which helped to significantly improvethe paper

References

[1] ldquoIEEE 80216e-2006 Standard Part 16 Air Interface for FixedandMobile BroadbandWireless Access SystemsmdashAmendmentfor Physical and Medium Access Control Layers for CombinedFixed and Mobile Operation in Licensed Bandsrdquo IEEE 2006

[2] G Li and H Liu ldquoDownlink radio resource allocation formulti-cell OFDMA systemrdquo IEEE Transactions on WirelessCommunications vol 5 no 12 pp 3451ndash3459 2006

[3] A Belghith L Nuaymi and P Maille ldquoPricing of real-timeapplications in WiMAX systemsrdquo in Proceedings of the 68thSemi-Annual IEEE Vehicular Technology Conference (VTC rsquo08)pp 1ndash6 September 2008

[4] I G Fraimis V D Papoutsis and S A Kotsopoulos ldquoA decen-tralized subchannel allocation scheme with Inter-cell Interfer-ence Coordination (ICIC) for multi-cell OFDMA systemsrdquo inProceedings of the 53rd IEEEGlobal Communications Conference(GLOBECOM rsquo10) December 2010

[5] V Chandrasekhar J G Andrews and A Gatherer ldquoFemtocellnetworks a surveyrdquo IEEE Communications Magazine vol 46no 9 pp 59ndash67 2008

[6] Y Kim and M L Sichitiu ldquoFairness schemes in 80216jmobile multihop relay networksrdquo in Proceedings of the 53rdIEEE Global Communications Conference (GLOBECOM rsquo10)December 2010

[7] V Gunasekaran and F C Harmantzis ldquoAffordable infrastruc-ture for deploying WiMAX systems Mesh v Non Meshrdquo inProceedings of the IEEE 61st Vehicular Technology Conference(VTC rsquo05) vol 5 pp 2979ndash2983 June 2005

[8] H Shetiya and V Sharma ldquoAlgorithms for routing and central-ized scheduling in IEEE 80216 mesh networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo06) vol 1 pp 147ndash152 April 2006

[9] C-Y Hong and A-C Pang ldquoLink scheduling with QoS guar-antee for wireless relay networksrdquo in Proceedings of the 28thConference on Computer Communications IEEE (INFOCOMrsquo09) pp 2806ndash2810 April 2009

[10] L Fu Z Cao and P Fan ldquoSpatial reuse in IEEE 80216 basedwireless mesh networksrdquo in Proceedings of the InternationalSymposium on Communications and Information Technologies(ISCIT rsquo05) pp 1311ndash1314 October 2005

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 14: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

14 Mathematical Problems in Engineering

[11] L-W Chen Y-C Tseng Y-CWang D-WWang and J-J WuldquoExploiting spectral reuse in routing resource allocation andscheduling for IEEE 80216 mesh networksrdquo IEEE Transactionson Vehicular Technology vol 58 no 1 pp 301ndash313 2009

[12] S Ramanathan andE L Lloyd ldquoScheduling algorithms formul-tihop radio networksrdquo IEEEACM Transactions on Networkingvol 1 no 2 pp 166ndash177 1993

[13] I F Akyildiz XWang andWWang ldquoWirelessmesh networksa surveyrdquo Computer Networks vol 47 no 4 pp 445ndash487 2005

[14] G Li andH Liu ldquoOn the capacity of broadband relay networksrdquoin Proceedings of the Conference Record of the 38th AsilomarConference on Signals Systems and Computers pp 1318ndash1322November 2004

[15] M K Awad and X Shen ldquoOFDMA based two-hop cooperativerelay network resources allocationrdquo in Proceedings of the IEEEInternational Conference on Communications (ICC rsquo08) pp4414ndash4418 May 2008

[16] H-YWei S Ganguly R Izmailov and Z J Haas ldquoInterference-aware IEEE 80216WiMaxmesh networksrdquo in Proceedings of theIEEE 61st Vehicular Technology Conference (VTC rsquo05) vol 5 pp3102ndash3106 June 2005

[17] L Tassiulas and S Sarkar ldquoMaxmin fair scheduling in wirelessnetworksrdquo in Prceedings of the IEEE Infocom pp 763ndash772 June2002

[18] S C Liew and Y J Zhang ldquoProportional fairness in multi-channel multi-rate wireless networksrdquo in Proceedings of theIEEEGlobal Telecommunications Conference (GLOBECOM rsquo06)December 2006

[19] A Sayenko O Alanen J Karhula and T Hamalainen ldquoEnsur-ing the QoS requirements in 80216 schedulingrdquo in Proceedingsof the 9th ACM Symposium on Modeling Analysis and Simula-tion ofWireless andMobile Systems (ACMMSWiM rsquo06) pp 108ndash117 October 2006

[20] M Andrews and L Zhang ldquoScheduling algorithms for multi-carrier wireless data systemsrdquo in Proceedings of the 13th AnnualACM International Conference on Mobile Computing and Net-working (MobiCom rsquo07) pp 3ndash14 September 2007

[21] S BaiW Zhang Y Liu andCWang ldquoMax-min fair schedulingin OFDMA-based multi-hop WiMAX mesh networksrdquo inProceedings of the IEEE International Conference on Communi-cations (ICC rsquo11) June 2011

[22] S Deb V Mhatre and V Ramaiyan ldquoWiMAX relay net-works Opportunistic scheduling to exploit multiuser diversityand frequency selectivityrdquo in Proceedings of the 14th AnnualInternational Conference on Mobile Computing and Networking(MobiCom rsquo08) pp 163ndash174 September 2008

[23] K Sundaresan W Wang and S Eidenbenz ldquoAlgorithmicaspects of communication in ad-hoc networks with smartantennasrdquo in Proceedings of the 7th ACM International Sympo-sium onMobile AdHoc Networking and Computing (MOBIHOCrsquo06) pp 298ndash309 May 2006

[24] Y Xu SWan J Tang and R SWolff ldquoInterference Aware rout-ing and scheduling in wireless backhaul networks with smartantennasrdquo in Proceedings of the 6th Annual IEEE Commu-nications Society Conference on Sensor Mesh and Ad HocCommunications and Networks (SECON rsquo09) June 2009

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Page 15: Research Article Fairness Time-Slot Allocation and Scheduling with QoS Guarantees …downloads.hindawi.com/journals/mpe/2013/293962.pdf · 2019. 7. 31. · Guarantees in Multihop

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of