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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008 2509

Call Admission Control Optimizationin WiMAX Networks

Bo Rong, Member, IEEE , Yi Qian, Senior Member, IEEE , Kejie Lu, Senior Member, IEEE ,Hsiao-Hwa Chen, Senior Member, IEEE , and Mohsen Guizani, Senior Member, IEEE

Abstract—Worldwide interoperability for microwave access(WiMAX) is a promising technology for last-mile Internet access,particularly in the areas where wired infrastructures are notavailable. In a WiMAX network, call admission control (CAC) isdeployed to effectively control different traffic loads and preventthe network from being overloaded. In this paper, we proposea framework of a 2-D CAC to accommodate various features of WiMAX networks. Specifically, we decompose the 2-D uplink anddownlink WiMAX CAC problem into two independent 1-D CACproblems and formulate the 1-D CAC optimization, in which thedemands of service providers and subscribers are jointly taken

into account. To solve the optimization problem, we develop autility- and fairness-constrained optimal revenue policy, as wellas its corresponding approximation algorithm. Simulation resultsare presented to demonstrate the effectiveness of the proposedWiMAX CAC approach.

Index Terms—Call admission control (CAC), optimization,orthogonal frequency-division multiple access (OFDMA), time-division duplex (TDD), worldwide interoperability for microwaveaccess (WiMAX).

I. INTRODUCTION

THERE exist many regions in the world where wired

infrastructures (i.e., T1, DSL, cables, etc.) are difficultto deploy for geographical or economic reasons. To pro-

vide broadband wireless access to these regions, many re-

searchers advocate worldwide interoperability for microwave

access (WiMAX) [1], which is an IEEE 802.16 standardized

wireless technology based on an orthogonal frequency-division

multiplexing (OFDM) physical-layer architecture.

Manuscript received April 17, 2007; revised August 12, 2007 andSeptember 24, 2007. This work was supported in part by the National Science

Foundation (NSF) under Award 0424546 and an NSF Experimental Programto Stimulate Competitive Research start-up grant in Puerto Rico and in part bythe National Science Council of Taiwan under Grant NSC96-2221-E-110-035and Grant NSC96-2221-E-110-050. The review of this paper was coordinatedby Dr. E. Hossain.

B. Rong and K. Lu are with the Department of Electrical and ComputerEngineering, University of Puerto Rico at Mayagüez, Mayagüez, PR 00681USA (e-mail: [email protected]; [email protected]).

Y. Qian is with the National Institute of Standards and Technology,Gaithersburg, MD 20899 USA (e-mail: [email protected]).

H.-H. Chen is with the Department of Engineering Science, National ChengKung University, Tainan 701, Taiwan, R.O.C. (e-mail: [email protected]).

M. Guizani is with the Department of Computer Science, Western MichiganUniversity, Kalamazoo, MI 49008-5201 USA (e-mail: [email protected]).

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2007.912595

To support a variety of applications, IEEE 802.16 has defined

four types of service [2]: 1) unsolicited grant service (UGS);

2) real-time polling service (rtPS); 3) non-real-time polling

service (nrtPS); and 4) best effort (BE) service. In a WiMAX

network with heterogeneous traffic loads, it is essential to find

a call admission control (CAC) solution that can effectively

allocate bandwidth resources to different applications. Moti-

vated by this, in this paper, we propose a WiMAX CAC frame-

work, which effectively meets all operational requirements of

WiMAX networks. In this CAC framework, we decomposethe 2-D uplink (UL) and downlink (DL) WiMAX CAC prob-

lem into two independent 1-D CAC problems. We further

formulate the 1-D CAC as an optimization problem under a

certain objective function, which should be chosen to maximize

either the revenue of service providers or the satisfaction of

subscribers.

With respect to 1-D CAC optimization problems, most pre-

vious studies were focused only on two approaches: 1) the

optimal revenue strategy (also known as the stochastic knap-

sack problem) [3]–[9] and 2) the minimum weighted sum

of blocking strategy [10]. In this paper, we will show that

these two strategies are, in fact, equivalent. Therefore, we

can mainly concentrate on the investigation of the optimalrevenue strategy and view the minimum weighted sum of

blocking strategy as the basis for fast calculation algorithms.

Clearly, the optimal revenue policy only considers the profit

of service providers. As an effort to conduct a multiobjec-

tive study, in this paper, we will also take into account the

requirements from WiMAX subscribers and develop a policy

with a satisfactory tradeoff between service providers and

subscribers.

The major contributions of this paper include the following:

1) the development of a framework of CAC for WiMAX

networks; 2) the investigation on various CAC optimization

strategies; and 3) the proposal of a series of constrained greedyrevenue algorithms for fast calculation. Through detailed per-

formance evaluation, the study carried out in this paper will

show that the proposed CAC solution can meet the expectations

of both service providers and subscribers.

The rest of the paper is outlined as follows: We first introduce

the CAC model for WiMAX networks in Section II. We will

then calculate the UL and DL capacity in Section III. In

Sections IV and V, we will introduce different 1-D CAC

optimization strategies and develop their corresponding ap-

proximation algorithms. In Section VI, the performance of

the proposed CAC optimization approach is demonstrated by

simulation results. Finally, Section VII concludes this paper.

0018-9545/$25.00 © 2008 IEEE

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2510 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 57, NO. 4, JULY 2008

Fig. 1. CAC deployment in a WiMAX PMP network.

II. CAC DEPLOYMENT IN WIMAX NETWORKS

A. WiMAX Networks

WiMAX technology promises to support both mesh and

point-to-multipoint (PMP) networks. A WiMAX mesh network

usually suits for constructing wide-area wireless backhaul net-

works such as citywide wireless coverage. On the other hand,

a WiMAX PMP network is used for providing the last-mile

access to broadband ISPs. In this paper, we will only discuss

the issues related to the WiMAX PMP network, which consists

of one base station and N subscribers.

As specified in the IEEE 802.16 standards [11], [12],

WiMAX employs OFDM in its physical-layer architecture.

In particular, IEEE 802.16 standards have defined a special

flavor of the OFDM system, namely, orthogonal frequency-

division multiple access (OFDMA), which employs a largerfast-Fourier-transform space (2048 and 4096 subcarriers) that

can be further divided into subchannels. The subchannels

are introduced to separate the data into logical streams on

DL transmission. Those logical streams may employ different

modulation/coding schemes and amplitude levels to address

subscribers with different channel characteristics. The subchan-

nels are also used for multiple-access purposes on UL. In prac-

tice, subscribers are assigned with subchannels through media

access control messages sent in the downstreams. Without the

loss of generality and for discussion brevity, in this paper,

we mainly concern ourselves with the scenario where each

WiMAX subscriber occupies exactly one subchannel.

To satisfy different operational environments, WiMAX

OFDMA supports five types of subcarrier allocation schemes to

formulate subchannels: 1) partial usage of subchannels (PUSC)

on UL and DL; 2) optional PUSC on UL; 3) full usage of

subchannels (FUSC) on DL; 4) optional FUSC on DL; and

5) adaptive modulation and coding (AMC) on UL and DL.

The first four subcarrier allocation schemes employ distributed

subcarrier permutation, whereas AMC employs adjacent sub-

carrier permutation. Since distributed subcarrier permutation

performs well in both fixed and mobile environments, it

becomes the dominant subcarrier permutation strategy for

WiMAX applications.

Once the subcarrier allocation is determined, the powerassigned to each subcarrier becomes another important issue

Fig. 2. Decomposition of UL CAC and DL CAC.

that affects the data transmission rate of a certain subscriber. For

UL, the transmission power of each subscriber depends on its

own transmitter. For DL, all subscribers share the total power onthe base station. To simplify the implementation, most WiMAX

base stations employ an equal power assignment scheme, which

grants every subcarrier the same DL power.

Frequency-division duplex (FDD) and time-division duplex

(TDD) are two of the most prevalent duplexing schemes used

in wireless systems. WiMAX can employ either of them to

separate UL and DL communication signals. FDD is usually

deployed in symmetric communication scenarios, where the

applications require equal bandwidth on UL and DL. On the

contrary, TDD is usually deployed in asymmetric communica-

tion scenarios.

In this paper, we assume that WiMAX is to provide the“last-mile” Internet access, which is a typical asymmetric

communication scenario. Accordingly, we will study WiMAX

OFDMA with TDD duplexing. For the kth WiMAX subscriber,

we assume that its UL and DL data transmission rates are trU kand trDk , respectively. If α% time slots on the subchannel are

allocated to DL traffic, then the DL bandwidth capacity is given

by BDk = α%trDk (thus, α% becomes the TDD DL bandwidth

proportional factor). Similarly, the UL bandwidth capacity can

be calculated by BU k = (1 − α%)trU k .

B. CAC Deployment

To handle a multiservice WiMAX network, it is very impor-tant to implement the CAC mechanism [13], [14]. First, CAC


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RONG et al.: CALL ADMISSION CONTROL OPTIMIZATION IN WiMAX NETWORKS 2511

TABLE IPARAMETER DECOMPOSING MODEL (reravg

i= (rerU

ibU i+ rerD

ibDi)/(bU

i+ bD

i))

is a critical step for the provision of quality-of-service (QoS)-

guaranteed services, because it can prevent the system from

being overloaded. Second, CAC can help a WiMAX network

provide different classes of traffic loads with different priorities

by manipulating their blocking probabilities.

As illustrated in Fig. 1, we propose to add a CAC manager

to the WiMAX base station. This CAC manager provides CAC

functions to all N subscribers under the base station. Moreover,

the access bandwidth capacity and the traffic load profile of

different subscribers are distinct and independent. Accordingly,

the CAC manager is composed of N CAC modules, in which

the kth CAC module only takes care of the kth subscriber’s

local network. In the rest of this paper, our study will be

concentrated on the design of an individual CAC module.When an application in the kth subscriber’s local network

initiates a connection to access the Internet, it sends a connec-

tion request to the kth CAC module with upstream bandwidth

requirement bU and downstream bandwidth requirement bD.

Then, the CAC manager simultaneously performs an admission

control check on the kth subscriber’s UL and DL. In this re-

spect, the CAC in a WiMAX network can naturally be modeled

by a 2-D CAC problem.

C. Decomposition of WiMAX CAC

A 2-D model for the WiMAX CAC can be formulated as fol-lows. For the local network of a given WiMAX subscriber, sup-

pose that M classes of bidirectional traffic loads share BU units

of UL bandwidth resource and BD units of DL bandwidth

resource, respectively. With regard to class i traffic, we assume

the following: 1) The requests arrive from a random process

with an average rate λi; 2) the average connection holding

time is 1/µi s; 3) the UL and DL bandwidth requirements

of a connection are fixed to bU i and bDi , respectively; and

4) the UL and DL revenue rates of a connection are rerU iand rerDi , respectively. Then, the WiMAX CAC is responsible

for accepting or rejecting a connection request according to a

certain policy.For investigation simplicity, we decouple the 2-D WiMAX

CAC problem into two independent 1-D CAC problems in this

paper. As shown in Fig. 2, the CAC module employs a UL CAC

policy and a DL CAC policy to separately make an admission

test on UL and DL, and only the connection requests that passes

both admission tests can be eventually accepted.

Either UL CAC or DL CAC can be modeled as a 1-D

CAC problem as follows. For the local network of a given

WiMAX subscriber, suppose that M classes of traffic loads

share B units of access bandwidth resource. With respect

to class i traffic, we assume the following: 1) The requests

arrive from a random process with an average rate λi; 2) the

average connection holding time is 1/µi s; 3) the bandwidthrequirement of a connection is fixed to bi; and 4) the revenue

Fig. 3. Framework for UL CAC or DL CAC.

rate of a connection is reri. We can then define the bandwidthrequirement vector as b = (b1, b2, . . . , bM ) and the system state

vector as n = (n1, n2, . . . , nM ), where ni is the number of

class-i connections in the system. Based on these parameters,

we can further define ΩCS as the set of all possible system

states, which can be expressed as ΩCS = n|n · b ≤ B. Under

this definition, the subscript CS stands for “complete sharing,”

which means that an incoming connection will be accepted if

sufficient bandwidth resources are available in the system. We

can now define a CAC policy, which is denoted by Ω, as an

arbitrary subset of ΩCS. Given Ω, a connection request will be

accepted if and only if the system state vector remains in Ω after

the connection is accepted.In this paper, we decompose the WiMAX CAC into UL

CAC and DL CAC with the parameter setup, as shown in

Table I. Although UL CAC and DL CAC are running as two

independent 1-D processes, their parameters are still related.

On one hand, UL CAC and DL CAC have their own special

characteristics such as distinct bandwidth capacity and band-

width requirements. On the other hand, they do share some

common features such as the number of traffic classes M ,arrival rate λi, service time 1/µi, and revenue rate ravgi . It is

noted that in Table I, we confer the same revenue rate ravgi to

UL CAC and DL CAC, despite the fact that originally, the UL

revenue rate is rU i

and the DL revenue rate is rDi

. The reason

is that the revenue could be achieved from a connection if and

only if it can pass both UL and DL CAC tests. Therefore, from

the perspective of 2-D WiMAX CAC, UL CAC and DL CAC

should have the same revenue rate. In this paper, we name this

mechanism as UL/DL revenue rate binding.

D. Framework for WiMAX CAC

The aforementioned CAC manager is composed of N CAC

modules, in which the kth CAC module contains two inde-

pendent parts, i.e., UL CAC and DL CAC. To fit the special

features of a WiMAX environment, we present a WiMAX CAC

framework in Fig. 3, which can be applied to either UL CAC orDL CAC.


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As illustrated in Fig. 3, the proposed framework consists of

three major modules: 1) CAC policy; 2) traffic load estimation;

and 3) bandwidth capacity estimation. Clearly, the CAC policy

is the most important module of all. To construct a successful

WiMAX network, the CAC policy has to consider the expec-

tations of both service providers and subscribers. Here, we

suppose that the UL and DL CAC policies independently work with their parameter setups, as shown in Table I, and utilize the

same optimization strategy.

In a WiMAX network, the traffic load and the subcarrier

channel condition are changing from time to time. Conse-

quently, UL and DL CAC policies have to be adaptive to these

dynamics. The traffic load estimation module should record

every connection request, regardless of whether it is eventually

accepted or not. Then, the UL and DL traffic load profiles

are periodically captured based on this record and sent to the

CAC policy module. As for the dynamic of channel condition,

the bandwidth estimation module retrieves the channel state

information (CSI) from the physical layer at regular intervals

of time. Then, the UL and DL bandwidth capacities of a given

subscriber are calculated from the CSI and sent to the CAC

policy module. To operate adaptively, the CAC policy module

should adjust its parameters based on the updated information

from the other two modules.

To mitigate the channel errors in the physical layer, it is ap-

propriate to apply link-layer fragmentation and retransmission

to WiMAX [15]. In this respect, the CAC policy module also

needs to interact with the WiMAX link layer. In particular, after

a connection request is accepted, the CAC policy module has to

transfer the bit error rate (BER) requirement of this connection

to the fragmentation and retransmission module in the link

layer.For the proposed framework in Fig. 3, we need to consider

two major issues: 1) how to calculate UL and DL bandwidth ca-

pacity and 2) what the design of a 1-D CAC policy is. Although

it is also important to capture the traffic load profile, we do not

particularly discuss this issue here as it has been extensively ad-

dressed in many previous works on wired networks [16], [17].

In Section III, we will investigate the UL and DL bandwidth ca-

pacity of a given subscriber. In Sections IV and V, we will study

the design of a 1-D CAC policy as an optimization problem.

III. BANDWIDTH CAPACITY

In this section, we calculate the UL and DL bandwidthcapacity of the kth subscriber based on CSI. We begin with the

approach for DL capacity, and then, this approach will be easily

extended to UL.

Fig. 4 illustrates the N -subscriber WiMAX DL channel

model, in which H k(f ) and N k(f ) denote the channel fre-

quency response function and noise power density function of

the kth subscriber, respectively. The quality of each subscriber’s

subchannel is indicated by the signal-to-noise ratio (SNR)

function SNRk(f ), which is defined as

SNRk(f ) = |H k(f )|2 /N k(f ) (1)

where SNRk(f )(1 ≤ k ≤ N ) is the CSI that the CAC man-ager needs. Since the CAC manager is placed in the base

Fig. 4. WiMAX DL channel model.

station, it can collect SNRk(f ) easily from the physical

layer.

For analytical simplicity, in this paper, we are only interestedin the investigation of the most common scenario, where each

WiMAX subscriber occupies exactly one subchannel. Once the

subcarrier allocation and power assignment of the subchannels

are known, the DL bandwidth capacity of the kth WiMAX

subscriber can be calculated with the following notations:

N number of subscribers;

J number of subcarriers;

S J set of all subcarriers, defined as 1, 2, . . . , j , . . . , J ;

∆f physical bandwidth of each subcarrier;

Dk subcarrier set assigned to subscriber k;

SNRk[ j] the SNR function of subscriber k on the frequencyof subcarrier j;

p[ j] transmit power on subcarrier j;

ck[ j] achievable transmission efficiency (data rate per

hertz) of subscriber k on the frequency of

subcarrier j, assuming that subcarrier j is allo-

cated to subscriber k( j ∈ Dk).

To assign subcarrier set Dk to subscriber k, we assume that

a nonoverlapped partition is used such thatDk

Dl = φ, k = lN

k=1 Dk ⊆ S J (2)

where φ is a null set.

According to [18]–[20], ck[ j] can be expressed as

ck[ j] = f [log2 (1 + βp[ j]SNRk[ j])] (3)

where β = 1.5/ − ln(5BER) is a constant, and f (.) depends

on the adaptation scheme. For example, if the continuous-rate

adaptation is concerned, we have f (x) = x; if a variable M -ary

quadrature amplitude modulation (M -QAM) with modulation

levels 0, 2, 4, 6,. . . is employed, we have f (x) = 2(1/2)xinstead.

Then, the DL data transmission rate of subscriber k is

given by

trDk =j∈Dk

ck[ j]∆f. (4)


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Consequently, the DL bandwidth capacity of the kth subscriber

can be calculated by BDk = α% trDk . Equations (1)–(4) can

also be used to compute the UL data transmission rate of

subscriber k, denoted as trU k , if the variables in these equa-

tions are replaced by UL parameters. Then, the UL bandwidth

capacity of the kth subscriber can be obtained by BU k = (1 −

α%) trU k .

IV. ONE -D IMENSIONAL CAC OPTIMIZATION

In this section, we first review the existing CAC optimization

strategies in the literature. We then propose a utility- and

fairness-constrained optimal revenue strategy as an effort to

benefit both service providers and subscribers.

A. Existing 1-D CAC Optimization Strategies

The previous study on 1-D CAC optimization was mainly

focused on two approaches, i.e., the optimal revenue strategy

and the minimum weighted sum of blocking strategy.

1) Optimal Revenue Strategy: In general, service providers

expect a CAC policy that can produce high revenues. To achieve

this goal, [3]–[9] studied the CAC optimization problems with

the optimal revenue strategy, which is also known as the sto-

chastic knapsack problem. The optimal revenue strategy can be

introduced in the context of WiMAX as follows.

Let rerUGS, rerrtPS, rernrtPS, and rerBE be the revenue

rates of UGS, rtPS, nrtPS, and BE service, respectively. Then,

we use reri to denote the revenue rate of a class-i connection,

which can be one of rerUGS, rerrtPS, rernrtPS, and rerBE, de-

pending on which type of service is required. Correspondingly,

we can calculate the “long-term average revenue” of a CACpolicy by

R(Ω) =n∈Ω

(n · r)P Ω(n) (5)

where P Ω(n) is the steady-state probability that the system is

in state n, r = (r1, r2, . . . , rM ) is the reward vector, and ri =reribi is the average revenue generated by accepting a class-iconnection. For a given WiMAX system, (5) can be separately

applied to UL and DL. In the most common case, UL and

DL have different parameter setups but have the same revenue

rate reri.In this paper, we use Ω∗ to denote the optimal revenue policy.

Intuitively, Ω∗ prefers the traffic load with a high-revenue

output.

2) Minimum Weighted Sum of Blocking Strategy: A CAC

optimization strategy was proposed in [10] to minimize the

“weighted sum of blocking,” which is defined as

W B = weighted sum of blocking =

M i=1

wiP bi (6)

where P bi stands for the blocking probability of class-i traffic,

and wi stands for the weight of class-i traffic. By adjusting the

value of wi, the minimum weighted sum of blocking strategycan give different traffic classes different priorities.

B. Equivalence of Two CAC Optimization Strategies

It is noted that if a policy Ω satisfies the coordinate convex

condition and the arrival and service processes are both memo-

ryless, then P Ω(n) can be calculated by (as shown in [21])

P Ω(n) =1

G(Ω)

M i=1

ρniini! , n ∈ Ω (7)

where G(Ω) =

n∈Ω

M i=1 ρnii /ni!, and ρi = λi/µi.

Moreover, the blocking probability of class-i traffic is

P bi(Ω) =G

Ωbi

G(Ω)

(8)

where Ωbi = n|n ∈ Ω & n + ei /∈ Ω, and ei is an

M -dimension vector of all zeros, except for its ith element.

Based on the above equations, we can have the following

lemma.

1) Lemma 1: For any CAC policy that satisfies the coordi-nate convex condition, the long-term average revenue defined

in (5) can always be calculated by

R(Ω) = A − W B (9)

where A =M

i=1 riρi is a constant, W B =M

i=1 wiP bi, and

wi = riρi.In (9), R(Ω) is the revenue that policy Ω can achieve or

the revenue of accepted traffic, A =M

i=1 riρi is the revenue

of arriving traffic, and W B =M

i=1 wiP bi =M

i=1 riρiP biis the revenue of rejected traffic. Obviously, the revenue of

accepted traffic can be calculated by subtracting the revenue of rejected traffic from the revenue of arriving traffic. Therefore,

Lemma 1 holds for any policy that satisfies the coordinate

convex condition.

Lemma 1 also implies that the revenue can be maximized

when the weighted sum of blocking is minimized. Therefore,

the minimum weighted sum of blocking strategy is equivalent

to the optimal revenue strategy if the condition wi = riρiholds. In this paper, we mainly consider the optimal revenue

strategy, since it has more explicit meaning in practice. As for

the minimum weighted sum of blocking strategy, we consider

it only as an alternative way to express the optimal revenue

strategy, which will be employed to develop fast calculation

algorithms in Section V.

C. Utility- and Fairness-Constrained Optimal

Revenue Strategy

The optimal revenue strategy highlights only the demand of

service providers. Nevertheless, in a practical WiMAX system,

we also need to consider the requirements of subscribers.

1) Utility Requirement: Generally speaking, subscribers

prefer a CAC policy that can achieve maximal utility or, equiva-

lently, the maximum access bandwidth [22], [23]. Let B denote

the physical access bandwidth and SB denote the statistical

bandwidth that the subscriber can achieve after the CAC policytakes effect. Then, the utility function is defined as SB/B.


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Since B is a constant, the maximization of the utility function

leads to the maximization of the statistical bandwidth SB . In

this paper, we use Ω+ to denote the optimal utility CAC policy.

Different from Ω∗, which denotes the optimal revenue policy,

Ω+ allocates more bandwidth resources to the traffic load that

can yield high utility.

Following (5), we derive the “statistical bandwidth” thatpolicy Ω can achieve as

SB(Ω) =n∈Ω

(n · b)P Ω(n) (10)

where we have replaced the reward vector r given in (5) with

the bandwidth requirement vector b.

Based on (10), the “utility” of policy Ω is given by

U (Ω) =1

BSB(Ω) =

1

Bn∈Ω

(n · b)P Ω(n). (11)

It is noted that if all traffic classes have the same revenue rate,

i.e., rer1 = rer2 = · · · = rerM , Ω∗ turns into Ω+.

2) Fairness Requirement: When the optimal revenue or op-

timal utility strategy is employed, there may exist a great bias

among the blocking probabilities of different traffic classes.

This bias can result in unfairness such that some traffic classes

is severely blocked, whereas others can easily access the net-

work. Therefore, in addition to the utility requirement, the

fairness among different traffic classes becomes another major

issue that subscribers might be concerned about [24], [25].

Fairness requirement guarantees that the blocking probabilities

of all traffic classes will be kept relatively uniform such that no

particular traffic class will be unfairly treated.

In this paper, we mainly address the fairness at the CAC

level, which means that the applications of every service class

have a chance to achieve access bandwidth. Therefore, different

fairness policies can be applied in the underlying service model,

such as a service policy of packet scheduling. For instance,

in the packet scheduling level, unfairness may be necessary to

guarantee the QoS provisioning.

To achieve absolute fairness (AF), each traffic class is given

the same blocking probability, whereas the utility of the CAC

policy is maximized. This paper mainly considers the scenarioof a stressful network where the arriving traffic load is higher

than the bandwidth capacity. Then, the blocking probability of

each traffic class is given by

P bAF = 1 −U (ΩAF)BM i=1

biλiµi

≥ P bAFlb (12)

where P bAFlb = 1 − (B/M

i=1 biλi/µi) is the lower bound of

P bAF. As defined, the AF policy has the highest utility among

all policies that can offer equal blocking probabilities. There-fore, in practice, P bAF can have a value very close to P bAFlb .

3) Constrained Optimal Revenue Strategy: The objective

of CAC optimization can be chosen to satisfy either service

providers or subscribers. Usually, a contradiction exists be-

tween the expectations of service providers and subscribers.

Therefore, we have to develop a constrained CAC optimization

strategy that can give a good tradeoff. In other words, we need

a CAC policy that can balance the optimal revenue requirementfrom the service providers and the optimal utility and fairness

requirements from the subscribers. This leads to a concept of a

utility- and fairness-constrained optimal revenue policy, which

is proposed in this paper.

The fairness constraint requires that the highest blocking

probability among all traffic classes (or, in short, the highest

blocking probability) is lower than the threshold P Bth. In this

paper, we use ΩF ∗ to represent the fairness-constrained opti-

mal revenue policy. Clearly, the blocking probability threshold

P Bth must be higher than P bAFlb ; otherwise, no CAC policy

can be found to meet the fairness constraint. Therefore, P Bth

is subject to the relationship P bAFlb < P Bth < 1. Correspond-

ingly, we define the normalized blocking probability thresh-

old as pbth, which ranges from zero to one (0 < pbth < 1).

The relationship between pbth and P Bth can be formulated

by pbth = (P Bth − P bAFlb )/(1 − P bAFlb ) or P Bth = (1 −P bAFlb ) pbth + P bAFlb .

The utility constraint requires that the utility of a CAC policy

must be higher than the threshold U th. In this paper, we use

ΩUF ∗ to represent the utility and fairness constrained optimal

revenue policy. If the fairness constraint is already known, it

is clear that the utility threshold U th must satisfy 0 < U th <U (ΩF +), where U (ΩF +) denotes the utility of the fairness-

constrained optimal utility strategy. Otherwise, no ΩUF ∗ can

be found to satisfy both utility and fairness constraints. Corre-spondingly, we define the normalized utility threshold as uth,

which satisfies U th = uththU (ΩF +) (0 < uth < 1). It is also

noted that when P Bth = 1 or pbth = 1, ΩUF ∗ degenerates into

the utility-constrained optimal revenue policy ΩU ∗.

Practically, it is convenient to use uth and pbth, instead of

U th and P Bth, to describe the utility and fairness constraints,

since the valid ranges of U th and P Bth depend on the band-

width capacity and traffic load, whereas the valid ranges of uth

and pbth are always from zero to one.

V. ONE -D IMENSIONAL CAC OPTIMIZATION ALGORITHMS

In this paper, we mainly study the optimal revenue policy Ω∗

and constrained optimal revenue policies ΩU ∗, ΩF ∗, and ΩUF ∗,

which are likely to be used by service providers to construct a

commercial WiMAX network. In addition, we are interested in

Ω+ as well, since it can serve as a benchmark for utility perfor-

mance. To specify the above policies, brute-force searching is a

straightforward method. For example, to achieve Ω∗, one needs

to calculate the long-term average revenue of each possible pol-

icy using (5). To achieve ΩUF ∗, one needs to calculate the long-

term average revenue, the blocking probabilities, and the utility

of each possible policy using (5), (8), and (11). Nevertheless,

the previous studies pointed out that the brute-force searching

has an unbearable complexity [3], [5]. Even if the optimalsolution could be found, it is usually very complicated and,


8/4/2019 21 Get PDF



therefore, extremely difficult to implement due to excessively

high storage and table lookup time requirements. As a result,

many researchers endeavored to develop some simply struc-

tured approximate solutions. For example, to find the optimal

revenue policy of a “complete partition” (CP) structure, Ross

and Tsang [3] proposed a finite-stage dynamic programming

algorithm, which has a complexity of O(B2

M ). Here, thealgorithm complexity is measured by the size of the searching

space that a CAC optimization algorithm has to explore [3]. In

the rest of this section, we will develop a series of CP-structured

heuristic algorithms, which have a complexity of O(BM ).

A. CP-Structured Admission Control Policy

A CP policy allocates each traffic class a certain amount of

nonoverlapped bandwidth resource. In this manner, the block-

ing rate of one traffic class will not influence that of others.

Because of this partitioning characteristics, a CP policy can

be decomposed into M independent subpolicies, and the ith

subpolicy takes care of class-i traffic. In other words, a CPpolicy separates the overall bandwidth resource B into M nonoverlapped parts, denoted by B1

CP, B2CP, . . . , BM

CP, where

BiCP belongs to class-i traffic.

For a given CP policy, the ith subpolicy can be modeled by an

M/M/N/N queuing system, in which the number of servers is

si = BiCP/bi. Therefore, according to (5) and (7), the long-term

average revenue obtained from class-i traffic is given by

Ri(CP) =

sij=0

ri j

ρj

i

j!sik=0

ρki

k!

(13)

where the overall long-term average revenue of the CP policy

is defined as R(CP) =M

i=1 Ri(CP). Moreover, the statistical

bandwidth of class-i traffic is given by

SBi(CP) =

sij=0

bi j

ρj

i

j!sik=0

ρki

k!

. (14)

Correspondingly, the overall statistical bandwidth and

the utility of the CP policy can be calculated by

SB(CP)=M

i=1SBi(CP) and U (CP)=(1/B)M

i=1SBi(CP),

respectively.

According to the Erlang B formula, the blocking probabilityof class-i traffic is [26]

P bi(CP) = B(si, ρi) =

ρsii

si!sik=0

ρki

k!

. (15)

It is noted that the Erlang B formula can be calculated by the

following recursion [26]:

B(si + 1, ρi) =ρiB(si, ρi)

si + 1 + ρiB(si, ρi)(16)

where we have B(0, ρi) = 1.

The above discussions have shown that the optimal CPproblem is to find the best bandwidth partitioning scheme.

In this paper, we define the CP policy of “optimal revenue,”

“optimal utility,” “utility-constrained optimal revenue,”

“fairness-constrained optimal revenue,” and “utility- and

fairness-constrained optimal revenue” as CP∗, CP+,

CPU ∗, CPF ∗, and CPUF ∗, respectively, which can be viewed

as the approximate solution for Ω∗, Ω+, ΩU ∗, ΩF ∗, and

ΩUF ∗

. In the following sections, we will address the issues ondeveloping heuristic algorithms for CPF ∗ and CPUF ∗. With

some appropriate adjustment, these heuristic algorithms can be

used to approximate CP∗, CP+, and CPU ∗.

B. Fairness-Constrained Greedy Revenue Algorithm to

Approximate CPF ∗

To achieve a heuristic algorithm for CPF ∗, we have to deal

with the issues on the optimal revenue strategy and the fairness

constraint. In the following text, we first develop a greedy

revenue approximation method for the optimal revenue strategy,

and then, we will add the fairness constraint to it.

Supposing that class-i traffic is assigned j ( j = BiCP/bi)

servers, from Lemma 1, we can derive the corresponding rev-

enue as

Ri(CP)|BiCP

=jbi = riρi − riρiB( j,ρi). (17)

If one server is withdrawn or the server number is reduced to

( j − 1), the following equation holds:

Ri(CP)|BiCP

=(j−1)bi = riρi − riρiB( j − 1, ρi). (18)

Accordingly, we define the revenue brought by the jth server as

RiS( j,ρi) = Ri(CP)

BiCP

=jbi − Ri(CP)BiCP

=(j−1)bi

= riρi [B( j − 1, ρi) − B( j,ρi)]

= riF iS( j,ρi) (19)

where F iS( j,ρi) = ρi[B( j − 1, ρi) − B( j,ρi)] is the load car-

ried by the jth server in the M/M/N/N queuing system,

andsi

j=1 RiS( j,ρi) = Ri(CP). Then, the revenue rate of the

jth server is

r

i

S( j,ρi) =

RiS( j,ρi)

bi =

riρi [B( j − 1, ρi) − B( j,ρi)]

bi .(20)

Initially, (19) was introduced in the theory of marginal eco-

nomic analysis [27] by intuition. In this paper, we use Lemma 1

to give it a detailed explanation. Since F iS( j,ρi) is decreas-

ing with j [28], RiS( j,ρi) and riS( j,ρi) are decreasing with

j as well.

Based on the above analysis, we propose a greedy revenue

approximation method to obtain the optimal revenue. The

greedy revenue approximation method always allocates the

bandwidth resource to the traffic class of the highest revenue

rate in each iteration. Taking into account the fairness constraint

as well, a fairness-constrained greedy revenue algorithm toapproximate CPF ∗ is presented in Algorithm 1.


8/4/2019 21 Get PDF



Algorithm 1: Fairness-Constrained Greedy Revenue Algo-

rithm for CPF ∗

1) Input pbth;

2) Capture the traffic load profile in the kth subscriber’s

local network;

3) Collect the CSI from the physical layer, calculate BU k

for UL CAC or BDk for DL CAC, and let B = B

U k or

B = BDk ;

4) /∗ PHASE 1: Allocate bandwidth resources to satisfy

the fairness constraint ∗/

5) Bfree= B; P bAFlb = 1−(B/M

i=1 biλi/µi); P Bth= pbthP bAFlb ;

6) for i = 1 to M do

7) BiCP = 0; si = 0; B(si, ρi) = 1; P bi = B(si, ρi);

8) end for


10) while P bi > P Bth do

11) Bfree= Bfree−bi; BiCP = Bi

CP + bi; B(si + 1,ρi) = (ρiB(si, ρi)/si + 1 + ρiB(si, ρi));

12) P bi = B(si + 1, ρi); SBi = SBi + biρi[B(si,ρi) − B(si + 1, ρi)]; si = si + 1;

13) end while

14) BiCP(F ) = Bi

CP;

15) end for

16) /∗ PHASE 2: Allocate the remaining free bandwidth

resources according to optimal revenue strategy ∗/17) I = M + 1;

18) for all i(0 ≤ i ≤ M ): B(si + 1, ρi) = (ρiB(si, ρi)/si+1 +ρiB(si, ρi)); riS = (riρi[B(si, ρi)−B(si+1,ρi)]/bi);

19) while I > 0 do

20) I = arg max1≤i≤M riS;21) if bI ≤ Bfree then

22) /∗ allocate bI bandwidth resource to class I

traffic ∗/23) Bfree= Bfree−bI ; BI

CP= BI CP+bI ; sI = sI +1;

24) B(sI +1, ρI )=(ρI B(sI , ρI )/sI +1+ρI B(sI , ρI ));

rI S = (rI ρI [B(sI , ρI )−B(sI +1, ρI )]/bI );

25) else

26) rI S = 0;

27) if M

i=1 riS = 0 then

28) I = −1; // bandwidth allocation is finished.

29) end if

30) end if 31) end while

32) return BiCP(F ), 1 ≤ i ≤ M as the bandwidth allo-

cation to satisfy fairness constraint;

33) return BiCP, 1 ≤ i ≤ M as the final bandwidth al-

location decision for CPF ∗;

As for the dynamic of traffic load, the DL traffic load

estimation module records every connection request in its

database, regardless of whether it is accepted or not. Then,

the traffic load profile is periodically captured based on this

record and sent to the CAC policy module. As for the dynamic

of channel condition, the DL bandwidth estimation module

retrieves the CSI from the physical layer at regular intervalsof time. Then, the DL bandwidth capacity of a given sub-

scriber is calculated from the CSI and sent to the CAC policy

module.

Algorithm 1 proceeds in two phases. In the first phase, it

allocates class-i traffic BiCP(F ) bandwidth resource so that the

fairness constraint can be guaranteed. In the second phase, it

iteratively employs the greedy method to implement the optimal

revenue strategy. For instance, steps 18 and 24 of the algorithminitialize and update the revenue rates of different traffic classes,

respectively, and then, step 20 picks up one of the maximum

revenue rates.

Algorithm 1 can exactly locate CPF ∗ before step 26 is

reached. The iterations may incur approximation errors if and

only if the bandwidth capacity boundary condition Bfree <max1≤i≤M bi becomes true. If so, the greedy method cannot

be thoroughly implemented because the capacity limit can

interfere with the process of locating the traffic class of the

maximal revenue rate. If compared to CPF ∗, the revenue error

generated by Algorithm 1 can be strictly bounded by the

following inequality:

Rerr < R(CPF ∗, B) − R

CPF ∗, B − max

1≤i≤M bi

(21)

where Rerr stands for the revenue approximation error, and

R(Ω, C ) stands for the revenue obtained from policy Ω with

bandwidth capacity C .Next, we investigate the complexity of the fairness-

constrained greedy revenue algorithm. Clearly, the first phase of

this algorithm has a complexity of O(B). Moreover, there are

O(B) iterations in the second phase of this algorithm. During

each iteration, this algorithm searches through M possible

system states to locate the traffic class that yields the maximalrevenue rate. Therefore, the size of the whole searching space

or the complexity of the second phase is O(BM ). Combining

phases 1 and 2, we can conclude that this algorithm has a

complexity of O(BM ).

It is noted that if we let pbth = 1, Algorithm 1 degenerates

into the pure greedy revenue algorithm for CP∗.Ifwelet rer1 =rer2 = · · · = rerM = 1, Algorithm 1 degenerates into the

fairness-constrained greedy utility algorithm for CPF +. If we

let pbth = 1 and rer1 = rer2 = · · · = rerM = 1, Algorithm 1

degenerates into the pure greedy utility algorithm for CP+.

C. Utility- and Fairness-Constrained Greedy

Revenue Algorithm

To develop a CP-structured heuristic algorithm for ΩUF ∗, we

have to address three issues: 1) optimal revenue; 2) fairness

constraint; and 3) utility constraint. Since the optimal revenue

and the utility constraint have been discussed in the previous

sections, we focus only on the utility constraint in this section.

Similar to the revenue, for class-i traffic, we define the

statistical bandwidth brought by the jth server as

SB iS( j,ρi) = biF iS( j,ρi) = biρi [B( j − 1, ρi) − B( j,ρi)]

(22)where the relation SBi(CP) =

sij=1 SB i

S( j,ρi) holds.


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Then, the utility of the jth server is given by

U iS( j,ρi) =SB i

S( j,ρi)

bi

= F iS( j,ρi)

= ρi [B( j − 1, ρi) − B( j,ρi)] . (23)

To deal with the utility constraint, we can use (23) to cal-

culate the utility in each iteration step. Combining the utility

constraint with the CP-structured heuristic algorithm for ΩF ∗,

we obtain a utility- and fairness-constrained greedy revenue

algorithm to approximate CPUF ∗, as presented in Algorithm 2.

Algorithm 2: Utility- and Fairness-Constrained Greedy Rev-

enue Algorithm for CPUF ∗

1) Input uth, pbth;

2) Capture the traffic load profile in the kth subscriber’s

local network;

3) Collect the CSI from the physical layer, calculate BU k

for UL CAC or BDk for DL CAC, and let B = BU

k or

B = BDk ;

4) /∗ PHASE 1: Allocate bandwidth resource for fairness

constraint and calculate U th ∗ /5) Achieve Bi

CP(F ), 1 ≤ i ≤ M and locate CPF + by

running Algorithm 1 with parameter setup rer1 =rer2 = · · · = rerM = 1;

6) Bfree = B −M

i=1 BiCP(F ); U th = uthU (CPF +);


8) BiCP = Bi

CP(F ); si = BiCP(F )/bi; B(si, ρi) =

(ρsii /si!/sik=0 ρki /k!); B(si + 1, ρi) = (ρiB(si,

ρi)/si + 1 + ρiB(si, ρi)); riS = (riρi[B(si, ρi) −

B(si + 1, ρi)]/bi); U iS = ρi[B(si, ρi) − B(si +

1, ρi)]; SBi =si

j=0 bi j(ρji/j!/si

k=0 ρki /k!);

9) end for

10) /∗ PHASE 2: Allocate the remaining free bandwidth

resources according to utility constrained optimal rev-

enue strategy. ∗/11) T = M + 1;

12) while T > 0 do

13) SetU = i|i satisfies (U iSbi +M

i=1 SBi/(B −Bfree + bi)) > U th; /∗ the set of traffic classes

qualified for utility constraint. ∗/

14) T = arg maxi∈SetUr

i

S;15) if bi|i=T ≤ Bfree then

16) Bfree = Bfree − bi|i=T ; BiCP|i=T = Bi

CP|i=T +bi|i=T ;

17) SBi|i=T = SBi|i=T + U iSbi|i=T ; si|i=T =si|i=T + 1;

18) B(si+ 1, ρi)|i=T = (ρiB(si, ρi)/si+1 +ρiB(si,ρi))|i=T ;

19) riS |i=T = (riρi[B(si, ρi)−B(si+1, ρi)]/bi)|i=T ;20) U iS |i=T = ρi[B(si, ρi) − B(si + 1, ρi)]|i=T ;21) else

22) /∗ Capacity limit begins to take effect. ∗/23) riS |i=T = 0; U iS |i=T = 0;

24) U th = 0; /∗ change to use the pure greedy rev-enue algorithm. ∗/

25) if M

i=1 riS = 0 then

26) T = −1; /∗ the algorithm is completed. ∗/27) end if

28) end if

29) end while

30) Return BiCP, 1 ≤ i ≤ M as the final bandwidth al-

location decision;

There are two phases in Algorithm 2. In the first phase,

we employ Algorithm 1 to allocate each traffic class a certain

amount of bandwidth resource such that the fairness constraint

can be guaranteed. In the meantime, Algorithm 1 can also locate

CPF +, from which U th is calculated.

Then, in the second phase, we employ the utility-constrained

optimal revenue strategy to allocate the remaining bandwidth.

To meet the utility constraint, in each iteration of phase 2, only

the traffic classes that can make the utility higher than U th

are chosen as qualified candidates for bandwidth allocation (as

shown in step 13). Moreover, this algorithm can achieve high

revenues as well, since it always selects the candidate with the

highest revenue rate to assign bandwidth resource (as shown in

step 14). It is noted that if we let pbth = 1, Algorithm 2 de-

generates into the utility-constrained greedy revenue algorithm

for CPU ∗.

Next, we will address the issues on complexity of the utility-

and fairness-constrained greedy revenue algorithm. Clearly, in

the first phase, Algorithm 1 is employed, and its complexity is

O(BM ). In the second phase, there are O(B) iterations. During

each iteration, this algorithm searches through O(M ) possible

system states in SetU to locate the traffic class of maximal

revenue rate. Therefore, the size of the whole searching space

or the complexity of the second phase is O(BM ). Combiningphases 1 and 2, we can conclude that this algorithm has a

complexity of O(BM ).

VI. SIMULATION RESULTS

In this section, we conduct a simulation study to evaluate

the performance of our proposed WiMAX CAC optimization

scheme. The simulations are programmed on the Matlab plat-

form, using the analytical results developed in the previous

sections. In particular, we first compare the capability of dif-

ferent 1-D CAC policies, then study the 2-D WiMAX CAC in

a subscriber’s local network, and finally, we show the overallbenefit of our proposed WiMAX CAC scheme in a WiMAX

PMP network.

For the 1-D CAC optimization, we present the numerical

results as shown in Figs. 5–7 to demonstrate the performance

of different CAC policies with three metrics (revenue, utility,

and fairness) while varying the arrival rate of class-3 traffic.

Here, Ω∗, Ω+, ΩU ∗, ΩF ∗, and ΩUF ∗ are obtained by brute-

force searching. In this simulation scenario, the total bandwidth

capacity B is set to be 75 Mb/s, the revenue rate is priced

as rerUGS = 5, rerrtPS = 2, rernrtPS = 1, and rerBE = 0.5,

and the traffic load is configured as those shown in Table II.

Moreover, for the utility constraint, we set uth = 90%, and for

the fairness constraint, we set pbth = 65%. In Figs. 5 and 6,the revenue and utility are normalized by R(Ω∗) and U (Ω+),


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Fig. 5. Revenue of different CAC optimization policies while varying thearrival rate of class-3 traffic.

Fig. 6. Utility of different CAC optimization policies while varying the arrivalrate of class-3 traffic.

respectively. In Fig. 7, the highest blocking probability remains

unchanged.

As shown in Figs. 5–7, Ω∗/Ω+ gives a good performance

only in terms of revenue/utility. On the other hand, ΩU ∗/ΩF ∗

performs well in terms of both revenue and utility/fairness.

Finally, Ω

UF ∗

satisfactorily performs in terms of all threemetrics, including revenue, utility, and fairness.

To reduce the algorithm complexity, we have developed

a utility- and fairness-constrained greedy revenue algorithm

for ΩUF ∗. This approximation algorithm can also be utilized

to approximate Ω∗, Ω+, ΩU ∗, and ΩF ∗ if we appropriately

degenerate the utility or fairness constraint. Numerical results

are shown in Table III to illustrate the average error of the

approximation algorithm, whereas the traffic load is configured

the same as that listed in Table II. For convenience, the revenue

and utility approximation errors are normalized by R(Ω∗) and

U (Ω+), respectively. We can conclude from Table III that our

approximation algorithm can provide an adequate approxima-

tion to the exact solution. Here, the CP → Ω error means the er-ror generated from the CP-structured solution if compared with

Fig. 7. Highest blocking probability of different CAC optimization policieswhile varying the arrival rate of class-3 traffic.

the exact solution, the CP approximation error means the error

generated from the approximation algorithm if compared with

the CP-structured solution, and the total approximation error

means the sum of the CP → Ω error and the CP approximation

error.

Next, we evaluate the performance of 2-D WiMAX CAC in

a subscriber’s local network using the decomposing approach

proposed in Section II. In the simulation scenario, we em-

phasize the utility- and fairness-constrained optimal revenue

policy ΩUF ∗ and its approximation algorithm, because they

take into account all the requirements of service providers and

subscribers. Considering the parameter decomposing model

given in Table I, we suppose that UL CAC and DL CAC employthe same policy, i.e., ΩUF ∗ or its approximation algorithm, with

normalized utility threshold uth and normalized blocking prob-

ability threshold pbth identically configured for UL and DL.

Numerical results are shown in Figs. 8 and 9 to demonstrate the

performance of ΩUF ∗ and its approximation algorithm based

2-D WiMAX CAC while varying uth and keeping pbth con-

stant at 65%. In the simulation, we set the UL/DL bandwidth

capacity in a subscriber’s local network to be 60/75 Mb/s.

Moreover, the UL traffic load is configured the same as that

given in Table IV, whereas the DL traffic load is configured in

Table II, except that the arrival rate of class-3 traffic is fixed

to be 64 calls/h. The revenue rates of both UL CAC and DLCAC are priced as rerUGS = 5, rerrtPS = 2, rernrtPS = 1,

and rerBE = 0.5.

Fig. 8 illustrates the revenue and utility of 2-D WiMAX

CAC, which can be derived from the UL/DL revenue and utility

as follows: 1) The revenue of 2-D CAC is defined as the sum

of the UL revenue and the DL revenue, and 2) the utility of

2-D CAC is defined as the average of the UL utility and the

DL utility. For analytical simplicity, in Fig. 8, the revenue is

normalized by that of the ΩF ∗ based 2-D CAC, and the utility

is normalized by that of the ΩF + based 2-D CAC.

As illustrated in Fig. 8, when uth = 0, ΩUF ∗ turns to be ΩF ∗,

yielding a solution of high revenue but low utility. Similarly,

when uth = 1, ΩUF ∗ turns to be ΩF +, yielding a solutionwith high utility but low revenue. Thus, we should choose an


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TABLE IITRAFFIC LOAD CONFIGURATION

TABLE IIIAVERAGE ERROR OF THE APPROXIMATION ALGORITHM (REVENUE /UTILITY /HIGHEST BLOCKING PROBABILITY)

Fig. 8. Revenue and utility of ΩUF ∗ and its approximation algorithm in2-D CAC.

Fig. 9. Highest blocking probability of ΩUF ∗ and its approximation algo-rithm in 2-D CAC.

appropriate value for uth (i.e., 90% in this case) to give ΩUF ∗

balanced revenue and utility. In addition, Fig. 8 also shows that

the approximation algorithm has similar performance as ΩUF ∗.

The fairness feature of 2-D WiMAX CAC is illustrated inFig. 9, which indicates that the highest blocking probability

of ΩUF ∗ and its approximation-algorithm-based 2-D CAC is

strictly bounded by the blocking probability threshold derived

from pbth.

Finally, we investigate the performance of ΩUF ∗ and its

approximation-algorithm-based 2-D CAC in a WiMAX PMP

network, which employs a OFDMA–TDD mode of 32 sub-

scribers with PUSC on the UL and FUSC on the DL. In our

simulations, the UL and DL channels are assumed to have

a bad-urban delay profile [29] and suffer from shadowing

with 8-dB standard deviation. Let the amount of available

subcarriers be 1024 and each subcarrier occupy 10 kHz of

physical bandwidth. The distances between the subscribers and

the base station are randomly chosen from 2 to 10 km, and the

acceptable BER is set to be 10−6. We assign each subcarrier the

same UL and DL power resource and configure the TDD DL

proportion factor α% as 60%.As for the traffic pattern, 32 subscribers are programmed to

have different UL and DL traffic loads, which are uniformly

distributed in [40 Mb/s, 100 Mb/s] and [60 Mb/s, 140 Mb/s],

respectively. To emulate an environment of broadband wireless

access, we suppose that the WiMAX network is dominated

by multimedia applications. Correspondingly, among the UL

and DL traffic loads of a certain subscriber, the proportions of

UGS, rtPS, nrtPS, and BE traffic, which are denoted by P P UGS,

P P rtPS, P P nrtPS, and P P BE, are set to be random variables,

which are defined as follows:

P P BE uniformly distributed in [10%, 30%];

P P UGSuniformly distributed in

[10%(1 − P P BE),

30%(1 − P P BE)];P P rtPS uniformly distributed in [20%(1 − P P BE),

60%(1 − P P BE)];P P nrtPS defined as (1 − P P BE − P P UGS − P P rtPS).

As for the revenue rate, we assume that rerUGS = 5,

rerrtPS = 2, rernrtPS = 1, and rerBE = 0.5. As for the utility

constraint and the fairness constraint, we set uth = 90% and

pbth = 65% for both UL CAC and DL CAC.

Simulation results are presented in Figs. 10 and 11 to demon-

strate the average performance of the 2-D CAC using ΩUF ∗

or its approximation algorithm among 32 subscribers. As men-

tioned earlier, Ω∗ and Ω+ have the best performance in terms

of revenue and utility, respectively. To facilitate the analysis,in Fig. 10, we use the average revenue/utility of Ω∗/Ω+ to


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TABLE IVUPLINK TRAFFIC LOAD CONFIGURATION

Fig. 10. Average revenue and utility of ΩUF ∗ and its approximation algo-rithm in 2-D WiMAX CAC of 32 subscribers.

Fig. 11. Average highest blocking probability of ΩUF ∗ and its approximation

algorithm in 2-D WiMAX CAC of 32 subscribers.

normalize the average revenue/utility. Figs. 10 and 11 show that

the 2-D CAC with ΩUF ∗, or its approximation algorithm, can

achieve high revenue and utility while still meeting the fairness

constraint.

VII. CONCLUSION

In this paper, we have proposed a framework for WiMAX

CAC, in which the 2-D CAC problem is decomposed into

two independent 1-D CAC problems. Then, we make the

1-D CAC an optimization problem and evaluate its differentstrategies. From the perspective of service providers, optimal

revenue is the major concern. However, from the perspective of

subscribers, optimal utility and fairness are the requirements.

To successfully deploy a WiMAX system, we have to take

into account the expectations of both service providers and

subscribers. Accordingly, we develop a utility- and fairness-

constrained optimal revenue policy, as well as its approximation

algorithm. Simulation results verify that our proposed WiMAX

CAC approach can meet the requirements of both service

providers and subscribers.

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Bo Rong (M’07) received the B.S. degree fromShandong University, Jinan, China, in 1993, the M.S.degree from the Beijing University of Aeronauticsand Astronautics, Beijing, China, in 1997, and thePh.D. degree from the Beijing University of Postsand Telecommunications in 2001.

After receiving the Ph.D. degree, he was a Soft-ware Engineer with a startup company in Beijingfor one year. Then, he was a Postdoctoral Fellowwith the Department of Electrical Engineering, Ecolede Technologie Superieure, Universite du Quebec,

Quebec City, QC, Canada, for three years. He is currently a Postdoctoral Fellow

with the Department of Electrical and Computer Engineering, University of Puerto Rico at Mayagüez. His current research interests focus on modeling,simulation, and performance analysis for next-generation wireless networks.

Yi Qian (M’95–SM’07) received the Ph.D. degreein electrical engineering with a concentration intelecommunication networks from Clemson Univer-sity, Clemson, SC.

He is currently with the National Institute of Stan-dards and Technology, Gaithersburg, MD. He was anAssistant Professor with the Department of Electri-cal and Computer Engineering, University of Puerto

Rico at Mayagüez (UPRM), from July 2003 to July2007. At UPRM, he regularly taught courses onwireless networks, network design, network manage-

ment, and network performance analysis. Prior to joining UPRM in July 2003,he worked for several start-up companies and consulting firms in the areas of voice over IP, fiber optical switching, Internet packet video, network optimiza-tions, and network planning as a Technical Advisor and a Senior Consultant. Hewas also with the Wireless Systems Engineering Department, Nortel Networks,Richardson, TX, as a Senior Member of Scientific Staff and as a TechnicalAdvisor for several years. While with Nortel Networks, he was a Project Leaderfor various wireless and satellite network product design projects, customerconsulting projects, and advanced technology research projects. He was also incharge of wireless standard development and evaluations. He has publicationsand is a holder of patents in all these areas. He is a coauthor of the book

Information Assurance: Dependability and Security in Networked Systems

(Morgan Kaufmann, 2008). His current research interests include network secu-rity, network design, network modeling, simulations and performance analysis

for next-generation wireless networks, wireless sensor networks, broadbandsatellite networks, optical networks, high-speed networks, and the Internet.

Dr. Qian is a member of the Association for Computing Machinery.

Kejie Lu (S’01–M’04–SM’07) received the B.S.and M.S. degrees in telecommunications engineeringfrom the Beijing University of Posts and Telecom-munications, Beijing, China, in 1994 and 1997,respectively, and the Ph.D. degree in electrical en-gineering from the University of Texas at Dallas,Richardson, in 2003.

From 2004 and 2005, he was a Postdoctoral Re-search Associate with the Department of Electrical

and Computer Engineering, University of Florida,Gainesville. Since July 2005, he has been an As-

sistant Professor with the Department of Electrical and Computer Engineer-ing, University of Puerto Rico at Mayagüez. His research interests includearchitecture and protocol design for computer and communication networks,performance analysis, network security, and wireless communications.

Hsiao-HwaChen (S’89–M’91–SM’00) received theB.Sc. and M.Sc. degrees from Zhejiang University,Zhejiang, China, in 1982 and 1985, respectively, andthe Ph.D. degree from the University of Oulu, Oulu,Finland, in 1991.

He is currently a Full Professor with the Depart-

ment of Engineering Science, National Cheng KungUniversity, Tainan, Taiwan, R.O.C. He is the authoror a coauthor of more than 250 technical papers inmajor international journals and conference proceed-ings and five books and three book chapters in the

areas of communications. He served or is currently serving as an EditorialBoard Member and/or Guest Editor of the Wireless Communications and

Mobile Computing Journal and the International Journal of CommunicationSystems. He is the founding Editor-in-Chief of the Security and Communication

Networks Journal.Dr. Chen has served as the Symposium Cochair of major international

conferences, including the IEEE Vehicular Technology Conference (VTC), theIEEE International Conference on Communications (ICC), the IEEE GlobalCommunications Conference (Globecom), and the IEEE Wireless Communica-tions and Networking Conference (WCNC). He served or is currently servingas an Editorial Board Member and/or Guest Editor of IEEE Communications

Magazine, the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, IEEE Wireless Communications Magazine, the IEEE TRANSACTIONS ON

WIRELESS COMMUNICATIONS, and IEEE Vehicular Technology Magazine.


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Mohsen Guizani (S’87–M’90–SM’98) received theB.S. (with distinction) and M.S. degrees in elec-trical engineering and the M.S. and Ph.D. degreesin computer engineering from Syracuse University,Syracuse, NY, in 1984, 1986, 1987, and 1990,respectively,

He is currently a Full Professor and Chair of theDepartment of Computer Science, Western Michigan

University, Kalamazoo. He was the Chair of the De-partment of Computer Science, University of WestFlorida, Pensacola, from 1999 to 2003. He was an

Associate Professor of electrical and computer engineering and the Director of graduate studies with the University of Missouri, Columbia, from 1997 to 1999.Prior to joining the University of Missouri, he was a Research Fellow withthe University of Colorado at Boulder. From 1989 to 1996, he held academicpositions at the Computer Engineering Department, University of Petroleumand Minerals, Dhahran, Saudi Arabia. He has more than 140 publicationsin refereed journals and conference proceedings in the areas of high-speednetworking, optical networking, and wireless networking and communications.He currently serves on the editorial boards of many national and international

journals, such as the Journal of Parallel and Distributed Systems and Networks

and the International Journal of Computer Research. He was a Guest Editor forthe Journal of Communications and Networks and several other publications.He is the Founder and Editor-in-Chief of Wireless Communications and MobileComputing.

Dr. Guizani currently serves on the editorial boards of the IEEETRANSACTIONS ON VEHICULAR TECHNOLOGY and IEEE Communications

Magazine. He has served as a Guest Editor for the IEEE Communications Mag-azine and the IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS.He served as the General Chair of the International Conference Parallel andDistributed Computing Systems (PDCS) in 2002 and 2003, the IEEE VehicularTechnology Conference (VTC) in 2003, and the International Conference onWireless Networks, Communications, and Mobile Computing (WirelessCom)in 2005. He has also served as the Program Chair for many conferences. He wasdesignated by the IEEE Computer Society as a Distinguished National Speakerthrough 2005.

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