Interference and Capacity Analysis in Wireless Mesh...

Interference and Capacity Analysis inWireless Mesh Network

By

Muhammad Zeeshan

(Master of Computer Engneering, CASE-UET Taxila, 2009)

2009-NUST-DirPhD-IT-32

A thesis submitted in partial fulfillment of the requirements for the degree of

Doctor of Philosophy

School of Electrical Engineering and Computer Science,

National University of Sciences and Technology (NUST),

Islamabad, Pakistan.

August 2016

Copyright c©2016, Muhammad Zeeshan

Approval

It is certified that the contents and form of the thesis entitled “Interference

and Capacity Analysis in Wireless Mesh Network” submitted by

Muhammad Zeeshan have been found satisfactory for the require-

ment of the doctor of philosophy degree.

Advisor: Dr. Anjum Naveed

Signature:

Date:

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Committee Member 1: Dr. Hassaan Khaliq Qureshi (co-advisor)

Signature:

Date:

Committee Member 2: Dr. Adnan Khalid Kiani

Signature:

Date:

Committee Member 3: Dr. Muhammad Usman Ilyas

Signature:

Date:

Committee Member 4: Dr. Akhlaque Ahmed (external)

Signature:

Date:

Abstract

CSMA based MAC protocols are known to incur throughput im-

balance when employed in multi hop wireless networks and exist-

ing literature lacks efficient MAC protocol for wireless mesh net-

works. Accurate modeling of interference and its affect on through-

put of flows in the WMN is critical in designing future wireless

networking protocols. This thesis performs a thorough analysis of

interference and capacity in wireless multi hop network based on

CSMA/CA MAC behavior. It is hypothesized that accurate mod-

eling of interference at MAC level can maximize overall network

capacity. In first part of thesis, twenty five unique possible two flow

topologies have been classified into six categories based on MAC

layer behavior and per flow throughput and closed form expres-

sions for occurrence probabilities of the identified categories have

been derived with particular observation that carrier sensing range

based categories have high occurrence probability and cannot be ig-

nored. MAC behavior of each category is discussed. In the second

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part, accurate computation of conditional packet loss probability and

busy time is done based on geometrical configuration of the interfer-

ing links and also predicted per-flow throughput while addressing

CSMA’s coordination problem. Unlike previous work, our analyt-

ical throughput model can clearly differentiate between links inter-

fering from transmission range and carrier sensing range. Analyt-

ical and empirical results demonstrate improved accuracy, indicate

throughput imbalances and provide better understanding of CSMA

based protocol behavior in multi-hop wireless networks that can be

used to design fair, scalable, and efficient MAC layer protocols.

Certificate of Originality

I hereby declare that this submission is my own work and to the

best of my knowledge it contains no materials previously published

or written by another person, nor material which to a substantial

extent has been accepted for the award of any degree or diploma

at National University of Sciences & Technology (NUST) School

of Electrical Engineering & Computer Science (SEECS) or at any

other educational institute, except where due acknowledgement has

been made in the thesis. Any contribution made to the research by

others, with whom I have worked at NUST SEECS or elsewhere, is

explicitly acknowledged in the thesis.

I also declare that the intellectual content of this thesis is the prod-

uct of my own work, except for the assistance from others in the

project’s design and conception or in style, presentation and linguis-

tics which has been acknowledged.

Author Name: Muhammad Zeeshan

Signature:

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Acknowledgment

First of all I am very grateful to Allah (SWT) for blessing me strength

and courage to pursue this research.

I am thankful to my supervisor Dr. Anjum Naveed and would

like to express my sincere gratitude for his kind guidance and splen-

did support throughout the duration of my PhD. I also appreciate

his enthusiasm, motivation, patience and immense knowledge. His

guidance rescued me and helped me in all stages of PhD including

course work, research work and thesis. He also helped me groom

my professional behaviors and enabled me to market my potential

with a purpose to achieve maximum goals.

I also like to acknowledge Principal/Dean Dr. Syed Muhammad

Hassan Zaidi and Prof. Dr. Arshad Ali and really appreciate their

valuable support. I would also like to thank my research guidance

committee comprising on members: Dr. Hassan Khaliq Qureshi,

Dr. Adnan Khalid Kiani, Dr. Muhammad Usman Ilyas and Dr.

Akhlaque Ahmad for their encouragement, support, time and help-

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ful feedback on preliminary version of this thesis. I would also like

to thank my previous reseach guidance committee comprising on

members: Prof. Dr. Amir Qayyum, Dr. Ali Khayam, Dr. Junaid

Qadir, Dr. Adeel Baig and Dr. Zawar Hussain Shah. I would also

like to extend my heartfelt thanks to all of my external thesis evalua-

tors: Dr. Feng Xia (DUT, China), Dr. Muhammad Shahzad (NCSU,

USA) and Khurram Saleem Alimgeer (COMSATS, Islamabad). It

really is a time taking task to review a thesis, and I really am in-

debted for their helpful and detailed comments. I would also like to

thanks all my teachers because their cumulative grooming and guid-

ance helped me succeed. I am also thankful to Mr. Kashif Sattar,

my lab mate and a good friend for his continuous moral and social

support.

Most importantly, I would like to thank my parents and family

for their confidence in me and unconditional support for pursuing

Ph.D.

Muhammad Zeeshan

Dedication

I dedicate this thesis to my mother Mrs. Kaneez Fatima, she served

as government teacher for 25 years, she always encouraged and sup-

ported me to peruse higher education and social values. Her role in

my life has always been, and remains a support system in all situa-

tions of happiness and sorrow.

Muhammad Zeeshan

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Author’s Publications

• Muhammad Zeeshan, Asad Ali, Anjum Naveed, Alex X. Liu,

Ann Wang, and Hassaan Khaliq Qureshi, ”Modeling Packet

Loss Probability and Busy Time in Multi-hop Wireless Net-

works”, EURASIP Journal on Wireless Communications and

Networking 2016, no. 1 (2016): 1-16. (IF=0.72).

• Muhammad Zeeshan, Anjum Naveed, ”Medium Access Be-

havior Analysis of Two Flow Topologies in IEEE 802.11 Wire-

less Networks”, EURASIP Journal on Wireless Communica-

tions and Networking 2016, no. 1 (2016): 1. (IF=0.72).

• Muhammad Zeeshan, Anjum Naveed, Interference and capac-

ity analysis in multi-hop wireless mesh networks, in PhD Fo-

rum of 21st IEEE International Conference on Network Proto-

cols ICNP-2013, Gttingen, Germany.

• Muhammad Zeeshan, Kashif Sattar, Zawar Shah, Imdad Ullah,

Routing and Spectrum Decision in Single Transceiver Cogni-

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tive Radio Network, 2013 IEEE 78th Vehicular Technology

Conference: VTC2013-Fall 2-5 September 2013, Las Vegas,

USA.

• Salman Ali, Muhammad Zeeshan, Anjum Naveed, A capacity

and minimum guarantee-based service class-oriented scheduler

for LTE networks, EURASIP Journal on Wireless Communica-

tions and Networking 2013, no. 1 (2013): 1-15. (IF=0.87).

• Muhammad Zeeshan, Salman Ali, A Spectrum Exploitation

Scheme with Channel Assignment for Genetic Algorithm Based

Adaptive-Array Smart Antennas in Cognitive Radio Environ-

ment, IEEE International Conference on Communications (ICC)

2012, Ottawa Canada.

• Salman Ali, Muhammad Zeeshan, A Utility Based Resource

Allocation Scheme with Delay-Scheduler for LTE Service-Class

Support, IEEE Wireless Communications and Networking Con-

ference (WCNC 2012), Paris France.

• Salman Ali, Muhammad Zeeshan, A Delay Scheduler Coupled

Game Theoretic Resource Allocation Scheme for LTE Net-

works, 9th Frontier of Information Technology 2011 (FIT 2011)

Islamabad Pakistan.

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• Muhammad Zeeshan, Muhammad Fahad Manzoor, Junaid Qadir,

Backup Channel and Cooperative Channel Switching On-Demand

Routing Protocol for Multi-Hop Cognitive Radio Ad Hoc Net-

works (BCCCS), IEEE International Conference on Emerging

Technologies 2010 (ICET 2010) Islamabad Pakistan.

Contents

1 INTRODUCTION 1

1.1 Two Flow Interaction . . . . . . . . . . . . . . . . . 7

1.2 CSMA/CA Behavior in WMN . . . . . . . . . . . . 8

1.3 Interference Models . . . . . . . . . . . . . . . . . . 9

1.4 Per-flow Throughput Prediction . . . . . . . . . . . 11

1.5 Research Summary . . . . . . . . . . . . . . . . . . 14

1.5.1 Research Hypothesis . . . . . . . . . . . . . 14

1.5.2 Research Contributions . . . . . . . . . . . . 15

1.6 Structure of the Thesis . . . . . . . . . . . . . . . . 16

2 Literature Review 18

2.1 IEEE Standards . . . . . . . . . . . . . . . . . . . . 18

2.2 Parameters for Capacity Estimation . . . . . . . . . 22

2.3 Interference and Capacity Analysis . . . . . . . . . . 25

2.4 Applications of Capacity Analysis . . . . . . . . . . 34

2.5 Summary . . . . . . . . . . . . . . . . . . . . . . . 37

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CONTENTS xiii

3 Two flow classification and occurrence probability 39

3.1 Two Flow Topologies . . . . . . . . . . . . . . . . . 40

3.1.1 Senders Connected . . . . . . . . . . . . . . 40

3.1.2 Symmetric Sender Receiver Connected . . . 41

3.1.3 Asymmetric Sender Receiver Connected . . 43

3.1.4 Receivers Connected . . . . . . . . . . . . . 46

3.1.5 Symmetric Not Connected . . . . . . . . . . 46

3.1.6 Asymmetric Not Connected . . . . . . . . . 47

3.2 Categories occurrence probability . . . . . . . . . . 49

3.2.1 Senders Connected . . . . . . . . . . . . . . 51

3.2.2 Symmetric Sender Receiver Connected . . . 52

3.2.3 Asymmetric Sender Receiver Connected . . 53

3.2.4 Receivers Connected . . . . . . . . . . . . . 53

3.2.5 Symmetric Not Connected . . . . . . . . . . 54

3.2.6 Asymmetric Not Connected . . . . . . . . . 54

3.2.7 Occurrence Probability Values . . . . . . . . 54

3.3 Summary . . . . . . . . . . . . . . . . . . . . . . . 56

4 Interference and throughput analysis 57

4.1 Protocol Behavior of CSMA/CA . . . . . . . . . . . 58

4.2 Senders Connected . . . . . . . . . . . . . . . . . . 61

4.3 Symmetric Sender Receiver Connected . . . . . . . 62

CONTENTS xiv

4.4 Asymmetric Sender Receiver Connected . . . . . . . 67

4.5 Receivers Connected . . . . . . . . . . . . . . . . . 71

4.6 Symmetric Not Connected . . . . . . . . . . . . . . 73

4.7 Asymmetric Not Connected . . . . . . . . . . . . . 78

4.8 Summary . . . . . . . . . . . . . . . . . . . . . . . 84

5 Throughput modeling in WMN 85

5.1 Packet loss probability modeling . . . . . . . . . . . 87

5.1.1 Loses due to sender sensing . . . . . . . . . 90

5.1.2 Loses due to asymmetric incomplete state . . 91

5.1.3 Loses due to symmetric incomplete state . . 93

5.1.4 Loses due to destination connected . . . . . . 94

5.2 Busy time computation . . . . . . . . . . . . . . . . 96

5.3 Simulation and model validation . . . . . . . . . . . 105

5.3.1 Fraction of busy time sensed . . . . . . . . . 106

5.3.2 Conditional packet loss probability . . . . . 108

5.3.3 Contribution of packet loss probability due

to information asymmetry . . . . . . . . . . 109

5.3.4 Transmission probability comparison . . . . 109

5.3.5 Analytical throughput . . . . . . . . . . . . 110

5.3.6 Simulation throughput . . . . . . . . . . . . 111

5.4 Summary . . . . . . . . . . . . . . . . . . . . . . . 112

CONTENTS xv

6 Conclusion 121

6.1 Future work . . . . . . . . . . . . . . . . . . . . . . 126

List of Abbreviations

ANC Asymmetric Not Connected

AIS Asymmetric Incomplete State

ASRC Asymmetric Sender Receiver Connected

CTS Clear To Send

CSR Carrier Sense Range

DIFS DCF Inter-Frame Space

DCF Distributed Coordination Function

EDCA Enhanced distributed channel access

MAC Medium Access Control

MCCA Mesh Coordinated Channel Access

NAV Network Allocation Vector

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List of Abbreviations

RC Receiver Connected

RTS Ready To Send

SC Sender Connected

SSRC Symmetric Sender Receiver Connected

SNC Symmetric Not Connected

SIS Symmetric Incomplete State

SIFS Short Inter-Frame Space

WMN Wireless Mesh Network

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List of Figures

1.1 Two flow interaction topology . . . . . . . . . . . . 8

3.1 Senders Connected Topologies . . . . . . . . . . . . 42

3.2 Sample nodes placement. . . . . . . . . . . . . . . . 43

3.3 Symmetric Sender Receiver Connected Topologies . 44

3.4 Asymmetric Sender Receiver Connected Topologies . 45


3.6 Receivers Connected Topologies . . . . . . . . . . . 47

3.7 Symmetric Not Connected Topologies . . . . . . . . 48


3.9 Asymmetric not connected Topologies . . . . . . . . 49

3.10 Occurrence probabilities of categories . . . . . . . . 55

4.1 Throughput (Senders connected flows). . . . . . . . 62

4.2 SSRC channel view . . . . . . . . . . . . . . . . . . 65

4.3 ASRC channel view . . . . . . . . . . . . . . . . . . 69

4.4 Per flow throughput . . . . . . . . . . . . . . . . . . 72

xviii

LIST OF FIGURES xix

4.5 RC channel views . . . . . . . . . . . . . . . . . . . 74

4.6 Per flow throughput of SNC . . . . . . . . . . . . . 79

4.7 ANC channel view . . . . . . . . . . . . . . . . . . 82

4.8 Per flow throughput of ANC . . . . . . . . . . . . . 83

5.1 Two flow topology . . . . . . . . . . . . . . . . . . 89

5.2 Overlapping regions . . . . . . . . . . . . . . . . . . 104

5.3 Network topology and connectivity graph . . . . . . 113

5.4 Analytical comparison of busy time probability . . . 114

5.5 Analytical comparison of conditional packet loss prob-

ability . . . . . . . . . . . . . . . . . . . . . . . . . 115

5.6 Contribution of packet loss probability due to infor-

mation asymmetry . . . . . . . . . . . . . . . . . . 116

5.7 Comparison between analytical transmission proba-

bilities . . . . . . . . . . . . . . . . . . . . . . . . . 117

5.8 Analytical comparison of throughput . . . . . . . . . 118

5.9 Comparison between analytical normalized through-

put . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

5.10 Comparison between simulation and analytical through-

put . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

List of Tables

4.1 ERP IEEE 802.11g Parameters . . . . . . . . . . . . 63

4.2 SSRC Computation Parameters . . . . . . . . . . . . 66

4.3 SNC Computation Parameters . . . . . . . . . . . . 77

5.1 Analytical Parameters for Throughput Computation . 106

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Chapter 1

INTRODUCTION

Wireless mesh network (WMN) is an emerging wireless technol-

ogy in which nodes perform dual role of being clients as well as

routers and forwards packets for other flows in the network. Unique-

ness lies in the fact that all the nodes participating in WMN are

self-organizing, self-configuring and group of nodes create, config-

ure and maintain ad hoc network among them. Main advantage of

WMN is its use for extending the coverage area of fixed infrastruc-

ture networks. Nodes can connect to wireless router using wireless

interface and get connected to internet through bridge/gateway ca-

pability of wireless routers that can interconnect WMN with various

types of infrastructure, wired and wireless networks. Network re-

liability and connectivity in WMN increases as the size of network

grow. Low installation and maintenance cost along with interoper-

ation with existing networks make WMN a fascinating technology

1

CHAPTER 1. INTRODUCTION 2

that ensures network connectivity and reliability [1].

Many variant of multi hop wireless networks have already made

their way and deployments will increase in near future. These may

include but not limited to medical, emergency, environmental, bat-

tlefield sensor networks, telematics applications for individual drivers,

public safety and security, broadband internet, vehicular network,

home or office networks, cognitive radio networks and even data

center networks. In short, deployment of multi hop wireless tech-

nologies will surely transform our daily life with innovative applica-

tions having greater impact. Connectivity provided by mesh routers

is flexible and more reliable as localized data is not required to travel

all the way to backhaul routers, power adjustment and changing lo-

cations of mesh router provides better tool against dead zones in

the wireless network. Most popular use of WMN these days is one

laptop per child program where WMN is being used for connec-

tivity between students in areas where no internet connectivity or

any physical link is available [2]. WMNs are attractive to commer-

cial internet suppliers because of their support for ad hoc multi hop

networking and low installment and maintenance cost. WMNs are

envisaged as promising technology but more research efforts are re-

quired to actualize its true potentials. Internet of Things (IoT) is one

such example of wireless mesh technologies, this MAC analysis can


greatly help in evolution of efficient MAC protocol for Internet of

Things.

WMN suffers severe throughput degradation due to interfering

links within single carrier sensing range and only one link at a time

can transmit data on same frequency channel. Due to interference,

capacity of the wireless channel is divided between numbers of con-

tending links. Furthermore, many transmission opportunities are

wasted when more than one interfering links try to transmit simulta-

neously using CSMA MAC protocols. Gupta et al. [3] have implied

that increased number of nodes in a unit area directly affect the net-

work capacity due to the fact that more number of nodes are trying

to transmit on the same time hence increasing more interference and

loss of transmission opportunities. Later, Garetto et al. [4] revealed

the fact that number of contending nodes are not the only reason

for throughput degradation, and highlighted that generic coordina-

tion problem in CSMA MAC is fundamental reason for collisions

and consequently unfair throughput distribution in multi hop wire-

less networks.

Capacity estimation of WMN as well as routing, MAC, chan-

nel assignment and topology control protocols relay on interference

estimation and modeling for interference prediction and mitigation.

Consequently, accurate interference modeling plays a significant role


in the estimation and improvement of WMN capacity. A number

of interference models have been proposed during the past decade.

These models include: (i) Protocol model of interference, (ii) Phys-

ical model of interference, (iii) Extended protocol model of interfer-

ence and (iv) Location aware model of interference [4]. However,

none of these models accurately capture the effect of interference.

Although model proposed by Garetto et al. [4] predicts interference

with reasonable accuracy, however the model does not differenti-

ate between interference from within transmission range and carrier

sensing range. Consequently, the accuracy decreases. The focus

of this dissertation is interference and capacity analysis in wireless

mesh network.

Work in this thesis extends and completes body of work on two

flow interactions and also optimizes per flow throughput prediction

[4, 5]. First, two flow topologies have been reclassified by sepa-

rately considering the transmission and the carrier sensing ranges

[6]. The interaction between the two single hop flows is considered

under CSMA/CA MAC protocol for throughput estimation of two

flow topologies. It is observed that the presence of sender or receiver

of interfering link within the carrier sensing range results in signifi-

cantly different MAC behavior compared to the presence of the two

nodes outside the carrier sensing range. This research divides the


two flow topologies into six categories, depending upon CSMA/CA

interaction. Among six categories, three are newly identified cate-

gories that are different from the categories identified by Garetto et

al. [5] as well as Razak et al. [7]. Occurrence probability of each

category has been computed using spatial analysis. For this purpose,

possible geometric area where the nodes of the particular topology

can exist has been considered, compared to the over all geometric

area of occurrence for two interfering links. Analysis shows that the

categories that are based on interference interactions from within the

carrier sensing range only, have high occurrence probability values

(aggregate of 0.69). Throughput achieved by the two links under

each category has been computed analytically based on MAC pro-

tocol behavior. Analytically computed throughput values have been

compared with the simulation throughput values using Opnet based

Simulations. The comparison shows near perfect match in analytical

and simulated values, suggesting the completeness of the categoriza-

tion.

Main challenges in per-flow throughput prediction in WMN in-

cludes accurate calculation of conditional packet loss probability

and busy time sensed by each station. Calculation of these both

parameters is totally dependent on geometrical location of contend-

ing stations and clear differentiation between links interfering from


transmission range and carrier sense range whereas prior art is un-

able to make this differentiation. Proposed model also devise a sim-

plified disk model for measuring busy time sensed by a station in

dense wireless mesh network. Then, it accurately model conditional

packet loss probability for each station based on geometrical loca-

tions of all the interfering stations around it. Proposed modeling of

busy time and packet loss probability can clearly make the differ-

entiation between interference from transmission and carrier sense

range. Proposed model also compute per flow throughput for all the

flows in the network based on its own calculation of busy time and

packet loss probability. Analytical results validate throughput model

and also support the argument that this model can clearly differen-

tiate between interfering links from transmission and carrier sense

range. Proposed model is more accurate in per-flow throughput pre-

diction in comparison with existing literature [4, 7, 5]. This work

provides better understanding of CSMA based MAC protocols in

arbitrary networks and aids toward designing more effective future

networking protocols.


1.1 Two Flow Interaction

The euclidean distance between two nodes A and B is given as

d(A, B). A node can have three possible placements with reference

to another node depending upon the signal strength received from

the other node. If node B is placed around node A such that it can

successfully decode the transmissions from node A, then the node B

is within the transmission range (TR) of node A, i.e., d(A, B) ≤ TR.

Such placement is referred as Connected in this work. On the other

hand, if node B can sense the channel to be busy when node A

transmits but cannot successfully decode the information because

of weak radio signals, then the node B is outside transmission range

but within the carrier sensing range (CSR) of node A, i.e., TR <

d(A, B) ≤ CSR. This placement is referred as Sensing. Finally,

if node B cannot sense the transmissions of node A, then node B is

outside the carrier sensing range of node A, i.e., d(A, B) > CSR.

This placement is referred as Disconnected. The placement is re-

ferred as Not Connected if it is either Sensing or Disconnected. The

placements are referred as interference interactions throughout the

rest of the work.

Consider two single hop flows Aa and Bb where A and B are the

transmitting nodes while a and b are the respective receiving nodes.


Flow Links

Interference Interaction Links

BA

ba

Figure 1.1: Two flow interaction topology

The receiving nodes are within the transmission range of the respec-

tive transmitting nodes. Four interference interactions AB, ab, Ab

and Ba exist between the nodes of the two flows, as shown in Fig-

ure 1.1. Interference interaction AB is between the two transmitters

and is referred as Senders interaction. On the similar lines, the inter-

action ab is referred as receivers interaction while the interactions

aB and Ab are referred as sender receiver interactions. A two flow

topology is considered symmetric if the interference interactions Ab

and Ba are of same type i.e., if Ab is sensing then Ba is also sensing.

1.2 CSMA/CA Behavior in WMN

Interference in wireless networks significantly limits the network ca-

pacity. Among a set of interfering links using a common frequency

channel, transmission of a link is successful only if all other links


remain silent for the entire period of transmission. Medium access

control (MAC) protocol is employed to arbitrate the access to the

wireless channel among competing links. IEEE 802.11 networks use

carrier sense multiple access with collision avoidance (CSMA/CA)

as MAC protocol. The random access mechanism of CSMA/CA

does not ensure interference free transmissions, specifically when

the sender nodes of the interfering links are not within the transmis-

sion range of each other. Consequently, many transmission oppor-

tunities are wasted when more than one interfering links simultane-

ously attempt transmissions. Thorough MAC behavior analysis can

reveal the impact of interference on the achievable throughput of the

interfering links.

1.3 Interference Models

Interference is critical for wireless mesh network and researchers

have proposed few models to analyze interference in WMNs [3, 4,

8, 9, 10, 11, 12, 13, 14, 15]. Physical model [3] identifies a success-

ful transmission if and only if signal to interference and noise ratio

experienced at receiver is above an acceptable threshold. Whereas

protocol model [3] identifies a successful transmission if and only if

no other transmitter within carrier sensing range of receiver tries to


transmit during current transmission. Both these interference mod-

els are not compatible to be used with CSMA MAC protocols em-

ployed in WMNs.

According to SNIR based protocol model two links can utilize

full link capacity simultaneously in a situation when one of the trans-

mitters is in carrier sense range of other but realizing the CSMA

MAC protocol, this may not be possible and both links share capac-

ity equally among them as this is a coordinated symmetric scenario

with exposed node. The same scenario does not satisfy the proto-

col interface model as well, as second transmitter is within carrier

sensing range of the receiver [7]. Tang et al. [8] extended the pro-

tocol interference model and identify the transmission successful if

and only if there is no other transmitter or receiver in carrier sens-

ing ranges of both transmitting and receiving nodes. They treated

all interfering links in the same fashion assuming equal impact on

throughput degradation whereas Garetto et al. [5] proved that vary-

ing distance between interfering links varies throughout degradation

as well.

Analyzing the performance of 802.11 DCF, Giuseppe Bianchi [9]

showed that in the absence of hidden node [16] problem with perfect

capture, wireless nodes within radio transmission range exhibits fair-

ness for all nodes contending for channel access. Two flow topolo-


gies describe the interactions between nodes in wireless multi hop

networks and aid in performance characterization of both the flows.

If all four nodes are within a single radio transmission range then

by using CSMA protocol they exhibit fairness in performance and

channel contention between four nodes and performance analysis of

coordinated scenarios can be predicted accurately [9].

1.4 Per-flow Throughput Prediction

When all stations in multi-hop wireless networks are not in single ra-

dio range, carrier sense multiple access based MAC protocols (two-

way or four-way handshake) are known to exhibit severe through-

put imbalances and few flows are even starved completely [5]. It is

very critical to analytically model such behavior and predict per-flow

throughput for designing efficient networking protocols. Flow star-

vation can be modeled by computing conditional packet loss proba-

bility and busy time duration sensed by each station in the network.

Accurate modeling of MAC behavior is very critical for modeling

starvation and predicting per-flow throughput. However, traditional

metrics like aggregate throughput and latency are not suitable for

this purpose.

Given a link and its interfering link, the placement of the sender


and the receiver of the interfering link within transmission or carrier

sensing range defines the MAC behavior and its impact on achiev-

able throughput of the two links. Garetto et al. [5] analyzed the

MAC behavior of the two interfering links under different geomet-

ric placements inside and outside transmission range. The authors

have categorized the two flow topologies with different geographic

placements into three categories. Under the assumption of same

transmission and carrier sensing range, the analysis carried out by

Garetto et al. [5] accurately predicts the impact of MAC behavior

and interference on throughput of the two single hop flows. How-

ever, the study do not consider the impact of carrier sensing range

on the MAC behavior and the resultant throughput. Razak et al. [7]

extended this research by considering separate carrier sensing and

transmission ranges; however, the simulation results show that the

topologies within the single category do not share same throughput

profile. Furthermore, important categories based on nodes within

carrier sensing range have not been considered.

Modeling packet loss probability is very critical in per-flow through-

put prediction and it depends on MAC behavior which is strongly

tied with geometry of contending links. Per-flow throughput predic-

tion and starvation modeling in [17] is based on embedded two flow

classification of [5], which actually defines geometrical relations be-


tween two contending flows and their MAC behavior. As mentioned

earlier, two flow classification of [5] assumes same transmission and

carrier sense range and do not clearly differentiate between links in-

terfering from transmission and carrier sense range. Therefore pro-

posed throughput modeling in [17] is for radio range i.e., carrier

sense range and such modeling do not differentiate between trans-

mission and carrier sense range. Interfering link being in transmis-

sion range means that stations can receive and decode each other’s

RTS/CTS and are able to set network allocation vector (NAV) but

this is not the case when stations are in sensing range of each other

and this is a fundamental differentiation to consider while modeling

throughput due to MAC behavior in WMN.

Most of the existing literature addresses some aspects of per flow

throughput prediction, few [18, 19] of them ignored the inherent

coordination discrepancy when CSMA based MAC protocols are

employed in multi-hop WMN. This inherent coordination discrep-

ancy was first modeled in [17] and is largely due to information

asymmetry between contending flows. Some of the literature is un-

able to model behavior of comprehensive MAC protocol like 802.11

[20, 21, 22, 23]. Analysis of 802.11 protocols is mostly done for

backlogged stations [18, 9, 24], only model in [17] predicts per-flow

throughput for any given flow rates in the WMN. In [17], they also


highlighted that few dominant flows acquire the maximum transmis-

sion opportunities where as most of the flows are starved and this

starvation is due to an inherent coordination discrepancy in CSMA

based MAC protocols when employed in WMN.

1.5 Research Summary

Primary focus of this thesis is to analyze affect of interference on

achieved throughput for flows in multi hop wireless networks. We

first propose two flow classification with more realistic assumption.

Then based on these two flow categories, we model busy time and

packet loss probability of single station in WMN with an objective to

predict its achieved per-flow throughput. Following is the research

hypothesis and contributions of this thesis.

1.5.1 Research Hypothesis

Links interfering from carrier sense range results in severe through-

put imbalance for flows contending in multi hop wireless networks.

Accurate differentiation between links interfering from transmission

range and carrier sense can significantly improve overall capacity

of the network. Better understanding of CSMA/CA based MAC’s

behavior in WMN is critical for designing efficient future wireless


networking protocols.

1.5.2 Research Contributions

This thesis investigates the effectiveness of the proposed hypothesis

through a two phase study including two flow classification and per-

flow throughput prediction. Following are the salient contributions

of this thesis.

• Classification of two-flow interactions is performed based on

geometric location of the stations which surely is more real-

istic and practical assumption. This classification is also val-

idated as computation of closed form expressions for occur-

rence probabilities of all identified categories resulted into

0.99999 total probability.

• Extensive discussion on MAC behavior and throughput com-

putation of each identified category. Also highlight insights

regarding throughput imbalance in each of the six categories.

• Also devised a simplified disk model for calculating busy time

sensed by each station in general multi hop WMN. This model

inherently embed geometrical location of all interfering trans-

mitters and receivers around that particular station. This is


clearly able to differentiate between stations interfering from

transmission and carrier sense range.

• Accurate modeling of packet loss probability for each station

in multi hop WMN and this modeling can clearly differentiate

between interference from transmission range and carrier sense

range.

• We predict per flow throughput for each station based on its

packet loss probability and experienced busy time. Model val-

idation and simulation results show that proposed packet loss

probability, busy time and throughput modeling improved the

accuracy of per-flow throughput prediction and also improve

overall understanding of MAC behavior in multi hop WMN.

1.6 Structure of the Thesis

This thesis focuses on analysis of interference and capacity in multi

hop wireless mesh networks and attempts to predict per-flow through-

put accurately based on practical and realistic assumptions. Chapter

2 reviews the prior state of the art in two-flow analysis and per-flow

throughput prediction in MWN along with applications of interfer-

ence and capacity analysis. Chapter 3 presents two-flow classifica-

tion and closed form expressions for occurrence probability compu-


tation of each identified two-flow category. Chapter 4 thoroughly

presents MAC behavior and its affect on throughput of the contend-

ing flows in each two-flow category. Chapter 5 presents computation

of busy time and packet loss probability of single station and details

of per-flow throughput modeling are also discussed. Chapter 6 con-

cludes this thesis and details of possible future directions for this

work are also described.

Chapter 2

Literature Review

This chapter initially reviews IEEE standardization efforts on wire-

less mesh standard i.e., 802.11s & 802.15.4 and then briefly details

parameters used in literature for capacity estimation in wireless net-

works. Section 2.3 presents comprehensive review of work done

on interference and capacity analysis in wireless mesh network and

Section 2.4 highlight applications of interference and capacity mod-

eling.

2.1 IEEE Standards

Latest version of IEEE 802.11s standard released in 2012 [25] spec-

ifies the MAC and physical specifications for mesh networks. It

comprises of a mandatory coordination function called Enhanced

distributed channel access (EDCA) and an optional coordination

18

CHAPTER 2. LITERATURE REVIEW 19

function named Mesh coordination channel access (MCCA). EDCA

is a modified version of Distributed coordination function (DCF of

802.11n) with smaller durations for Arbitration inter frame space

(AIFS) and reduced maximum window size values to accommodate

priority traffic in the wireless network. Smaller AIFS are used for

higher priority flows whereas larger AIFS is used for low priority

flows. Similarly lower value of maximum window size is selected

for priority flows and vice versa. EDCA was originally designed

to provision quality of service (QoS) at MAC layer for single hop

WLAN in IEEE 802.11e but later it is also recommended to be used

as MAC for multi hop WLAN in IEEE 802.11s. EDCA is known

to incur throughput imbalances among the same or even higher pri-

ority flows and there are known situations in which higher priority

flows also starve [26]. Researchers have made many efforts to make

improvements in EDCA in recent years but more work is done for

QoS provisioning analysis for real time flows in WLAN..

MCCA is an optional coordination function in IEEE 802.11s mesh

mode. MCCA is a distributed transmission opportunity allocation

algorithm in which mesh stations coordinate their intended transmis-

sion duration using request and acknowledgment procedures. MCCA

enabled mesh stations also coordinate their Resource Allocation Vec-

tors (RAV) to two hop neighbors using regular MCCAOP advertise-


ments [26, 27]. MCCA enabled mesh stations are also required to

contend for channel access among non-MCCA stations within their

reserved duration. Even after reservation, MCCAOP owner cannot

have guaranteed access because of simultaneous transmissions made

by Non-MCCA mesh stations [28].

Talking about coexistence of EDCA and MCCA with traditional

DCF; EDCA was originally designed to provide QoS at MAC layer

in single hop WLAN i.e., IEEE 802.11e. Same is recommended

as MAC for 802.11s, it translates traffic into four different priority

classes by differentiating the arbitration inter frame space (AIFS)

slot length and back off windows size [25]. While co existing with

DCF, EDCA with AIFS value equal to 2 performs well and pro-

vides an effective mechanism for priority flows to get channel ac-

cess. Whereas the performance of EDCA is almost the same as

thats of legacy DCF when AIFS is equal to 3. Differentiated AISF

length is more effective in providing QoS as compared to differen-

tiation of back off window size [29]. MCCA is an optional access

mechanism for mesh stations whereas EDCA is mandatory, so it is

most likely that MCCA enabled mesh stations will be contending

with non-MCCA stations (both EDCA and legacy DCF), who are

unaware of reservations made by MCCAOP (MCCA opportunity)

owner. Any reservation made by MCCA enabled stations will not


be guaranteed due to collision introduced by non-MCCA mesh sta-

tions hence the performance of MCCA enabled station is very dete-

riorating in general WLAN [25, 28, 29]. Being an optional access

mechanism, no efforts have been made to improve the performance

of MCCA.

IEEE 802.15.4 standard details media access control and physi-

cal layer specification and has been extensively used in low power

and low rate wireless networks as being fundamentally developed

for low rate wireless personal area networks. It promises to pro-

vide a standard for communication among devices with low cost,

low power and very low complexity. It operates in two modes in-

cluding beaconless and beacon enabled mode. Beaconless (unslot-

ted) mode is more suitable for networks where there are fewer colli-

sions whereas the beacon enabled mode (slotted) is more suitable for

networks with periodic communications and having more collisions

[30]. A central coordinator node is required in beacon enabled mode

which is responsible for synchronization among communicating de-

vices. All reduced functionality client nodes need to be connected

to a coordinating node and this node is responsible to provide time

synchronization for channel access. Beacon less mode do not need

synchronization and it more works like 802.11 DCN using unslotted

CSMA/CA algorithm for channel access [31].


IEEE 802.15.4 is being extensively used in wireless personal area

network (WPAN), wireless sensor networks (WSN) and control sys-

tems in various industries [30, 32]. It can be used with 6LoW-PAN

[33] and also with other upper layer internet protocols for providing

embedded wireless internet connectivity. Misic et al. [34] did a com-

prehensive analysis of MAC layer parameters for 802.15.4 PAN in

beacon enabled mode. They modeled various parameters including

number of nodes, buffer size, and packet arrival rate and inter beacon

delay and derived various performance parameters as well including

idle probability, access probability, distribution of queue length in

nodes, probability distribution for packet service time. They con-

cluded that access probability can be maximized by carefully choos-

ing values for packet and network sizes and packet arrival rate. Zhu

et al. also investigated the behavior of 802.15.4 PAN but their only

assumed unsaturated traffic pattern and did not consider the FEC

coding [35].

2.2 Parameters for Capacity Estimation

Primary metric quantitatively indicates the quality of wireless links

and in existing literature there are four primary metrics used exten-

sively for network quality measurements [36]. Most of the com-


monly used metric is Packet Delivery Ratio (PDR), which is a ratio

of packet correctly received to total number of packets transmitted

on a link or transmitted by sender. PDR is a packet level quantifi-

cation and calculated in both directions for satisfying 802.11 MAC

protocol and useful to identify information asymmetry present in

multi hop wireless mesh network. Second parameter used for wire-

less link quality measurement is Bit Error Rate (BER), which is the

ratio of erroneous bits to total number of bits received during a cer-

tain period of time and BER evaluates bit level reliability [37].

Other two primary parameters are Signal to Interference plus

Noise Ratio (SINR) and Received Signal Strength Indication (RSSI).

SINR is threshold based limit for received signal power at receiver

which may exceed the sum of interference and noise and it indi-

cates the quality of received signal. Whereas RSSI is signal strength

observed at receivers antenna while packet is being received and

quantifies the quality of received signal [37].

Kim et al. in [38] proposed a packet delivery ratio based mea-

surement framework for Efficient and Accurate link quality moni-

toR (EAR) for measuring link quality for multi hop wireless mesh

networks. EAR operates dynamically in one of three modes of mea-

surement including passive, cooperative and active monitoring strate-

gies. One of its salient features is effective identification of infor-


mation asymmetry in wireless links by calculation of PDR in both

direction of link which potentially improves the network utilization.

EAR is easily deployable due to its compatibility with existing multi

hop wireless networks and 802.11 based devices without any modi-

fication in any of these two layers of networks. Comparison between

simulation and experimentation results showed that EAR accurately

quantified link quality measurement with minimal overhead in multi

hop wireless networks. Problem with EAR is that its link quality

prediction is only based on packet delivery ratio, whereas there are

other measuring parameters including BER, SINR and received sig-

nal strength indication (RSSI) which are ignored by this framework.

Kurth et al. in [39] performed extensive packet delivery ration

based experimentation in 802.11-type wireless mesh network for

measuring quality and symmetry of wireless links and concluded

that channels are not homogenous. Commonly used simulators like

ns2 are based on radio propagation model which do not take into

account the practical link characteristics. They recommended that

multi-channel protocol designs must consider information symmetry

and quality of wireless link on the radio channel used for that spe-

cific link and provided some guidelines for existing multi-channel

protocol to improve their performance.

Nandiraju et al. in [40] proposed a buffer management scheme


for intermediate nodes in wireless mesh networks to fairly share

buffer for active sources and improving throughput of overall 802.11

based wireless mesh networks. Intermediate node uses proposed

QMMN algorithm to take decision on whether to admit arriving

packet in queue or discard it based on usage of granted buffer data

for that source node. All source nodes are given fair share of the

buffers on intermediate nodes that prohibit the aggressive sources

to send more data in the network. Through aggressive simulations

with tcp-alone and tcp-with-udp traffic they showed improved per-

formance for specified setting of 802.11 based wireless mesh net-

work.

2.3 Interference and Capacity Analysis

Literature relating MAC behavior analysis and capacity estimation

can be grouped into three sets. First set consists of interference mod-

els and ensuing MAC behavior analysis that considers interference

from within the transmission range. These models consider the im-

pact of interference from different links to be same, irrespective of

their relative geometric location [3, 8, 41, 42]. Second set com-

prises of location based MAC behavior and interference analysis

[5, 7, 4, 10]. Literature in this group focuses on change in MAC


behavior because of changing geometric relation of the interfering

links. Final set consists of capacity estimation based on physical

characteristics of wireless channel and mainly are based on network

measurements [43, 44, 45].

Capacity estimation of CSMA based wireless networks was first

performed by Boorstyn et al. [20]. Authors used Markov chain

based model to compute exact throughput in multi-hop CSMA based

wireless networks. However, the analysis was limited to few nodes,

given the complexity of computation. Same model was extended by

[22, 23] replacing links by stations. But [20] was not able to capture

the comprehensive access mechanism behavior specifically did not

model packet loss due to MAC behavior and also lacked binary ex-

ponential back-off mechanism. Being an NP-complete problem, it

is also not feasible to compute all the independent sets in a general

wireless networks as proposed by [20].

Bianchi [9] computed the achievable throughput by individual

nodes, given that all interfering nodes are within a transmission

range. Bianchi showed that in the absence of hidden node prob-

lem [16] and with perfect channel capture, wireless nodes exhibit

fairness for all nodes contending for channel access. Although re-

stricted to only one type of two flow interactions (i.e., coordinated

interfering links), Bianchi computed exact throughput values for dif-


ferent IEEE 802.11 DCF mode parameters. In a recent refinement in

Bianchi’s DCF modeling approach [9], Ilenia Tinnirello et. al. [46]

highlighted that hypothesis of statistical homogeneity and consecu-

tive channel slots being uncorrelated is not true. Authors proposed

a back-off decrement model to consider the correlation of consecu-

tive channel slots. Protocol and physical models of interference are

well known interference models [3] that have been used frequently

in literature for capacity estimation as well as MAC protocols and

channel assignment research. Both models lead to inaccurate inter-

ference estimation.

Analytical modeling of MAC protocol for single-hop wireless

network was presented in [47] for Aloha protocol and in [48] for

CSMA based MAC. Recently, analytical models for throughput char-

acterization have been proposed for 802.11 with backlogged stations

[9, 24]. Analysis of single-hop networks is easy and straightforward

as all the stations are within same contention region, have same pic-

ture of the channel and can coordinate for efficient channel utiliza-

tion. However this is not the situation for multi-hop general wireless

mesh networks. Prediction of per-flow throughput and starvation is

more challenging for multi hop WMN and existing literature either

worked with limited analytical details or detailed analysis only ex-

ists for restricted geometric topologies.


In [49], authors analyzed delay and capacity of CSMA based ac-

cess protocol for two hop wireless networks. Analyzing 802.11, [50]

developed a Markov chain throughput analysis model for flow-in-

middle (FIM) geometric configuration of stations and [51] presented

queuing theoretic analysis for Information Asymmetric configura-

tion of stations. But both these are based on specialized geometric

configuration and also do not model per-flow throughput in multi-

hop wireless networks.

Each flow in the network is viewed in isolation in station based

approach and packet loss probability is a function of transmission

probabilities of contending flows in the radio range. Approach based

on station is more efficient than transmission set as it does not in-

clude computation of independent sets [17]. Employing station based

approach, [19] models 802.11 with capture effects and also addressed

the hidden station problem but did not used binary exponential back-

off. [18] proposed a model for throughput computation of backlog

link in flows and employed most of the 802.11 mechanisms includ-

ing RTS/CTS, network allocation vector (NAV) and also modeled

channel errors for all links. But the proposed model do not consider

inherent coordination discrepancy which CSMA based protocols in-

curs when employed in multi hop wireless network.

Garetto et al. [5] have considered the two-flow interactions and


classified possible topologies into three categories of Senders Con-

nected (SC), Asymmetric Incomplete State (AIS), and Symmetric

Incomplete State (SIS) based on MAC behavior and throughput im-

balances. In their extended work, Michele Garetto et al. in [17]

highlighted inherent coordination discrepancy when CSMA based

protocol is employed in multi-hop wireless networks. They modeled

per-flow throughput prediction and identified dominant and starv-

ing flows in the network. For throughput prediction, they computed

unknown variables in throughput formula like busy period b expe-

rienced by an individual station and its average busy duration Tb,

also computed most complicated variable in an arbitrary topology

that is conditional packet loss probability p. As mentioned earlier

that computation of packet loss probability depends on geometric

configuration of the stations in the network and computation of con-

ditional packet loss probability in [17] depends on two flow analysis

in [5] and both approaches do not differentiate between interfering

links in transmission and carrier sense range.

Garetto et al. [4] computed per link forwarding capacity for gen-

eral multi-hop wireless networks using two-flow interactions. In

cases where transmission and sensing ranges are considered same,

the analytical results accurately predict throughput achieved through

simulations. However, the model does not capture the impact of in-


terference from links within sensing range. The work has been ex-

tended by Razak et al. [10, 7, 52]; however, significant gap exists

between analytical and simulated results. Research presented in this

document is focused on differentiating between interference intro-

duced from transmission range and from carrier sensing range. This

results in new categories that have high occurrence probability in

realistic multi-hop wireless networks.

Researchers recently proposed few throughput estimation mod-

els for multi hop wireless networks. Beakcheol Jang et. al. [53]

proposed analytical model for saturated throughput but only address

interference from hidden terminal for infrastructure 802.11 network.

Bruno Nardelli et. al. in [54] derived a closed form expression for

throughput characterizing hidden terminals, information asymme-

try and flow-in-the-middle. Thomas Begin et. al. [55] proposed

throughput prediction modeling framework which caters affect of

interference on capacity of contending flows in scenarios including

two flows in opposite direction and hidden node problem. These

models [53, 54, 55] address subset of the overall problem and are

unable to characterize throughput imbalances due to location of in-

terfering links.

Some of the recent work tried to estimate and model the through-

put of flows in the network based on gathered measurements. Anand


Kashyap et. al. in [45] analytically models affect of interference

on throughput based on measurements gathered from the same net-

work. They separately model sender and receiver side interference

and then predict throughput of the link but this model is unable

to differentiate between interference from transmission and carrier

sense range. Fairness mitigating algorithm FairMesh [43] can accu-

rately detect unfairness and tries to achieve approximate max-min

fairness by adjusting minimum congestion window. Emma Fitzger-

ald et. al. in [44] developed a distributed and cooperative algorithm

which merges multiple transmissions from neighboring nodes into

a combined schedule and finds appropriate gaps to accommodate

transmission of the said node. Both these studies [43, 44] are limited

as they are simulation based and both use general DCF as underlying

MAC protocol.

There are some studies on capacity scaling for mobile nodes in

multi hop wireless networks. Michele Garetto et. al. [56] did an

asymptotic capacity analysis for general mobile ad-hoc networks.

They highlighted the conditions under which node mobility can be

exploited to increase throughput of individual node and proposed

routing and scheduling scheme with an objective to optimize net-

work transport capacity. In [57], Authors extended previous capacity

scaling laws [56] for more wider class of wireless networks. In this


extension, they also considered heterogeneous nodes in clustered

topology, identified different regimes around one or more nodes

and characterized asymptotic capacity for each identified regime

and whole network. In another extension of the same study [58],

they also considered correlated movements of a group of nodes and

assume fast mobility with an objective to maximize throughput of

individual node. They discovered that correlated movement of wire-

less nodes have impact on delay and throughput of the network and

at times can lead to better throughput performance as compared to

independent node mobility.

Few studies are also done on proposing programmable MAC to

adopt to temporal interference profiles in general multi hop wire-

less network. Ilenia Tinnirello et. al. [59] proposes wireless MAC

processor with an ability to execute programmable MAC commands

on runtime to achieve desired MAC operation using low cost hard-

ware wireless cards. They implemented wireless MAC processor

for only three wireless scenarios as a proof of concept and validated

that future wireless MAC needs access flexibility and adaptability.

Giuseppe Bianchi et. al. in [60] propose MAClets, a software pro-

gram that can be executed over wireless cards, reconfigures MAC

protocol seamlessly and enable MAC adaptation to current spectrum

conditions for optimized performance. They validate the viability


and flexibility of the proposed concept with help of different experi-

ments. Later in [61], Giuseppe Bianchi et. al. argued that an abstract

description of MAC logic as extensible finite state machine appears

to be viable and effective solution for deploying and modeling real-

istic programmable MAC protocols.

Among other capacity estimation literature, Li et al. [62] have

performed the throughput analysis of a single access point for IEEE

802.11g radios. Dinitz [63] have proposed distributed algorithms for

wireless nodes to achieve optimal throughput in distributed multi-

hop wireless networks. The author have used protocol and physical

models for interference. Kawade et al. [64, 65] have compared the

performance of IEEE 802.11g and 802.11b radios under co-channel

interference by considering the physical layer characteristics. The

authors have concluded that IEEE 802.11g networks are more resis-

tant to co-channel interference while channel separation improves

performance of both types of networks. Weber et al. [66] have

computed the upper and lower bound network capacity for multih-

hop wireless networks using different physical channel conditions.

The authors have computed maximum physical transmission capac-

ity and optimal number of nodes that achieve the maximum capacity.

Fu et al. [67] have analyzed the general CSMA protocol and pro-

posed the concept of commulative interference model where hidden


node problem can be avoided. The authors have also proposed in-

cremental power carrier sensing that can help nodes identify the dis-

tance from potential interfering nodes and better plan the transmis-

sions. Vitturi et al. [68] have proposed new techniques for rate adap-

tation to cater the collisions problem and compared the performance

with automatic rate fallback technique. The authors have shown that

the performance of new techniques is better in terms of retransmis-

sions required. Qiao et al. [69] have also proposed transmit power

control and rate adaptation to achieve low energy consumption in

IEEE 802.11a/h systems. The objective is to minimize consumed

energy, although throughput gains have also been reported.

2.4 Applications of Capacity Analysis

Application of interference and capacity analysis includes channel

assignment, routing and topology control in multi hop wireless mesh

network. Related work in literature assumed any of the propose in-

terference models [4, 3, 8] discussed earlier and by using these mod-

els propose their own channel assignment, routing and topology con-

trol strategies, investigated and compared their results for improved

performance [70, 71, 72]. If interference model is changed, all appli-

cations based on interference analysis need to be reevaluated for the


more practical and accurate prediction of interfering links in multi

hop wireless mesh network. We discussed some application where

they assumed any of the existing interference models for their inves-

tigations based on interference analysis.

Alotaibi et al. in [70] proposed interference aware analytical

model for routing in multi-hop wireless mesh network for through-

put maximization for two given set of topologies. They assumed

protocol model of interference [3] and showed improved results of

their proposed MIPL analytical model in comparison with existing

Open Shortest Path First (OSPF) algorithms. They redefined inter-

ference into two types, in first type two senders are within carrier

sensing range of each other and in second type one of the senders

is in carrier sensing range of the other receiver and referred second

type as interference range. They developed a wage definition of in-

terference range; therefore the analytical model proposed by them

is based on limited analysis of interference and does not accurately

capture all interfering links in multi hop wireless network.

Liu et al. in [71] worked for topology control of multi-channel

multi-radio wireless mesh networks using directional antennas; they

proposed a three step antenna orientation technique with the objec-

tive to minimize interference. In first step constructed routing trees

with balanced traffic links, in second step radio assignment to links


so that traffic load per radio is kept balanced and in third step ad-

justed antenna orientation and channel assignment with the objec-

tive to minimize interference in the wireless mesh network. They

assumed extended protocol model with simplified interference range

RIi = qRTi where q >= 1 is the ratio of interference to transmission

range. Their results showed improvement in network capacity by

tuning antenna orientation and channel assignment but underlying

interference model does not capture interference accurately hence

showed capacity improvement may not contribute to practical de-

ployments of multi hop wireless mesh networks.

Kumar et al. in [72] proposed an analytical model for capacity

and interference aware link scheduling with channel assignment in

wireless mesh networks. They proposed interference aware routing

metric for improving network throughput, grouped and sorted links

based on this metric and constructed link assignment metric based

on interference aware metric. They proposed link scheduling and

channel assignment algorithms with an objective of throughput max-

imization by avoiding interference in wireless mesh network. Simu-

lation results showed improved throughput as compared to existing

techniques but again they assumed very wage underlying interfer-

ence model, followed protocol interference model [3] considering

interference range twice the transmission range for all radios in the


network. Similarly assuming such interference model does not cap-

ture interference accurately as in practical multi hop wireless mesh

network.

2.5 Summary

Accurate interference analysis in wireless mesh networks is critical

to routing, channel assignment, topology control and capacity es-

timation in multi hop wireless mesh networks. Existing literature

assumes any of the earlier proposed interference models including

protocol, physical, extended physical and location aware interfer-

ence model [4, 3, 8]. These models do not capture practical aspect

of interference because they do not differentiate between interfer-

ence from transmission and carrier sensing range. Physical and pro-

tocol models [3] of interference do not consider nodes within carrier

sensing range of transmitter, however these nodes are considered

as interfering and are not allowed to carry simultaneous transmis-

sions by CSMA based MAC protocols. Extended protocol model

[8] considers nodes within carrier sensing range of receiver as well

as transmitter, however it assumes that interference from all interfer-

ing links is same, which is not the case as explained by Garetto et al.

in [5].


Location aware interference model lately proposed by Garetto et

al. [4] is based on their own analysis of two flow topologies in [5] but

this work on two flow topologies does not differentiate between in-

terference originated form within transmission range or from carrier

sensing range. Their proposed model [4] captures interfering links

relatively better than earlier proposed models in [3, 8] but do need

improvements to capture all interfering links accurately in multi hop

wireless mesh networks. Most of the work done on interference and

capacity analysis of two-flow topologies in multi hop wireless net-

works [4, 10, 7, 5] lacks practical distinction between transmission

range, carrier sensing range and practical realization of interference.

Assumption of same transmission and carrier sensing range does not

provide accurate interference and capacity analysis model for multi-

hop WMN.

Chapter 3

Two flow classification and

occurrence probability

Within a multi-hop network, a sender receiver pair (referred as flow

throughout the rest of thesis) interacts with multiple flows in the

neighborhood. Each interaction impacts the throughput of the sur-

rounding flows, resulting in complex chain of interactions. In or-

der to understand such interactions and the resulting impact on the

achievable throughput of each flow, it is important to understand

the possible interactions between two flows in isolation. Based on

this understanding, a general model for wireless interactions in a

multi-hop wireless network is conceivable, which can predict the

achievable throughput of individual single hop flows. In this section,

possible interactions of two flows are categorized based on geomet-

ric location of the nodes of the flows. The differences of proposed

39

CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY40

categorization from the categories defined in prior work [5, 7] are

highlighted. In the subsequent section, the occurrence probability of

each proposed two-flow category is calculated.

3.1 Two Flow Topologies

Based on the interference interactions, there are a total of 34(81)

possible two flow topologies while 53 of these topologies are unique.

Given the restriction that the transmitters of flows must be within the

transmission range of the respective receivers and the fact that carrier

sensing range is ≈ 2.7 times the transmission range (through simu-

lations and experimentations), only 25 topologies are physically re-

alizable in a multi-hop wireless network. Remaining 28 topologies

have zero occurrence probability. The 25 unique possible topologies

have been classified into six categories, depending upon the types of

the four interference interactions and the MAC behavior. Following

sections explain the interference interactions of the categories.

3.1.1 Senders Connected

Senders Connected category represents the topologies where the trans-

mitters A and B of the single hop flows Aa and Bb are within the


transmission range of each other. That is:

d(A, B) ≤ TR

Remaining three interference interactions are not significant in

this case. Seven topologies belong to this category and are shown in

Figure 3.1. Node placement of a sample topology is shown in Fig-

ure 3.2(a). This category exists in the classification by Garetto et al.

[5] with the same name. Razak et al. [7] have divided this category

into two categories of senders connected symmetric interference and

senders connected asymmetric interference. However, as shown in

subsequent section, the MAC behavior and resulting throughput pro-

file of all topologies belonging to this category is same and form a

single category.

3.1.2 Symmetric Sender Receiver Connected

If the interference interaction AB is not connected (but within CSR)

and interference interactions Ab and aB are both connected then

the topology belongs to the category of symmetric sender receiver

connected. The topologies fulfill following criteria:

d(A, B) > TR & d(A, B) ≤ CSR

d(a, B) ≤ TR & d(A, b) ≤ TR

d(a, b) ≤ CSR


BA

ba

C

C

C

C

(a)

BA

ba

C

C

S

C

(b)

BA

ba

C

C

S

S

(c)

BA

ba

C

S

S

S

(d)

BA

ba

C

S

S

C

(e)

BA

ba

C

S

C

C

(f)

BA

ba

C

S

S

(g)

Figure 3.1: Senders Connected Topologies


(a) SC (b) SSRC

Figure 3.2: Sample nodes placement.

Two topologies belong to this category as shown in Figure 3.3. Sam-

ple node placement is shown in Figure 3.2(b). Garetto et al. in their

extended work [4] refer to this category as near hidden terminals.

Same category exists with the name of symmetric incomplete state

in their original work [5] as well as in work by Razak et al. [7]

but contains an additional topology. The additional topology is not

realistic when CSR ≥ 2 ∗ TR.

3.1.3 Asymmetric Sender Receiver Connected

If the interference interaction AB is not connected (but within CSR)

and one of the interference interactions Ab and aB is connected

while other interaction is either disconnected or sensing, then the


BA

ba

S

S

C

C

(a)

BA

ba

S

C

C

C

(b)

Figure 3.3: Symmetric Sender Receiver Connected Topologies

resulting topology belongs to the category of asymmetric sender re-

ceiver connected. Three topologies belong to this category as shown

in Figure 3.4(a), 3.4(b), 3.1.3. The topologies belonging to this cat-

egory fulfill following distance criteria:

d(A, B) > TR & d(A, B) ≤ CSR

d(A, b) ≤ TR & d(a, B) > TR

d(a, b) ≤ CSR

This category exists with the name of asymmetric incomplete state

in the categorization of Garetto et al. [5] and Razak et al. [7]. How-

ever, an additional topology (Figure 3.4(a)) is part of this category in

the proposed categorization because of different sensing range and

transmission range.


BA

ba

S

S

S

C

(a)

BA

ba

S

S

C

(b)

BA

ba

S

C

S

C

(c)

Figure 3.4: Asymmetric Sender Receiver Connected Topologies

(a) ASRC (b) RC



3.1.4 Receivers Connected

This category consists of the topologies where the interference in-

teractions AB, aB and Ab are not connected (i.e., either sensing or

disconnected) and the interference interaction ab is connected. The

euclidean distances of interference interactions are:

d(A, B) > TR

d(a, B) > TR & d(A, b) > TR

d(a, b) ≤ TR

Two topologies belong to this category as shown in Figure 3.6(a),

3.6(b). A sample node placement is shown in Figure 3.5(b). Razak

et al. [7] have referred to this category as interfering destinations

incomplete state. However, a different MAC behavior has been ob-

served in the proposed work compared to the one reported by Razak

et al.. This is explained in the subsequent section.

3.1.5 Symmetric Not Connected

This is new category and does not exist in any of the prior cat-

egorization. If none of the four interference interactions is con-

nected and the sender receiver interactions aB and Ab are symmet-

ric then the topologies belong to the category of symmetric not con-

nected. Seven topologies belong to this category and are shown in


BA

ba

S

C

S

S

(a)

BA

baC

S

S

(b)

Figure 3.6: Receivers Connected Topologies

Figures 3.7. Sample node placement is also shown in Figure 3.8(a).

The topologies satisfy following distance criteria:

d(A, B) > TR

(TR < d(a, B) ≤ CSR & TR < d(A, b) ≤ CSR) OR

(d(a, B) > CSR & d(A, b) > CSR)

d(a, b) > TR

3.1.6 Asymmetric Not Connected

This category is also new and does not exist in any prior catego-

rization. If none of the four interference interactions is Connected

and the sender receiver interactions aB and Ab are asymmetric then

the topologies belong to the category of asymmetric not connected.

Four topologies belong to this category as shown in Figures 3.9.

Figure 3.8(b) is geometric representation of a sample topology. The


BA

ba

S

S

S

S

(a)

BA

ba

S

S

S

(b)

BA

ba

S

S

(c)

BA

baS

S

S

(d)

BA

ba

S

S

(e)

BA

ba

S

(f)

BA

baS

(g)

Figure 3.7: Symmetric Not Connected Topologies

(a) SNC (b) ANC



BA

ba

S

S

S

(a)

BA

ba

S

S

(b)

BA

ba

S

(c)

BA

baS

S

(d)

Figure 3.9: Asymmetric not connected Topologies

topologies satisfy following interference interaction distance crite-

ria:

d(A, B) > TR

TR < d(A, b) ≤ CSR & d(a, B) > CSR

d(a, b) > TR

3.2 Categories occurrence probability

How frequently the topologies belonging to each category can exist

in a general multi-hop wireless network? Specifically, what is the

occurrence probability of the newly identified categories? Answer


to these questions is important in identifying the impact of each cat-

egory on interference profile of the links in general multi-hop wire-

less networks. Geometric analysis has been employed to find out

the occurrence probability of the categories. Perfect circular disks

are assumed for area under transmission range, carrier sensing range

and the network with the disk radii defined as rtr , rcsr and rn respec-

tively. Network radius is assumed to be rn = 0.5 × (2 × rtr + rcsr )

which covers maximum possible distance for a valid placement of

the nodes such that the resulting flows are interfering. Note that at

times the carrier sensing range of nodes can be outside the total net-

work area; however, the ratio of area of interest and the total area

remains unaffected.

For each category, four interference interactions AB, Ab, aB and

ab are considered individually. For each pair of nodes within the in-

terference interaction, one node is assumed to be at a fixed location.

The area around first node where the second node can possibly exist

is computed, given the placement constraints introduced by the spe-

cific category. Under the assumption of circular disk ranges, the area

is mostly equivalent to either the area of a disk or the area of intersec-

tion of two disks with known radii. The ratio of computed area to the

maximum possible network area gives the probability of occurrence

of the interference interaction. Multiplying the occurrence probabil-


ities of four individual interactions gives the occurrence probability

of the category.

The expressions for disk area and the area of interaction of two

disks are frequently used throughout the computations. The expres-

sion for area of circular disk with radius r using onion method is

given as: ∫ r

02πxdx (3.1)

The expression for area of intersecting circles of same radius r and

distance between radii as d is given as:

2d2cos−1(d2r

)− d2

√4r2 − d2 (3.2)

The occurrence probability of each category is computed in subse-

quent section using the two listed expressions. For sake of brevity,

the final expression for probability of each category is given with

brief description of the expression.

3.2.1 Senders Connected

The transmitters of both flows must be within the transmission range

of each other. This leads to a disk area with radius rtr . The proba-

bility of AB to be connected is achieved by integrating 2xr2n

over the

interval 0 to rtr . Given that AB is connected, maximum distance

between nodes A and b (a and B) is 2rtr . The probability of two


events can be achieved by integrating 2xr2n

over the interval 0 to 2rtr .

Finally, the two receivers can be located anywhere in the network.

The occurrence probability of senders connected category is given

as:

PSC =∫ rcsr

0

∫ 2rtr

0

∫ 2rtr

0

∫ rtr

0

2wr2n

2xr2n

2yr2n

2zr2n

dwdxdydz (3.3)

3.2.2 Symmetric Sender Receiver Connected

Topologies belonging to SSRC category have the interference inter-

action AB as sensing, i.e., rtr < d(A, B) ≤ rcsr . The interactions Ab

and aB should be connected. Therefore, the distance d(A, B) is re-

stricted to 2 ∗ rtr . Furthermore, the receiver a (or receiver b) should

be within transmission range of sender A (or sender B) as well as

B (A). Consequently, the possible placement area of a around node

B is given by the area of intersection of the two circles with radius

rtr and centers separated by the distance rtr . The area is given by

expression 3.2 where d(A, B) > rtr results in maximum distance be-

tween a and b to be√

3rtr . The probability of the category is given

as:PSSRC = (2d2cos−1(

d2r

)− d2

√4r2 − d2)2×∫ √3rtr

0

∫ 2rtr

rtr

2wr2n

2zr2n

dwdz(3.4)

where r = d = rtr .


3.2.3 Asymmetric Sender Receiver Connected

In this category the condition rtr < d(A, B) ≤ rcsr holds. Simi-

larly d(A, b) ≤ rtr and area around A where b can exist is given by

expression 3.2. However, for interaction aB, rtr < d(a, B) < rn.

Maximum possible distance between a and b can be 2rtr . The prob-

ability expression is given as:

PASRC =(2d2cos−1(d2r

)− d2

√4r2 − d2)×∫ 2rtr

0

∫ rn

rtr

∫ 2rtr

rtr

2wr2n

2yr2n

2zr2n

dwdydz(3.5)

where r = d = rtr .

3.2.4 Receivers Connected

The two receivers should be in transmission range of each other. The

interactions Ab and aB are sensing. Given the fact that d(a, b) < rtr ,

the conditions rtr < d(a, B) < 2rtr and rtr < d(A, b) < 2rtr must

hold. The probability of the category is given as:

PRC =(2d2cos−1(d2r

)− d2

√4r2 − d2)×∫ 2rtr

rtr

∫ 2rtr

rtr

∫ rn

rtr

2wr2n

2yr2n

2zr2n

dwdydz(3.6)

where r = d = rtr .


3.2.5 Symmetric Not Connected

The four interference interactions in this category are sensing with

only restriction on maximum possible area. The probability is given

as:

PSNC = (∫ rn

rtr

2zr2n

dz)4 (3.7)

3.2.6 Asymmetric Not Connected

In this case, the interference interaction aB must be disconnected.

The area of interest for this case is approximated by integrating 2z

over the range rn to rcsr , which is approximately equal to the area

outside CSR. The occurrence probability of the category is given as:

PANC =∫ rcsr

rn

∫ rcsr

rtr

∫ rn

rtr

∫ rn

rtr

2wr2n

2xr2n

2yr2n

2zr2n

dwdxdydz (3.8)

3.2.7 Occurrence Probability Values

The probability equations are dependent only on the transmission

and carrier sensing ranges. All probabilities are closed form ex-

pressions and can easily be computed. To verify the correctness of

expressions, a program has been implemented in Java. The program

considers a fixed network area with points arranged in the area as

uniform grid. Four nodes are placed on all possible points and their

interference interactions are computed to identify the category of the


Figure 3.10: Occurrence probabilities of categories

topology. Non-possible topologies have been eliminated and the re-

maining topologies normalized to attain the occurrence probabilities

of the categories. The probability values achieved through program

and the computed values using probability expressions have been

plotted in Figure 3.10. The plot shows excellent match between all

computed values and the values achieved through the program.

Figure 3.10 shows that the occurrence probability is significantly

high for the categories that are purely based on interactions because

of carrier sensing range (SNC = 0.45 and ANC = 0.24). In the sub-

sequent section, we show that these interference interactions sig-

nificantly affect the throughput of interfering links. Therefore, the

categories cannot be ignored.


3.3 Summary

This Chapter starts with a discussion of MAC behavior of two single

hop IEEE 802.11 standard based interfering flows. Then all possi-

ble two flow topologies have been identified using realistic trans-

mission and carrier sensing ranges. The identified categories have

been divided into six categories based on the MAC behavior as well

as geographic placement of the four interfering nodes. Closed form

expressions for occurrence probabilities of all identified categories

are computed to show that all categories have significant probability

of occurrence in a general multi-hop wireless network.

Chapter 4

Interference and throughput

analysis

IEEE 802.11 wireless interfaces use carrier sense multiple access

(CSMA) with collision avoidance (CA) protocol for acquiring wire-

less channel access. This Chapter starts with brief explaination of

CSMA/CA protocol as used in IEEE 802.11 (Only extended mode

is explained). Parameters affecting the throughput are discussed and

the throughput expressions derived by Bianchi [9] and Kumar et al.

[73] are listed. Subsequently, the expressions for the parameters in

the throughput expressions are derived for the two flows for each

category, throughput for different packet sizes is computed and the

computed values are compared with simulated results to highlight

the accuracy of the categorization and the throughput analysis.

57

CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 58

4.1 Protocol Behavior of CSMA/CA

In IEEE 802.11 MAC, time is considered to be slotted and the slot

interval is represented by σ. Based on CSMA protocol, when a node

has data to transmit, it sets a back-off counter by selecting a ran-

dom value from the range [0, Wi − 1]. For first attempt W0 = 16

for IEEE 802.11a/g radios. The counter is decremented whenever

the channel is found idle for the slot interval. If the channel is not

idle because of an on-going transmission from a neighboring node,

the back-off counter freezes. When the counter reaches zero and

the channel is idle, the node initiates transmission by sending ready

to send (RTS) frame. The transmitting node waits for the response

from intended receiver, which is in the form of clear to send (CTS)

frame. If the CTS is not received within certain period of time (SIFS

+ 2*Propagation delay), the RTS is assumed to be lost (due to col-

lision or because of busy channel at receiver end). In case of col-

lision, the node resets the back off counter by selecting a random

value from the range [0, 2i ∗W0 − 1] where i is the number of re-

transmission attempt and is known as back-off stage. The entire

procedure of channel access is repeated. If the CTS is received,

the channel is reserved for the particular transmission and the node

proceeds with transmission of Data packet, followed by ACK from


receiver. The four frames RTS, CTS, Data and ACK are separated

by Short Inter-Frame Space (SIFS) while ACK frame is followed by

DCF Inter-Frame Space (DIFS). In case of IEEE 802.11g radios, ev-

ery frame is followed by signalextension, which is idle interval of

6µs, necessary for proper reception of signal. The nodes other than

the transmitter and receiver that correctly receive the RTS or CTS

frame set the NAV for remaining period of transmission and freeze

their activity on the channel.

Assuming that the transmitting nodes are continuously back logged,

a wireless node can find the channel in one of the following four

states. (i) Idle with no transmission going on (ii) Busy because of

transmission of another node (iii) Successful transmit of the node

itself (iv) Unsuccessful transmit of the node itself with transmitted

frame colliding with transmission from another frame. Throughout

the analysis, it is assumed that if a packet is received collision free, it

can successfully be decoded and no errors occur because of channel

noise. Using random back-off mechanism of CSMA protocol, the

probability τ that a node transmits following an idle slot is given by

the equation [73]

τ =2(1− 2p)(1− pm+1)

q(1− pm+1) + W0(1− p − p(2p)m′(1 + pm−m′q))(4.1)

where q = 1 − 2p, m is maximum back-off stage and m′ is the

stage when upper limit of the range for random back-off reaches its


maximum value. p is conditional packet loss probability due to col-

lision. Keeping in view the above mentioned states, the throughput

(in Pkts/s) of a node is given as [5]

T =τ (1− p)

τ (1− p)Ts + τpTc + (1− τ )(1− b)σ + (1− τ )bTb(4.2)

where b is the probability that a node finds a slot to be busy while

Ts, Tc and Tb are the average durations of successful transmission,

collision and busy interval respectively as observed by the node.

For all two flow categories, the values of Ts, Tc and Tb are known.

Throughput of a sender can be computed, given the values of busy

probability b and conditional packet loss probability p. Both values

are dependent upon the interference interactions of the categories

and need to be computed for individual categories. The values of

all known parameters for extended access mode of IEEE 802.11g

radio assuming homogeneous network and extended rate physical

layer are given in Table 4.1. For other radio types, the values can be

updated to get the throughput results.

In the following, the MAC behavior based on interference in-

teractions for the identified categories is explained and the known

parameters are computed to compute the achievable throughput for

both flows of each category.


4.2 Senders Connected

MAC Behavior of this category is simplest to understand. The senders

A and B of the two flows are within the transmission range of each

other; therefore, the RTS packet transmitted by sender A is success-

fully received by sender B and vice versa. Therefore, sender B sets

its network allocation vector (NAV) and freezes its activity until the

transmission by sender A is complete. The occurrence of busy event

for any flow is equal to the occurrence of the transmission event of

the alternate sender, which has the probability τ . Therefore busy

probability of any sender is given by b = τ . Collision of RTS for

any sender occurs only when the two senders simultaneously start

RTS transmission following random back-off. Therefore, condi-

tional packet loss probability of any flow is given by p = τ . Channel

busy time Tb is equal to Ts. Replacing these values in equations 4.1

and 4.2 gives the value of throughput of a single flow. Based on ran-

dom access of CSMA/CA and completely symmetric channel view,

the throughput of both flows is equal. Bianchi [9] computed the

throughput for flows under this category and the results of two com-

putations are same. Figure 4.1 shows the throughput achieved by the

two flows in senders connected category for different packet sizes.

It can be seen that the analytically computed throughput perfectly


200 300 400 500 600 700 800 900 1000 11002

3

4

5

6

7

8

9

Data Payload Size (bytes)

Thr

ough

put (

Mbp

s)

model flow Aopnet flow A

Figure 4.1: Throughput (Senders connected flows).

matches the simulated throughput for all packet sizes. Maximum

achievable throughput for any flow is 10.68 Mbps for the packet

size of 1500 Bytes.

4.3 Symmetric Sender Receiver Connected

The senders A and B of the two flows in this category (and all subse-

quent categories) are not within the transmission range of each other.

Therefore, the RTS frame transmitted by sender A is not successfully


Parameter Value

Data Rate 54 Mbps, 216 bits/symbol

Basic Rate 6 Mbps, 24 bits/symbol

W0 16

Wmax 1024

m 6

m′ 6

Symbol duration 4µs

σ 9µs

SIFS 10µs

DIFS 28µs

PHY 20 + 6µs (Including signal extension)

RTS, CTS, MAC, ACK 20, 14, 34, 14 Bytes at basic rate

(ceil(bits/(bits/sym)) x 4µs) + PHY

Data at data rate, measured in symbol duration

Ts RTS + CTS + Data + ACK +

3SIFS + DIFS

Tc RTS + DIFS

Table 4.1: ERP IEEE 802.11g Parameters


decoded by sender B and vice versa. However, the channel is sensed

busy during RTS transmission, preventing the other sender from ini-

tiating a transmission. This is different from SIS category proposed

by Garetto et al. [5] where senders are assumed to be outside sensing

range and cannot sense the RTS transmitted by sender of the alter-

nate flow. The receivers of both flows are within the transmission

range of the alternate senders, i.e., interference interactions Ab and

aB are connected. This means that the receivers can successfully

decode the RTS frame transmitted by the alternate senders resulting

in setting NAV at alternate receiver. Similarly, senders can success-

fully decode the CTS packet transmitted by the alternate receivers.

Therefore, collision can only occur if one sender starts transmission

of RTS during the idle interval between RTS and CTS transmission

of the alternate flow.

To compute the throughput of the flows in SSRC category, we

start with busy probability. Busy probability b of each flow is equal

to the successful transmission probability of the alternate flow. To

compute successful transmission probability and the conditional packet

loss probability, we adopt the method used by Garetto et al. [5] for

analysis of SIS category (See section 5 of [5]). Collision occurs if

sender B starts RTS transmission during SignalExtension + SIFS

(6µs) interval between RTS and CTS frames of flow Aa. This de-


A RTS (A) CTS (a) ACK (a) DIFS

a RTS (A) CTS (a) ACK (a) DIFS

B ƒ CTS (a)

Receiver b RTS (A)

Channel sensed idle Channel busy Signalextension & SIFS

NAV

NAV

Sender Data (A)

Receiver Data (A)

Sender

Figure 4.2: SSRC channel view

pends upon two factors: (i) Number of transmission opportunities

where collision can occur, which is given by f = ceil((SIFS + 6)/σ)

as shown in Figure 4.2 and (ii) the back-off stage of sender B, which

defines the probability of transmission in a given slot for sender B.

The probability of transmission is given by γi = 21+Wi

where i is the

back-off stage. The interaction of the two senders during interval f

can be modeled as two dimensional Markov model. Each state of

the model represents the back-off stage of both senders, resulting

in m2 states. In a general state (i , j), the transition probabilities are

given by (1−γi)(1−γj), γi(1−γj)f , (1−γi)fγj and γiγj for no trans-

mission by any node, successful transmission of node i , successful

transmission of node j and unsuccessful transmission by both nodes

respectively. Steady state equations can be used to compute the state

probabilities π(i , j).

Expressions for computation of throughput along with the param-


Parameter Value

Throughput psTspsTs+pcTc+pIσ+psTs

psΣi ,jπ(i ,j)γi (1−γj )f

Σi ,jπ(i ,j)(γi (1−γj )f +γiγj )

pc

∑i ,j π(i ,j)γiγj∑

i ,j π(i ,j)(γi (1−γj )f +γiγj )

pI∑

i ,j π(i ,j)(1− γi)(1− γj)

γi2

Wi +1

f ceil((SIFS + 6)/sigma) = 2

Throughput 0.0011 pkts/µs

Table 4.2: SSRC Computation Parameters

eter values are summarized in Table 4.2. Figure 4.4(a) summarizes

the analytical and simulated results for SSRC category. A perfect

match can be seen in the two results for all packet sizes. It may be

noted that the aggregate throughput of the two flows is lesser than

the aggregate throughput of SC category. This is because of the

higher transmission losses and longer binary exponential back-offs,

attributed to the higher value of conditional packet loss probability.


4.4 Asymmetric Sender Receiver Connected

In this category, the two senders A and B are outside the transmis-

sion range of each other. The receiver of flow Bb is within the trans-

mission range of sender A while receiver of flow Aa is either within

carrier sensing range or outside the range of sender B. This results

in different view of channel for each flow. If RTS frame is trans-

mitted by sender A, it is received by receiver b, which sets the NAV

and remains silent for the entire transmission of the flow Aa. The

transmission of flow Aa can be unsuccessful if sender B starts the

RTS transmission during the interval between RTS and CTS frames

of flow Aa, which is sensed idle by sender B. In case of topology in

Figure 3.4(b), this interval increases by the duration of CTS frame

because sender B cannot sense the activity of receiver a. This in-

formation is used to compute collision probability of flow Aa. This

behavior of the category is significantly different from AIS cate-

gory proposed by Garetto et al. [5] where conditional packet loss

probability of flow Aa is zero because of assumption that the two

senders are outside the range of each other. Note that transmission

of flow Bb in all these scenarios will not be successful given the

fact that receiver b has set the NAV after receiving RTS frame from

sender A. Flow Bb can have a successful transmission only when


the RTS frame from sender B is initiated while flow Aa is in back-

off stage. In this case, sender A senses RTS frame and assuming the

channel to be busy, it does not initiate transmission. Subsequently

it receives CTS frame and sets the NAV resulting in busy period for

flow Aa and successful transmission on flow Bb. The probability

of this event is computed by considering the available transmission

opportunities for sender B that can lead to successful RTS transmis-

sion.

To compute the throughput of the two flows, first of all, the trans-

mission opportunities for flow Bb where a successful transmission

can occur are considered. A successful transmission on flow Bb can

only take place if sender B can transmit entire RTS frame during

SignalExtension + DIFS interval and the back-off period of sender

A. This interval is shown as D + iσ in Figure 4.3. Note that the

SIFS interval between frames is also sensed idle by sender B but is

too small for complete RTS transmission and can be ignored. Fur-

ther note that for topology in Figure 3.4(b), CTS and ACK packet

transmissions are also sensed as idle for sender B; however, a trans-

mission during this interval will not lead to successful transmission

because of the fact that receiver b can sense the transmissions from

receiver a. Conditional packet loss probability is the inverse of the

probability that sender B successfully transmits RTS frame during




B f

Receiver b RTS (A)


NAV

D

Sender Data (A)

Receiver Data (A)

Sender

Figure 4.3: ASRC channel view

interval D + iσ. Garetto et al. have computed this probability using

the expression

pB = 1−2(max(0, D +

∑W0i=0 iσ))

W0(2Ts + (W0 − 1)σ)(4.3)

where D = SignalExtension+DIFS. Using this equation, packet

loss probability of flow Bb can be computed in terms of all known

variables. Replacing pB in equation 4.1 gives transmission probabil-

ity τB for flow Bb. Throughput computation of flow Bb also requires

the value of busy probability bB which is equal to the transmission

probability τA of flow Aa. Therefore, we need to compute the trans-

mission probability of flow Aa in order to compute the throughput

of flow Bb.

Transmission probability τA of flow Aa is dependent upon the

conditional packet loss probability pA. In case of ASRC category,

RTS frame transmitted by sender A is sensed by sender B as busy


period. However, SignalExtension + SIFS interval following RTS

transmission is sensed as idle by sender B. If sender B initiates RTS

transmission during this event, it will result in unsuccessful recep-

tion of CTS from a at sender A, which is the event of collision for

flow Aa. Therefore, probability of packet loss for flow Aa can be

computed by modeling the probability of the event of RTS transmis-

sion by sender B during interval SignalExtension + SIFS between

RTS and CTS transmission by flow Aa. This event can be modeled

as one dimensional markov model with m states. The expressions

in Table 4.2 are valid for the purpose with the difference of number

of states and the variable γj replaced by τB. Note that variable f in-

cludes additional interval of CTS for the topology of Figure 3.4(b).

Conditional packet loss probability for flow Aa is given by the ex-

pression for pc. Computed value can be used to compute the value

of τA using equation 4.1. Given that busy probability bB of flow

Bb is equal to the transmission probability τA of flow Aa and busy

time is equal to Ts − DIFS − SignalExtension, all parameters for

throughput computation of flow Bb are known. Equation 4.2 can be

used to get the throughput value for flow Bb.

Busy probability bA of flow Aa is given in terms of throughput

(TB) of flow Bb as

bA =τTsTB + (1− τ )σTB

(1− τ )(1 + σTB − TbTB)(4.4)


The throughput of flow Aa can be computed using equation 4.2 in

terms of all known parameters. Figure 4.4(b) shows the through-

put of both flows using analytical and simulated results for different

packet sizes. It can be seen that there is a huge imbalance of through-

put between two flows for all packet sizes with flow Bb severely

suffering. This category can be considered as the main cause of bot-

tleneck links in a general multi-hop wireless network.

4.5 Receivers Connected

Receiver connected topologies have the interference interactions AB,

Ab and aB as not connected while interference interaction ab is

connected. The MAC behavior of the two topologies belonging to

this category is slightly different, although the throughput achieved

by the two flows in both categories is same. In case of topology of

Figure 3.6(a), interference interaction AB is sensing. This means

that sender B can sense the channel to be busy during RTS transmis-

sion of sender A as shown in Figure 4.5(a). However, SignalExtension+

SIFS interval following RTS transmission is sensed as idle and sender

B can initiate its own RTS transmission during this interval, result-

ing in a collision. Conditional packet loss probability of both flows

can be computed by considering this event. Analysis for SSRC cate-


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model flow Aopnet flow Amodel flow Bopnet flow B

(a) SSRC

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10

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put (

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(b) ASRC

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4

4.5

5

5.5

6

6.5

7


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(c) RC

Figure 4.4: Per flow throughput

gory can be used for the purpose with f = ceil((SignalExtension +

SIFS)/σ) = 2 and busy period to be equal to Ts − DIFS. On

the other hand, for topology of Figure 3.6(b), interference inter-

action AB is disconnected. Therefore, RTS frame transmitted by

sender A is not sensed as busy period by sender B and vice versa.

As a result, the interval f for which the sender B must not trans-


mit for transmission of flow Aa to be successful is given by f =

ceil((RTS + SIFS)/σ) = 8 as shown in Figure 4.5(b). This results

in higher conditional packet loss probability for both flows. How-

ever, the RTS and DATA frames transmitted by sender A are not

received by sender B as busy period while the CTS and ACK frames

transmitted by receiver a are sensed by sender B as busy. There-

fore, event of channel being busy as sensed by sender B is twice

the transmission event of sender A. The busy interval is equal to

CTS = ACK , which is much smaller compared to Ts − DIFS. The

updated throughput expression becomes:

RC throughput =psTs

psTs + pcTc + pIσ + 2psCTS(4.5)

Figure 4.4(c) shows the achievable throughput for the two flows

averaged for both topologies. The two flows get almost equal share

of throughput. However, the aggregate throughput is lesser than the

SC category as well as SSRC category because of higher packet loss

probability.

4.6 Symmetric Not Connected

Topologies belonging to this category do not have any of the inter-

ference interactions as Connected. Placement of flow Bb within the

carrier sensing range of flow Aa is possible within a large area of car-


S e n d e r A R T S ( A )

C T S ( a )

D a t a ( A )

A C K ( a )

D I F S

R e c e iv e r a R T S ( A )

C T S ( a )

D a t a ( A )

A C K ( a )

D I F S

S e n d e r B

ƒ

R e c e iv e r b

C T S ( a ) NAV

Ch a n n e l s e n s e d id le

Ch a n n e l b u s y

S ig n a l e x t e n s io n & S I F S

(a)

S e n d e r A R T S ( A ) C T S ( a ) D a t a ( A ) A C K ( a ) D I F S

R e c e iv e r a R T S ( A ) C T S ( a ) D a t a ( A ) A C K ( a ) D I F S

S e n d e r B ƒ

R e c e iv e r b C T S ( a ) N A V

Ch a n n e l s e n s e d id le

Ch a n n e l b u s y S ig n a l e x t e n s io n & S I F S

(b)

Figure 4.5: RC channel views

rier sensing range. Therefore, the distances d(A, B), d(a, B), d(A, b)

and d(a, b) can be as small as slightly greater than transmission

range and as large as exactly equal to carrier sensing range (which is

≈ 2.7 times the transmission range) or even outside carrier sensing

range. The throughput of the two flows under this category is driven

by the fact that frames transmitted by an interferer from closer lo-

cation within carrier sensing range are sensed as busy periods. On

the other hand, the frames transmitted by interferer at relatively dis-

tant location within carrier sensing range may cause errors but oth-

erwise can be rejected as interference, without making the channel


busy. Keeping this in view, the MAC behavior can be divided into

two parts. First part comprises of region where a node can sense

the frame transmission from other node as busy period. Second part

comprises of the region where such transmissions cause errors; how-

ever, signal strength is not high enough to make channel busy. Em-

pirical analysis shows that area around a sender up to rcsr − 0.5rtr

comprises of first part while the presence of interfering nodes within

the region beyond this threshold form the second part. Significant

area of occurrence of the topology of Figure 3.7(a) exists in first

part. For all remaining topologies belonging to this category, ap-

proximately half of the area of occurrence lies within first part while

the remaining half of the occurrence area lies in second part.

Within near sensing range, the MAC behavior of this category

is same as the MAC behavior of RC category with two differences.

First, in case of RC, CTS frame from one receiver is successfully

received by the other receiver, which sets the NAV for rest of the

transmission. On the other hand, in case of SNC category, CTS

is not successfully received, resulting in busy period at other re-

ceiver only for the duration of CTS. However, the idle interval of

SignalExtension+SIFS between the four frames (RTS, CTS, DATA

and ACK) is not big enough to allow any successful transmission.

Therefore, the entire transmission on one flow results in errors on


receiver of alternate flow in case any frame is transmitted by alter-

nate flow. Effectively, this difference in behavior does not affect the

throughput. Second, the interval f during which the flow Bb must

not have a transmission in order to have a successful transmission on

flow Aa varies for different topologies of this category. Similarly,

the busy interval and collision interval varies for each topology. The

parameters for different topologies are summarized in table 4.3. and

as such the analysis of RC category remains valid for first region of

SNC category. Once again, the difference in MAC behavior within

category does not impact the throughput of the flows. Figure 4.6(a)

shows analytically and simulated throughput. The two flows achieve

nearly equal throughput while a perfect match can be observed be-

tween simulated and analytical results.

The impact of interference from far sensing range on through-

put of the flows can be estimated by considering the received signal

strength, its impact on bit error rate and packet error rate. Ideal

channel conditions are assumed where only factor affecting the un-

successful reception of frame is the interference from other flow. Al-

though extremely simplifying, even under this assumption, through-

put of the two flows can be predicted accurately. This assumption

allows the computation of packet error probability for RTS frame.

Near sensing range analysis is used as basis while the conditional


Topology Param. Value

a,b f ceil((SignalExtension + SIFS)/σ)

a,b Tb Ts − DIFS

a,b Tc RTS + SIFS + CTS + DIFS

c,d f ceil((RTS + SIFS)/σ)

c,d Tb CTS/ACK

c,d Tc RTS + DIFS

e,f,g f ceil((CTS + SIFS − SigExt .)/σ)

e,f,g Tb (DATA + ACK − 2 ∗ SigExt .)0.5

e,f,g Tc RTS + SIFS + CTS + DIFS − SigExt .

Table 4.3: SNC Computation Parameters

packet loss probability and busy probability of the flows are adjusted

by the packet error probability to achieve the throughput of the two

flows that interfere from within far sensing range.

Friis transmission equation [74] is used to compute the received

signal strength from intended transmitter and the interfering trans-

mitter at the receiver. Ratio of signal received from intended sender

and the interfering transmitter gives the signal to noise ratio (SNR).

SNR can be used to get bit error rate using well known BER curves

and eventually packet error probability using the size of RTS frame.

The packet error probability decreases exponentially from distance

rcsr − 0.5rtr to rcsr with the values at two boundaries to be 0.97 and

0.03 respectively. Throughput of the flows for 512 bytes packet size


as a function of distance d(A, B) is shown in Figure 4.6(b). Empir-

ical values have also been plotted at selective points. It can be seen

that the throughput exponentially increase within the plotted range,

starting from minimum value equivalent to near sensing range and

ending at near independent throughput for two flows.

4.7 Asymmetric Not Connected

Topologies belonging to this category have interference interaction

Ab as sensing while the interference interaction aB is disconnected.

Like ASRC category, asymmetric channel view of the two flows re-

sults in imbalance among achievable throughput with one flow Aa

getting dominant portion of channel capacity while the other flow

Bb getting negligible throughput. Similar to SNC category, the dis-

tance between nodes of two flows affects the achievable throughput.

The MAC behavior of the category predicts the initial throughput

of the two flows at minimum possible distance. With the increasing

distance, the impact of one flow on the other is mitigated, gradually

making two flows independent of each other. For the throughput

computation, the MAC behavior is defined first and the throughput

of the two flows is computed. Subsequently, the results because of

the SNR based adjustments to the behavior are reported, similar to


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(a) SNC per flow throughput

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model flow Aopnet flow A

(b) SNC per flow throughput with increasing distance d(A, B)

Figure 4.6: Per flow throughput of SNC


SNC category.

For the analysis purposes, interference interaction Ab is consid-

ered as sensing while the interference interaction aB is considered

to be disconnected. The conditional packet loss probability of flow

Bb can be computed by considering the interval during which RTS

transmission from B will be received successfully by b. This inter-

val is given by D + iσ where D = SignalExtension + DIFS and

i is the average number of back-off slots. There is a difference

between MAC behavior of the topologies. For topologies 3.9(a)

and 3.9(b), sender A can sense RTS transmission from sender B;

therefore, B only needs to initiate the RTS transmission within the

specified interval for its transmission to be successful. On the other

hand, for topologies 3.9(c) and 3.9(d), Senders A and B are out-

side sensing range; therefore, sender B must complete the trans-

mission of entire RTS frame during the specified interval for the

transmission to be successful. For later case, D is updated to D =

SignalExtension + DIFS − RTS. Given the value of the inter-

val, equation 4.3 can be used to compute the conditional packet

loss probability for flow Bb. The busy probability of two group of

topologies also differs. For topologies 3.9(a) and 3.9(b), busy proba-

bility bB = τA because of the fact that B can sense the transmissions

of A. Busy interval is equal to Ts − (SIFS + ACK + DIFS). On the


other hand, busy probability of flow Bb for topologies 3.9(c) and

3.9(d) is zero. Throughput of flow Bb can be computed in terms of

all known parameters using Equation 4.2, provided the value of τA

is known.

To compute the throughput of flow Aa, the probabilities pA, bA

and the interval Tb are required. For topologies 3.9(a) and 3.9(b),

a collision on flow Aa occurs when sender B starts a transmission

following the RTS frame transmission by sender A. In this case, the

channel is sensed idle by sender B for the interval 2SignalExtension+

2SIFS + CTS because B is outside carrier sensing range of a. A

transmission attempt by B results in collision at A if RTS is transmit-

ted by B within interval SignalExtension + SIFS + CTS. Markov

model used to compute conditional packet loss probability for ASRC

category can be used to compute pA with f = ceil((SignalExtension+

SIFS + CTS)/σ) as shown in Figure 4.7. Busy probability bA is

computed as a function of throughput of flow Bb using Equation 4.4.

Busy interval for these topologies is given by Ts − DIFS. Equa-

tion 4.2 can be used to compute the throughput of flow Aa using all

known parameters.

In case of topologies 3.9(c) and 3.9(d), conditional packet loss

probability is zero, resulting in τA = 2/(W + 1). Successful trans-

missions on flow Bb result in busy intervals for sender A when re-




B

Receiver b


Sender Data (A)

Receiver Data (A)

Sender Df

Figure 4.7: ANC channel view

ceiver b transmits CTS/ACK frames. Therefore, busy probability

bA = 2τB and busy interval is equal to CTS/ACK . With all known

parameters, throughput can be computed using Equation 4.2. Fig-

ure 4.8(a) shows the analytical and simulated results for throughput

of the two flows for two different types of topologies. It can be

noted that although the MAC behavior is slightly different, there

is not much difference in achieved throughput for two types. The

imbalance between the throughput of the two flows is also obvious

from the results.

With the throughput values at near sensing range available, the

distance and SNR based analysis similar to SNC category is applied

for computation of throughput of the two flows with increasing dis-

tance. Figure 4.8(b) shows the achievable throughput as a function

of distance between sender A and receiver b for packet size of 512

Bytes. It can again be observed that although the analysis technique


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model flow A of Sc a&bopnet flow A of Sc a&bmodel flow B of Sc a&bopnet flow B of Sc a&bmodel flow A of Sc c&dopnet flow A of Sc c&dmodel flow B of Sc c&dopnet flow B of Sc c&d

(a) ANC per flow throughput

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(b) Per flow throughput for ANC with increasing distance d(A, b)

Figure 4.8: Per flow throughput of ANC


is based on simplifying assumption, the predicted throughput closely

matches the simulated results.

4.8 Summary

In this Chapter, MAC behavior of each identifies two flow category

is thoroughly discussed with the key observation that the presence

of interfering nodes within the carrier sensing range has significant

impact on the behavior and the throughput of five out of six identi-

fied categories. Based on the MAC behavior, extensive throughput

computations are performed for both flows under each category.

Chapter 5

Throughput modeling in WMN

This Chapter describe throughput modeling of a station in multi hop

wireless network. It is evident from existing literature [17],[24],[5]

that modeling private view of a station serves better purpose in pre-

dicting per-flow throughput. We follow the same approach to eval-

uate the CSMA/CA based channel access mechanism in WMN. We

made following assumptions: (i) ignore physical layer issues; (ii) fix

transmission and carrier sense range; (iii) stations within transmis-

sion range can decode message and also set NAV whereas stations in

carrier sense range can sense the channel busy but cannot decode the

message (RTS/CTS/DATA/ACK); (iv) collision is considered when

a station receives more than one packet at the same time from dif-

ferent stations within its carrier sensing range. (v) error free channel

and packets received from stations within transmission range is de-

coded correctly when there is no collision. Assumption of simplified

85

CHAPTER 5. THROUGHPUT MODELING IN WMN 86

physical layer channel does not affect the analysis as we are model-

ing MAC layer parameters.

While considering private view of a station, four different states

of a channel can be identified: (i) successful transmission; (ii) idle

channel; (iii) busy channel due to other station’s activity (iv) colli-

sion; and these states are denoted by Ts, Tσ, Tb and Tc respectively

and their probabilities are denoted by Πs, Πσ, Πb, Πc. τ is the prob-

ability that station tries to transmit after an idol slot, p is the proba-

bility that transmitted packet will be lost and b is the probability that

channel becomes busy after an idle slot due to activity of other sta-

tions [9]. Occurrence probability of each of the above channel state

are: Πσ = (1 - τ ) (1 - b), Πs = τ (1 – p), Πc = τ p, and Πb= (1 - τ ) b.

Throughput of a station is given by TP = Πs∆ , where ∆ (in seconds) is

average duration of all states on the channel and throughput is given

in [17]:

TP = τ (1−p)τ (1−p)T s+ τpT c+ (1−τ )(1−b)σ+(1−τ )bT b

(5.1)

G. Bianchi. in [9], computes an expression for τ which actually is

function of p and in [73] it is also shown that similar expression for

τ can be driven for general multi-hop wireless networks employing

arbitrary windows distribution and exponential back-off multipliers.

Complete expression of τ for CSMA Multi-hop network considering

maximum window size, maximum retransmit limit and is given as


[17]:

τ = 2q(1−pm+1)q(1−pm+1)+W0[1−p−p(2p)m′ (1+pm−m′q)]

(5.2)

where W0 represents minimum window size, m is upper limit for

retry, q = 1 − 2p and m′ is the value of backoff stage (m′ <= m).

T c and Ts are average durations of a colliding and successful trans-

mission and have already been evaluated in [9] and these two values

work same for both single-hop and multi-hop arbitrary topologies.

There are only two unknown quantities in throughput formula in

equation 5.1: (i) conditional packet loss probability p and (ii) prob-

ability of busy period b and T b is average duration of busy period.

We model both these quantities in following two sections, packet

loss probability is modeled in Section 5.1 whereas occurrence prob-

ability b of a busy period and its average duration T b are computed

in Section 5.2.

5.1 Packet loss probability modeling

In this Section, We model conditional packet loss probability p of

any station i in an arbitrary network. Conditional packet loss prob-

ability is the most critical and complicated variable to be computed

for predicting per-flow throughout in multi-hop WMN. Previous lit-

erature ignored comprehensive behavior of CSMA based MAC pro-


tocol and geometric location of the interfering links and these both

reasons cause stations to have large values of packet loss probability

p. Conditional packet loss probability depends on geometric config-

uration of flows in the immediate neighborhood. When all the sta-

tions are within transmission range of each other then DCF is able

to coordinate among stations and transmission attempts are within

well defined time durations. Conditional packet loss probability of

such scenario is given by 1 − (1− τ )n−1 here n denotes number of

stations in the network [9]. But there is inherent problem in DCF

when employed in multi hop network scenario that DCF is unable to

synchronize all stations in the network.

With an objective to clearly differentiate between interference

from transmission and carrier sense range, we identify and model

four possible types of packet losses that can occur due to CSMA

based MAC behavior in multi hop wireless network: loses because

of (i) sender sensing with probability pss; (ii) asymmetric incom-

plete state with probability pais; (iii) symmetric incomplete state

with probability psis; and (iv) destination connected with probabil-

ity pdc. In following sub sections we analyze each type and describe

exact geometric configuration. Probability of each identified type

is calculated independently and then combined to compute the total

packet loss probability. Transmissions which do not suffer from any


Figure 5.1: Two flow topology

of these loses are successful.

p (i) = 1−[1− pss

(i , i ′)] [

1− pais(i , i ′)]

[1− psis

(i , i ′)] [

1− pdc(i , i ′)] (5.3)

Figure.5.1 describes modeling topology in which there are two

contending flows l and l ′, where i and j are the transmitter and re-

ceiver of link l and i ′ and j ′ are transmitter and receiver of link l ′.

Each flow’s transmitter and receiver are within transmission range

of each other to comprise a flow and packet loss probability models

how link l ′ interferes the transmission of link l in different geomet-

rical configuration.


5.1.1 Loses due to sender sensing

Collision occurs at a station when it simultaneously receives data

from two other transmitting stations. We define sender sensing as

scenario in which both the senders are within carrier sense range of

each other (outside transmission range) and losses occurs at a re-

ceiver who is able to receive packets from these two senders at the

same time. We compute expression for pss (i , i ′) of collision proba-

bility that a link l(i , j) is interfered by station i ′ due to its simultane-

ous transmission, assuming distance d(i , i ′) < RS, d(j , i ′) < RS and

d (i , i ′) > RT where RS and RT represents carrier sense range and

transmission range. To compute pss (i , i ′) we need to compute con-

ditional probability c (i ′/i) that station i ′ tries to transmit a packet at

the same time when station i was already transmitting. Probability

pss is given by pss (i , i ′) = c (i ′/i) τ (i ′) and conditional probability

c (i ′/i) can be computed as:

c(i ′/i)

=Q(Φ)∑

D∈A(i) Q (D)(5.4)

Equation 5.4 computes probability of i ′ to initiate a transmission

when i is already transmitting and does this by dividing the proba-

bility of idle system state (no station is active) over probability of all

regions where station i can become active. Q (D), Q(Φ) and A (i)

are calculated in next section for busy time computation. Q (D) rep-


resent probability of stations in a region are jointly in the on period,

Q(Φ) is empty set representing a situation when none of the station

in any region is active and A (i) is a set of regions where station i can

become active.

5.1.2 Loses due to asymmetric incomplete state

Losses due to information asymmetry are of a serious concern as

they can cause very large values of packet loss probability and these

losses are more severe than any other type as far as starvation is con-

cerned. Accurate modeling of AIS scenario is very critical in defin-

ing the MAC behavior in arbitrary network. In information asym-

metric scenario both the transmitters are not in transmission range

of each other (d (i , i ′) > RT ) (but they can be in carrier sensing

range or disconnected) and one of the receiver is also not in trans-

mission range of the opposite transmitter (d (j ′, i) > RT ) (but can

be in carrier sense range or disconnected). And further we identify

two types of AIS scenarios, one scenario in which the other receiver

is in transmission range of the opposite transmitter (d (j , i ′) < RT )

and in second scenario the other receiver is in carrier sense range

of its opposite transmitter (d (j , i ′) > RT ) and (d (j , i ′) < RS). We

model these both scenarios independently and that’s actually how

our model differentiates between these two ranges (transmission and


carrier sense range).

In information asymmetric induced packet losses, link l(i , j) is

interfered from link l ′(i ′, j ′) if the above mentioned geometric con-

figuration stands true for both scenarios. In this scenario, station

i only has a chance of successful transmission if it is able to send

first packet (DATA for two-way and RTS for four-way handshake)

when link l ′ is not active. The packet loss probability when one

of the receivers is in transmission range of its opposite transmitter

(d (j , i ′) < RT ) is given:

pais−tr(i , i ′)

= X(i ′/i)τ(i ′)

(5.5)

And X (i ′/i) is given as:

X(i ′/i)

=T OFF

TON + T OFFe−

dTOFF (5.6)

In Equation 5.5, τ (i ′) is the probability that transmitter i ′ of link

l ′ tries to initiate a transmission right after a busy period ends and

X (i ′/i) is the probability that successful transmission of i is only

possible when first transmitted packet reached j during a period when

link l ′ was inactive and d is the size of first packet. Activity of link l ′

is modeled as On/Off periods sensed by receiver j when transmitter i

tries to transmit and On/Off periods are calculated during busy time

computation in Section 5.2. Packet loss probability pais−csr (i , i ′)

for the scenario when second receiver is in carrier sense range of its


opposite transmitter (d (j , i ′) > RT ) and (d (j , i ′) < RS) is given as:

pais−csr(i , i ′)

=T OFF

TON + T OFFe−

dTOFF (5.7)

Equation.5.7 computes the probability that successful transmis-

sion is only possible when first packet transmitted by station i reached

its receiver j during a period when link l ′ is inactive. Total probabil-

ity of pais (i , i ′) is given as:

pais(i , i ′)

= 1− [pais−tr(i , i ′)

+ pais−csr(i , i ′)] (5.8)

5.1.3 Loses due to symmetric incomplete state

Losses due to SIS incur between two link l(i , j) and l ′(i ′, j ′) when

both the transmitters are disconnected (d (i , i ′) > RS) and both the

receivers are within transmission or carrier sense range of the oppo-

site transmitters. This geometric configuration is also known as near

hidden terminal problem in existing literature. Packet loss in SIS

happens when one transmitter attempts to transmit during the time

when other transmitter was already transmitting its first packet and

both packets collide at the receivers. We model these types of losses

independently, packet loss probability when both the receivers are

in carrier sense range of their opposite transmitters (d (j , i ′) > RT ),

(d (j , i ′) < RS), (d (i , j ′) > RT ) and (d (i , j ′) < RS), is given as:

psis−csr(i , i ′)

= c(i ′, i)

[1− (1− τ(i ′))m] (5.9)


And when both the receivers are in transmission range of their

opposite transmitter (d (j , i ′) < RT ) and (d (i , j ′) < RT ), receivers

within transmission range can set their NAV and coordinate trans-

mission attempts. This probability is given as:

psis−tr(i , i ′)

= c(i ′, i)

[1− τ(i ′)]m (5.10)

We compute c (i ′, i) in Equation 5.4, m = bd/σc, m is transmis-

sion opportunities of station i ′ during station i was sending its first

packet and d is duration of first packet sent by station i . Depend-

ing on the packet size (13 micro second for RTS), these losses can

be higher but being symmetric these affect both the flows equally

and decrease in value of τ decreases chances of repeated collisions.

Equation for total probability of losses due to SIS is given as:

psis(i , i ′)

= psis−csr(i , i ′)

+ psis−tr(i , i ′)

(5.11)

5.1.4 Loses due to destination connected

In destination connected scenario, link l(i , j) suffers losses because

of the activity of link l ′(i ′, j ′) when both transmitters are in car-

rier sense range or disconnected (d (i , i ′) > RT ), both the receivers

are also in carrier sense range or disconnected from their oppo-

site transmitters (d (i ′, j) > RT ) and (d (j ′, i) > RT ). But both re-

ceivers are within transmission (d (j , j ′) < RT ) or carrier sensing


range (RT < d (j , j ′) < RS) of each other. With this geometric con-

figuration, the station that attempts first will have a successful trans-

mission and the station starts second will experience losses as its

receiver will not be able to reply CTS due to the activity of oppo-

site transmitter or receiver. For the scenario when two receivers are

within carrier sense range of each other (RT < d (j , j ′) < RS), We

compute this packet loss probability of station i such that i ′ attempts

to transmit during the active period of link l , is given as:

pdc−csr (i , i ′) =TON(i ′ )

TON(i ′ ) + T OFF (i ′ )(5.12)

Values of the variables TON(i ′) and T OFF (i ′) are iteratively com-

puted while monitoring activity of link l ′. In scenarios when both the

receivers are within transmission range of each other (d (j , j ′) < RT ),

the probability of packet loss is much higher because network allo-

cation vector will be set during transmission of CTS by j and hence

j ′ will not be able to reply CTS to its own transmitter i.e., i and i ′

will keep on trying to initiate transmission and its back-off windows

size will be increased as well. This probability is given as:

pdc−tr(i , i ′)

=TOFF (i ′ )

TOFF (i ′ ) + T ON (i ′ )τ(j ′)m (5.13)

Where m = bd/σc and d = CTS. In this equation, τ (j ′)m makes

sure that station i ′ is also aware of the activity of link l and is able

to set NAV as being in transmission range of station j . The total


probability of losses due to destination connected scenario is:

pdc(i , i ′)

= pdc−csr(i , i ′)

+ pdc−tr(i , i ′)

(5.14)

5.2 Busy time computation

In this section, we compute the duration of time when channel is

sensed busy by a station due to the activity of other stations around

it in WMN. According to IEEE 802.11 MAC there are two types of

situation in busy time sensing, one is virtual carrier sense when net-

work allocation vector (NAV) is set by stations during initial coor-

dination (RTS/CTS) but NAV can only be set to nodes within trans-

mission ranges of both transmitter and receiver. Second type of busy

time sensed due to physical carrier sense from the stations in trans-

mission/carrier sense ranges of both transmitter and receiver. Busy

time computation is simple when all stations are in single transmis-

sion range as in single-hop network and they can coordinate their

transmission using RTS/CTS mechanism of CSMA carrier avoid-

ance mechanism. But computing busy time becomes very challeng-

ing when there are stations in carrier sense range and their transmis-

sion can overlap on a sensing station.

Prior work in [17] modeled busy time average durations and rate

of arrival of busy events in a four step process including computa-


tion of maximal clique and their reduction, computation of active

regions and then finally busy time. But their proposed model do not

differentiate between busy time senses due to the activity of stations

within transmission range or carrier sense range (outside transmis-

sion range) because they treated these both ranges as single sensing

range. As compared to [17], uniqueness of our work lies in metic-

ulous differentiation between busy time sensed due to the activity

of stations in transmission and carrier sense range detailed in Algo-

rithm 4. We also devise computationally efficient algorithms [1-4]

for modeling busy probability b(i) and average busy duration T b(i).

According to Equation 5.1, these two quantities b(i) and T b(i) along

with conditional packet loss probability p(i) computed in Section

5.1 are required to predict per flow throughput of each transmitting

nodes in a dense WMN.

Algorithm 1 Busy probability and average busy duration1: procedure BUSYTIME(i) . any station in WMN

Compute activation rate and average busy duration of all regions

2: ActivationRateAvgDuration(i)

Compute busy probability and average busy duration of all stations

3: BusyProbAvgDuration(i)

4: return b(i) and T b(i) . for throughput computation

5: end procedure

Algorithm 1 details outline of busy probability and average du-


ration of a busy period sensed by station in network and for com-

putations of these quantities it invokes procedures in Algorithm 2,

3 and 4. We now briefly elaborate the functionality of these Al-

gorithms. Algorithm 2 computes activation rate and average busy

duration sensed by a station due to the activity of a group of stations

called regions around sensing station i . Initially n number of sta-

tions are placed in a rectangular area of width × length(w × l) in

pairs of a transmitter and a receiver making sure that each receiver

is in transmission range of its receptive transmitter and their coordi-

nates are saved. Next step finds all the stations within transmission

and carrier sense range of station i and also save the type of station

whether it is a transmitter or a receiver.

Next Algorithm 2 sequentially invokes OverlappingRegions(i)

procedure to compute overlapping active regions around station i

whom transmission activity is sensed by station i . We discuss com-

putation of overlapping regions in more details while describing Al-

gorithm 4. Initially we assume Poisson distribution for busy period

activation rate λ (i) and Exponential distribution for average dura-

tions T ON of busy activity but later these both quantities are itera-

tively recomputed until they are converged. Algorithm 2 then com-

putes activation rate λ (Uu) of each region by summing activation

rates of individual stations λ (i) in that region. And finally computes


Algorithm 2 Activation rate and average busy duration of region1: procedure ACTIVATIONRATEAVGDURATION(i)

2: Place n stations in w × l rectangular area and save Coordinates(n)

Find stations within transmission and carrier sense range of station i and

save in a vector

3: while i ≤ n do

4: TxRange(i)← All stations in i’s Tx range

5: CSRange(i)← All stations in i’s CS range

6: end while

Find regions around station i

7: OverlappingRegions(i)

8: Initially assume Poisson distribution for activation rate λ (i) for each

station i

Compute sum of activation rate λ (Uu) for all regions

9: for ∀u ∈ U do . for all regions in U

10: for ∀i ∈ Uu do . for all stations in Uu region

11: λ (Uu)← λ (Uu) + λ (i)

12: end for

13: end for

14: Initially assume Exponential distribution for average duration T ON(i) of

activity of each station i

Compute average activity duration T ON in all regions

15: for ∀u ∈ U do . for all regions in U

16: for ∀i ∈ Uu do . for all stations in Uu region

17: XUu ← λ (i) T ON (i)

18: end for

19: T ON (Uu)← XUuλ(Uu)

20: end for

21: return T ON (Uu)

22: end procedure


average activity duration T ON of all regions. Algorithm 2 returns

the value of average activity duration T ON back to main procedure

for further throughput computation of each transmitting station i .

Algorithm 3 computes the two required quantities b(i) and T b(i)

for throughput computation. It first computes the deactivation rate

µu for all the virtual nodes (previously referred to as active regions)

and also computes independent sets D of these virtual nodes us-

ing conflict graph. An independent set consists of virtual nodes in

which transmitting stations can make simultaneous successful trans-

missions and Qd is the probability of each independent set d . Ac-

tivation rate gu is computed iteratively keeping the total probability

QD of the system below one (QD ≤ 1), QD also includes the prob-

ability Qφ when none of the virtual node (i.e., region) is currently

active and transmitting. Average duration of idle period T idle(i) for

each station i is computed based on their activation rate gu and then

T idle(i) is used to compute the first required quantity that is average

duration of busy period T b(i) sensed by each station i . In the later

part of Algorithm 3, ne(i) is computed that are average number of

events sensed by a station i during a busy period and then finally

ne(i) is used to compute second required quantity i.e., probability

b(i) that station i senses a busy period right after an idle slot.

Algorithm 4 finds overlapping regions around i to compute acti-


Algorithm 3 Busy probability and average duration of station1: procedure BUSYPROBAVGDURATION(i)

Each region is now considered as a virtual node Compute deactivation rate µu

of all virtual nodes

2: for ∀u ∈ U do . for all virtual nodes in U

3: µu ← 1T ON (Uu)

4: end for

5: Find independent sets D of virtual nodes using conflict graph

Assign random probabilities Qd to independent sets and calculate QD

including Qφ

6: for ∀d ∈ D do . for all independent sets in D

7: for ∀u ∈ d do . for all virtual nodes in an independent set d

8: Qd ← guuu

9: end for

10: QD ← QD ×Qd

11: end for

12: QD ← QD ×Qφ . itterative computation of gu keeping QD ≤ 1

Compute average duration of idle period of station i


14: GU ← GU + gu

15: end for

16: while i ≤ n do . for all stations

17: λidle (i)← GU

18: end while


20: T idle(i)← 1λidle(i)

21: end while


Compute average duration of a busy period of i


23: T b(i)← T idle(i)[1−Qφ]Qφ

24: end while

Compute average number of events ne(i) sensed by a station i during a busy

period


26: λU ← λU + λu

27: end for


29: ne(i)← λ(U)T idle(i)+T b(i)

30: end while

Compute busy probability b(i) that busy period starts after an idle slot


32: b(i)← λ(U) ∆(i)[1−τ (i)] ne(i)

33: end while

34: return b(i) and T b(i)

35: end procedure


Algorithm 4 Find overlapping regions around station i1: procedure OVERLAPPINGREGIONS(i)

Find overlapping regions around station i

2: while i ≤ n do . ∀i ∈ n

Find stations within carrier sense range of i

3: while j ≤ n do . ∀j ∈ n

4: Compare coordinates of i and j

5: CSRange(i)← Coordinates(j) . If j is in CSR of i

6: end while

Draw three circles (radius = CSR) around station i with following points

as their centers so that these circles cover all nodes within CSR of station i

Figure.5.2(a, b)

7: Location(x , y )← Coordinates(i)

8: Dist ← [CSR/2]

9: Center1← Location(x + 0, y + Dist)

10: Center2← Location(x + Dist , y − Dist)

11: Center3← Location(x − Dist , y − Dist)

12: Save stations in each overlapping region of three circles in Uu

13: end while

14: return Uu . to algorithm 3

15: end procedure


(a) Three circles (b) Overlapping regions

Figure 5.2: Overlapping regions

vation of each station λi as well as for each region λu. Figure 5.2

elaborate region formation in which three circles with radius as car-

rier sense range are drawn around station i to cover all nodes around

it and regions are only made within carrier sense range of station

i because as per 802.11 CSMA/CA protocol, stations within trans-

mission range set their network allocation vector to schedule trans-

missions with coordination using RTS/CTS mechanism. Algorithm

4 returns set of stations i.e., Uu in each identified region u ∈ U and

Algorithm 2 use these regions for computation of activation rates

(λ(i) and λUu).


5.3 Simulation and model validation

For the validation of busy time, packet loss probability and through-

put modeling, we implemented and compared both analytical as well

as simulation results. We consider topology in Figure 5.3, in which

there are 25 transmitting and receiving pair of stations (total 50 sta-

tions) in 200 × 200 unit area. Figure 5.3(a) shows flows in the

network with arrow pointing towards the receiver of each flow and

Figure 5.3(b) expresses connectivity graph in carrier sense range of

each stations. Each transmitter randomly transmits to its receivers

which is within transmitter’s transmission range. With simulation

and experimentations we came to know that effective carrier sense

range is almost 2.5 to 2.7 times (using simulation and experimen-

tation) the transmission range and same is evident in the existing

literature [17, 5, 73].

Table 5.1 lists the values of analytical parameters taken. We

simulate the topology in Opnet’s free version with limitation of 80

stations and 5 millions events with standard protocol settings of

IEEE 802.11 CSMA/CA based MAC with data rate of 11Mbps with

packet size of 1000 bytes. As our modeling is specifically on MAC

behavior so using any type of 802.11 radio works the same as long as

we are using CSMA/CA based coordination function. We first make


comparison of analytical results of model with those of Michele

Garetto’s [17] and then compare our analytical results with our own

simulation results to validate the model. We discuss each compared

parameter individually and exact semantics of the comparison.

Parameter Value (ms)

Channel occupied by successful transmission Ts 9.6

Channel occupied by a collision Tc 0.417

Duration of first packet d 0.288

Duration of CTS dcts 0.24

Idle channel σc 0.02

Maximum retry limit m 6

Backoff stage at which window size is max m′ 5

Minimum window size W0 16

Table 5.1: Analytical Parameters for Throughput Computation

5.3.1 Fraction of busy time sensed

Figure 5.4 compares fraction of busy time sensed by each trans-

mitting station in the network for both proposed and reference [17]

throughput prediction models. Fraction of busy time sensed depends

on geometric location of the other stations around the transmitting

one. Unlike reference model, our throughput model can clearly dif-

ferentiate between interference from transmission and carrier sense

range using following:


1. Do not consider stations within transmission range of station

i for modeling its throughput assuming that RTS/CTS mecha-

nism worked to set the network allocation vectors of stations

within transmission range.

2. Record the number of other transmitting stations within car-

rier sense range of station i that are interfering with stations i’s

transmission.

3. Overlapping region formation in Algorithm 4 during busy time

computation only considers stations within carrier sense range

of station i as interference from carrier sense range is the worst

as hidden and exposed node stations are in carrier sense range

of station i .

4. Packet loss probability computation also differentiates between

nodes interfering from transmission range and carrier sense

range and models them separately for accurate computation of

packet loss probability.

Figure 5.4 shows that fraction of busy time sensed by each trans-

mitting station is higher in proposed model as compared to the ref-

erence model [17]. As busy time sense by a stations largely depends

on number and location of interfering links around that transmitting

station i , these values vary much from each other predicting the re-


alistic nature of general wireless network. Fraction of busy time

sensed is high in proposed model due to that fact that now it is able

to sense transmissions of links that are outside carrier sense range

while the reference model in [17] is only able to sense busy time

from within transmission range.

5.3.2 Conditional packet loss probability

Conditional packet loss probabilities of both the proposed and ref-

erence modeled in [17] is compared in Figure 5.5. We can observe

that conditional packet loss probability for the proposed model is

slightly higher for most of the flows. This is due to the fact that, pro-

posed model can clearly differentiate between links interfering from

transmission and carrier sensing range. Now the transmitting sta-

tions are severely interfered by the stations outside transmission but

within carrier sense range. This situation leads to increased number

of transmission opportunity losses and more information asymmet-

ric interfering flows which ultimately increase the packet loss prob-

ability.


5.3.3 Contribution of packet loss probability due to informa-

tion asymmetry

Losses due to information asymmetry are the main contributing in

overall packet loss probability of each flow in the network, this also

is evident from Figure 5.6. This also is a model validation because

unlike rest of the literature, our model separately calculates packet

loss probability due to information asymmetry in transmission range

from that of in carrier sense range. Model proposed in [17] is not

able to capture realistic higher packet loss probability due to their

limiting assumption of same transmission and career sense range. It

also indicated how important it is to accurately capture the effect of

information asymmetry on overall capacity of the network and cal-

culation of such losses can be greatly helpful in designing efficient

future wireless network protocols.

5.3.4 Transmission probability comparison

As mentioned earlier that proposed per flow throughput prediction

model accurately carters the affect of links interfering from out side

transmission range. It can be seen in Figure 5.7 that transmission

probability of proposed model is less than that of [17], it actually in-

dicates increased interference from contending flows and alternately

decreased throughput. Proposed model can clearly differentiate be-


tween interfering links from transmission and carrier sense range

and we now have established that fact that links interfering from car-

rier sense range severely affect the throughput of a flow in general

multi ho wireless network.

5.3.5 Analytical throughput

Analytical throughput comparison between two models is shown

in Figure 5.8. It is also prominent here that per-flow throughput

achieved in proposed model is slightly lower than the one in [17]. It

is very convincing that throughput decreases with increase in both

fraction of busy time sensed and packet loss probability. The in-

creased busy time sensed and packet loss probability will ultimately

decrease the throughput. And the reason behind this is: firstly the

stations inside transmission range now can set their NAV and freeze

their counter of binary exponential backoff, this reduces the through-

put as station now are able to coordinate transmission attempts within

transmission range. Secondly, now talking about stations outside

transmission range but inside carrier sense range, these stations now

interfere more severely because number of information asymmet-

ric links are increased now which ultimately decreases throughput

achieved by the flows. Figure 5.9 compares the normalized analyt-

ical throughput between proposed and model in [17]. We can see


that same throughput distribution trend among the flows in the net-

work but throughput predicted by proposed model is less than that

of model in [17] and again this is due to the fact that now we have

increased values for packet loss probability and busy time sensed by

each node.

5.3.6 Simulation throughput

Throughput of analytical model with the simulation results is com-

pared in Figure 5.10. We can see high accuracy and throughput

matching with the flows with very high and very low throughput but

there is some marginal gap for the flow with intermediate through-

put. Regarding flow with high throughput, they are mostly on the

edge of the network and enjoy less interference which allows them

to achieve higher throughput, where as flows with very low and al-

most zero throughput are mostly interfered by multiple asymmetric

flows hence are unable to achieve any throughput and are starved.

Where as the flows with intermediate throughput are mostly among

the lightly populated network region and have symmetric interfer-

ing flows around them that is why these flows keep on competing

most of the time and achieve intermediate throughput due to the fair

share nature of symmetric interference. Gap between intermediate

flows also show that fact that proposed analytical model predicts per


flow throughput with higher accurately as compared to the simula-

tion scenario. There surely is need to more comprehensive location

aware MAC protocols. Most of the current protocols are based on

typical CSMA/CA based MAC where as general multi hop wireless

networks requires efficient location aware MAC protocols for im-

proved performance and achieve higher aggregate network capacity.

5.4 Summary

In this Chapter, we model fraction of busy time and conditional

packet loss probability for realistic general wireless mesh scenario

based on an accurate geometric configuration of stations. We com-

pute per flow throughput of all the stations in general multi-hop

wireless network. Analytical results validated our model and also

supported the argument that our model can clearly differentiate be-

tween interfering links from transmission and carrier sense range.

Proposed model is more accurate in per-flow throughput prediction

in comparison with existing literature. This work provides better un-

derstanding of CSMA based MAC protocols in arbitrary networks

and aids toward designing more effective future networking proto-

cols.


(a) Flow topology

(b) Connectivity graph

Figure 5.3: Network topology and connectivity graph


Figure 5.4: Analytical comparison of busy time probability


Figure 5.5: Analytical comparison of conditional packet loss probability


Figure 5.6: Contribution of packet loss probability due to information asymmetry


Figure 5.7: Comparison between analytical transmission probabilities


Figure 5.8: Analytical comparison of throughput


Figure 5.9: Comparison between analytical normalized throughput


Figure 5.10: Comparison between simulation and analytical throughput

Chapter 6

Conclusion

This research aim at analyzing interference and capacity with an ob-

jective to accurately model and predict per flow throughput in multi

hop wireless mesh network. The research is based on hypothesis that

accurate modeling of interference at MAC level can maximize over-

all network capacity. Modeling of packet loss probability and busy

time sensed by a station in WMN is accurately done on the basis of

proposed two-flow classification. Modeling of per flow throughput

can clearly differentiate between interference from transmission and

carrier sense range. Accurate per flow throughput prediction along

with better understanding of CSMA MAC behavior is very critical

for designing future protocol for all variants of multi hop WMN and

this greatly helps in identifying dominating and starving flows in the

arbitrary network. This research will serve as basis for MAC behav-

ior analysis of generic multi-hop wireless networks.

121

CHAPTER 6. CONCLUSION 122

This work extends and completes the body of work on two flow

interactions and also optimizes per flow throughput prediction [9, 4,

5]. Bianchi [9] computed the achievable throughput by individual

nodes in a single cell when all interfering nodes are within single

transmission range. He showed that all wireless nodes in a single

cell exhibit fairness in the absence of hidden node problem [16] and

with perfect channel capture. Bianchi computed exact throughput

values for different IEEE 802.11 DCF mode parameters. Garetto et

al. [4] extended Bianchi’s work [9] to compute per flow link capacity

in general multi-hop wireless networks using two-flow interactions.

In cases where transmission and sensing ranges are considered same,

the analytical results accurately predict throughput achieved through

simulations. However, the model does not capture the impact of

interference from links within sensing range.

In this work first, two flow topologies have been reclassified by

separately considering the transmission and the carrier sensing ranges

[6]. The interaction between the two single hop flows is considered

under CSMA/CA MAC protocol for throughput estimation of two

flow topologies. It is observed that the presence of sender or re-

ceiver of interfering link within the carrier sensing range results in

significantly different MAC behavior compared to the presence of

the two nodes outside the carrier sensing range. This research di-


vides the two flow topologies into six categories, depending upon

CSMA/CA interaction. Among six categories, three are newly iden-

tified categories that are different from the categories identified by

Garetto et al. [5] as well as Razak et al. [7]. Occurrence probabil-

ity of each category has been computed using spatial analysis. For

this purpose, possible geometric area where the nodes of the partic-

ular topology can exist has been considered, compared to the over

all geometric area of occurrence for two interfering links. Analysis

shows that the newly identified categories that are based on inter-

ference interactions from within the carrier sensing range only, have

high occurrence probability values (aggregate of 0.69). Throughput

achieved by the two links under each category has been computed

analytically based on MAC protocol behavior. Analytically com-

puted throughput values have been compared with the simulation

throughput values using Opnet based Simulations. The comparison

shows near perfect match in analytical and simulated values, sug-

gesting the completeness of the categorization.

The root cause of such imbalances is the lack of coordination

when CSMA MAC protocols are employed in multi-hop wireless

networks. We accurately predict per-flow throughput in general multi-

hop wireless networks while addressing CSMA’s coordination prob-

lem. Unlike previous work, our analytical throughput model can


clearly differentiate between links interfering from transmission range

and carrier sensing range. Modeling of conditional packet loss prob-

ability and busy time sensed by each node is critical for per-flow

throughput prediction in arbitrary networks. The calculation of con-

ditional packet loss probability and busy time largely depends on

MAC behavior due to geometrical configuration of interfering nodes.

We accurately compute conditional packet loss probability and busy

time based on geometrical configuration of the interfering nodes

and predicted per-flow throughput. Our experimental results demon-

strate improved accuracy, indicate throughput imbalances and pro-

vides better understanding of CSMA based protocol behavior in

multi-hop wireless networks that can be used to design fair, scal-

able, and efficient MAC layer protocols. We assume perfect capture

channel and ignore all physical layer losses but it should be notes

that this analysis is done on MAC layers. Following are the summa-

rized contributions of this thesis.

• Classification of two-flow interactions is done based on geo-

metric location of the stations with more realistic and practical

assumption. This classification is also validated as computa-

tion of closed form expressions for occurrence probabilities of

all identified categories resulted into 0.99999 total probability.

• Extensive discussion on MAC behavior and throughput com-


putation of each identified category. Also highlighting insights

that result is specified throughput imbalance in each of the six

categories.

• Devised a simplified disk model for calculating busy time sensed

by a station in dense multi hop WMN and this model inherently

embed geometrical location of all interfering transmitters and

receivers around that particular station. This also helps dif-

ferentiate between stations interfering from transmission and

carrier sense range.

• Accurate modeling of packet loss probability for each station

in multi hop WMN and this modeling can clearly differentiate

between interference from transmission range and carrier sense

range.

• We predict per flow throughput for each station based on its

packet loss probability and experienced busy time. Model val-

idation and simulation results show that proposed packet loss

probability, busy time and throughput modeling improved the

accuracy of per-flow throughput prediction and also improve

overall understanding of MAC behavior in multi hop WMN.


6.1 Future work

This work completes the research efforts towards defining the MAC

behavior of two flow topologies and its impact on the throughput

of links. The work can be extended to general capacity analysis of

multi-hop wireless networks and can serve as the basis for modified

MAC protocol that can better mitigate the impact of interference,

specifically the interference from within carrier sensing range. This

work provides better understanding of CSMA based MAC proto-

cols in arbitrary networks and aids toward designing more effective

future networking protocols.

In recent years, wireless mesh technology proved itself to be one

of the most exciting networking technology. Its applications can be

seen in but are not limited to wireless Internet connectivity, multime-

dia, remote monitoring and control, emergency response, military

and field, community/enterprise services, smart transportation, in-

dustrial control, medical and health monitoring, environmental and

security systems, consumer electronics and may more. Two-flow

interaction classification and occurrence probability computation in

this thesis provides fundamental knowledge for designing efficient

higher layer protocols in all wireless mesh network application ar-

eas. Internet of things is a exciting new wireless mesh technology


and work is being done on standardizing its protocols. Current capa-

bilities and recommended improvements may provide IEEE 802.11

with decades of influence on human lives as IoT becomes common-

place. Efforts being made to provision IoT include IEEE P802.11ax

with focus on high efficiency in WLAN and IEEE P802.11ah with

focus on operation in sub gigahertz bands. Analysis in this thesis

can greatly help in selection and evolution of a better MAC layer

protocol for Internet of Things.

Decoding a packet in all current wireless technologies is a phys-

ical layer phenomenon and interference is treated as noise instead

of decoding multiple simultaneous signals at a receiver. An ac-

curate estimation of occurrence probability, location of interfering

links and understanding of impact of interference on throughput will

surely help in designing efficient spectrum decision and routing al-

gorithms in all application areas of wireless mesh networks.

Bibliography

[1] Ian F Akyildiz and Xudong Wang. A survey on wireless mesh

networks. Communications Magazine, IEEE, 43(9):S23–S30,

2005.

[2] Kenneth L Kraemer, Jason Dedrick, and Prakul Sharma. One

laptop per child: vision vs. reality. Communications of the

ACM, 52(6):66–73, 2009.

[3] Piyush Gupta and Panganmala R Kumar. The capacity of wire-

less networks. Information Theory, IEEE Transactions on,

46(2):388–404, 2000.

[4] Michele Garetto, Theodoros Salonidis, and Edward W

Knightly. Modeling per-flow throughput and capturing starva-

tion in csma multi-hop wireless networks. IEEE/ACM Trans-

actions on Networking (TON), 16(4):864–877, 2008.

[5] Michele Garetto, Jingpu Shi, and Edward W Knightly. Mod-

eling media access in embedded two-flow topologies of multi-

128

BIBLIOGRAPHY 129

hop wireless networks. In Proceedings of the 11th annual in-

ternational conference on Mobile computing and networking,

pages 200–214. ACM, 2005.

[6] Muhammad Zeeshan and Anjum Naveed. Interference and ca-

pacity analysis in multi-hop wireless mesh networks. In Net-

work Protocols (ICNP), 2013 21st IEEE International Confer-

ence on, pages 1–3. IEEE, 2013.

[7] Saquib Razak, Vinay Kolar, and Nael B Abu-Ghazaleh. Model-

ing and analysis of two-flow interactions in wireless networks.

Ad Hoc Networks, 8(6):564–581, 2010.

[8] Jian Tang, Guoliang Xue, and Weiyi Zhang. Interference-

aware topology control and qos routing in multi-channel wire-

less mesh networks. In Proceedings of the 6th ACM interna-

tional symposium on Mobile ad hoc networking and comput-

ing, pages 68–77. ACM, 2005.

[9] Giuseppe Bianchi. Performance analysis of the ieee 802.11

distributed coordination function. Selected Areas in Communi-

cations, IEEE Journal on, 18(3):535–547, 2000.

[10] Saquib Razak and Nael B Abu-Ghazaleh. Self-interference in

multi-hop wireless chains: geometric analysis and performance

BIBLIOGRAPHY 130

study. In Ad-hoc, Mobile and Wireless Networks, pages 58–71.

Springer, 2008.

[11] Pradeep Kyasanur and Nitin H Vaidya. Capacity of multi-

channel wireless networks: impact of number of channels and

interfaces. In Proceedings of the 11th annual international

conference on Mobile computing and networking, pages 43–

57. ACM, 2005.

[12] Jitendra Padhye, Sharad Agarwal, Venkata N Padmanabhan,

Lili Qiu, Ananth Rao, and Brian Zill. Estimation of link inter-

ference in static multi-hop wireless networks. In Proceedings

of the 5th ACM SIGCOMM conference on Internet Measure-

ment, pages 28–28. USENIX Association, 2005.

[13] Kamal Jain, Jitendra Padhye, Venkata N Padmanabhan, and

Lili Qiu. Impact of interference on multi-hop wireless network

performance. Wireless networks, 11(4):471–487, 2005.

[14] Ashish Agarwal and PR Kumar. Capacity bounds for ad hoc

and hybrid wireless networks. ACM SIGCOMM Computer

Communication Review, 34(3):71–81, 2004.

[15] Murali Kodialam and Thyaga Nandagopal. Characterizing the

capacity region in multi-radio multi-channel wireless mesh net-

BIBLIOGRAPHY 131

works. In Proceedings of the 11th annual international con-

ference on Mobile computing and networking, pages 73–87.

ACM, 2005.

[16] Fouad Tobagi, Leonard Kleinrock, et al. Packet switching in

radio channels: Part ii–the hidden terminal problem in carrier

sense multiple-access and the busy-tone solution. Communica-

tions, IEEE Transactions on, 23(12):1417–1433, 1975.

[17] Michele Garetto, Theodoros Salonidis, Edward W Knightly,

et al. Modeling per-flow throughput and capturing starvation

in csma multi-hop wireless networks. In INFOCOM, 2006.

[18] Marcelo M Carvalho and Jose Joaquin Garcia-Luna-Aceves.

A scalable model for channel access protocols in multihop ad

hoc networks. In Proceedings of the 10th annual international

conference on Mobile computing and networking, pages 330–

344. ACM, 2004.

[19] Harshal S Chhaya and Sanjay Gupta. Performance modeling

of asynchronous data transfer methods of ieee 802.11 mac pro-

tocol. Wireless networks, 3(3):217–234, 1997.

[20] Robert R Boorstyn, Aaron Kershenbaum, Basil Maglaris, and

Veli Sahin. Throughput analysis in multihop csma packet radio

BIBLIOGRAPHY 132

networks. Communications, IEEE Transactions on, 35(3):267–

274, 1987.

[21] M.S. Chen and R. Boorstyn. Throughput analysis of cdma

packet radio networks in the presence of noise. In INFOCOM.

In Proceedings of,. IEEE, 1985.

[22] Fouad A. Tobagi and Jose M. Brazio. Throughput analysis of

multihop packet radio networks under various channel access

schemes. In INFOCOM. In Proceedings of,, volume 83, pages

381–389. IEEE, 1983.

[23] Xin Wang and Koushik Kar. Throughput modelling and fair-

ness issues in csma/ca based ad-hoc networks. In INFOCOM

2005. 24th Annual Joint Conference of the IEEE Computer

and Communications Societies. Proceedings IEEE, volume 1,

pages 23–34. IEEE, 2005.

[24] Frederico Calı, Marco Conti, and Enrico Gregori. Dynamic

tuning of the ieee 802.11 protocol to achieve a theoretical

throughput limit. IEEE/ACM Transactions on Networking

(ToN), 8(6):785–799, 2000.

[25] Ieee standard 802.11-2012 part 11: Wireless lan medium ac-

cess control (mac) and physical layer (phy) specifications.

2012.

BIBLIOGRAPHY 133

[26] Lei Lei, Ting Zhang, Xiaoqin Song, Shengsuo Cai, Xiaom-

ing Chen, and Jinhua Zhou. Achieving weighted fairness in

wlan mesh networks: An analytical model. Ad Hoc Networks,

25:117–129, 2015.

[27] Dee Denteneer Sebastian Max Rakesh Taori Javier Cardona

Lars Berlemann Hiertz, Guido R. and Bernhard Walke. Ieee

802.11 s: the wlan mesh standard. Wireless Communications,

17(1):104–111, 2010.

[28] Md Shariful Islam, Muhammad Mahbub Alam, Choong Seon

Hong, and Sungwon Lee. emcca: An enhanced mesh coor-

dinated channel access mechanism for ieee 802.11 s wireless

mesh networks. Communications and Networks, Journal of,

13(6):639–654, 2011.

[29] Giuseppe Bianchi, Ilenia Tinnirello, and Luca Scalia. Under-

standing 802.11 e contention-based prioritization mechanisms

and their coexistence with legacy 802.11 stations. Network,

IEEE, 19(4):28–34, 2005.

[30] LAN/MAN Standards Committee et al. Part 15.4: wire-

less medium access control (mac) and physical layer (phy)

specifications for low-rate wireless personal area networks (lr-

wpans). IEEE Computer Society, 2003.

BIBLIOGRAPHY 134

[31] Niamat Ullah, M Sanaullah Chowdhury, Pervez Khan, Sana

Ullah, and Kyung Sup Kwak. Throughput and delay limits

of chirp spread spectrum-based ieee 802.15. 4a. International

Journal of Communication Systems, 25(1):1–15, 2012.

[32] IEEE Technical Report. Ieee p802.15g working group, ieee std.

802.15.4g, part. 15.4: Amendment 3: Wireless medium access

control (mac) and physical layer (phy) specifications for low-

rate wireless personal area networks (lr-wpans). 2012.

[33] Geoff Mulligan. The 6lowpan architecture. In Proceedings of

the 4th workshop on Embedded networked sensors, pages 78–

82. ACM, 2007.

[34] Jelena Misic, Shairmina Shafi, and Vojislav B Misic. The im-

pact of mac parameters on the performance of 802.15. 4 pan.

Ad Hoc Networks, 3(5):509–528, 2005.

[35] Jianping Zhu, Zhengsu Tao, and Chunfeng Lv. Perfor-

mance evaluation for a beacon enabled ieee 802.15. 4 scheme

with heterogeneous unsaturated conditions. AEU-International

Journal of Electronics and Communications, 66(2):93–106,

2012.

[36] Angelos Vlavianos, Lap Kong Law, Ioannis Broustis,

Srikanth V Krishnamurthy, and Michalis Faloutsos. Assess-

BIBLIOGRAPHY 135

ing link quality in ieee 802.11 wireless networks: which is the

right metric? In Personal, Indoor and Mobile Radio Commu-

nications, 2008. PIMRC 2008. IEEE 19th International Sym-

posium on, pages 1–6. IEEE, 2008.

[37] MN Jose and Mangues-Bafalluy Josep. A survey on routing

protocols that really exploit wireless mesh networks features.

IEEE Journal of Communications, 5(3):211–231, 2010.

[38] Kyu-Han Kim and Kang G Shin. On accurate measurement

of link quality in multi-hop wireless mesh networks. In Pro-

ceedings of the 12th annual international conference on Mo-

bile computing and networking, pages 38–49. ACM, 2006.

[39] Mathias Kurth, Anatolij Zubow, and Jens-Peter Redlich. Multi-

channel link-level measurements in 802.11 mesh networks. In

Proceedings of the 2006 international conference on Wireless

communications and mobile computing, pages 937–944. ACM,

2006.

[40] Nagesh S Nandiraju, Deepti S Nandiraju, Dave Cavalcanti, and

Dharma P Agrawal. A novel queue management mechanism

for improving performance of multihop flows in ieee 802.11 s

based mesh networks. In Performance, Computing, and Com-

BIBLIOGRAPHY 136

munications Conference, 2006. IPCCC 2006. 25th IEEE Inter-

national.

[41] Lili Qiu, Yin Zhang, Feng Wang, Mi Kyung Han, and Ratul

Mahajan. A general model of wireless interference. In Pro-

ceedings of the 13th annual ACM international conference

on Mobile computing and networking, pages 171–182. ACM,

2007.

[42] Kamesh Medepalli and Fouad A Tobagi. Towards performance

modeling of ieee 802.11 based wireless networks: A unified

framework and its applications. In Proceedings IEEE INFO-

COM 2006. 25TH IEEE International Conference on Com-

puter Communications, 2006.

[43] Wei Wang, Ben Leong, and Wei Tsang Ooi. Mitigating unfair-

ness due to physical layer capture in practical 802.11 mesh net-

works. Mobile Computing, IEEE Transactions on, 14(1):99–

112, 2015.

[44] Emma Fitzgerald, Saeed Bastani, and Bjorn Landfeldt. Inten-

tion sharing for medium access control in wireless lans. In

Proceedings of the 13th ACM International Symposium on Mo-

bility Management and Wireless Access, pages 21–30. ACM,

2015.

BIBLIOGRAPHY 137

[45] Anand Kashyap, Samrat Ganguly, and Samir R Das. A

measurement-based approach to modeling link capacity in

802.11-based wireless networks. In Proceedings of the 13th an-

nual ACM international conference on Mobile computing and

networking, pages 242–253. ACM, 2007.

[46] Ilenia Tinnirello, Giuseppe Bianchi, and Yang Xiao. Refine-

ments on ieee 802.11 distributed coordination function model-

ing approaches. Vehicular Technology, IEEE Transactions on,

59(3):1055–1067, 2010.

[47] Norman Abramson. The aloha system: another alternative for

computer communications. In Proceedings of the November

17-19, 1970, fall joint computer conference, pages 281–285.

ACM, 1970.

[48] Leonard Kleinrock, Fouad Tobagi, et al. Packet switching in

radio channels: Part i–carrier sense multiple-access modes and

their throughput-delay characteristics. Communications, IEEE

Transactions on, 23(12):1400–1416, 1975.

[49] Israel Gitman. On the capacity of slotted aloha networks and

some design problems. Communications, IEEE Transactions

on, 23(3):305–317, 1975.

BIBLIOGRAPHY 138

[50] Claude Chaudet, Isabelle Guerin Lassous, Eric Thierry, and

Bruno Gaujal. Study of the impact of asymmetry and carrier

sense mechanism in ieee 802.11 multi-hops networks through a

basic case. In Proceedings of the 1st ACM international work-

shop on Performance evaluation of wireless ad hoc, sensor, and

ubiquitous networks, pages 1–7. ACM, 2004.

[51] Saikat Ray, Jeffrey B Carruthers, and David Starobinski. Eval-

uation of the masked node problem in ad hoc wireless lans. Mo-

bile Computing, IEEE Transactions on, 4(5):430–442, 2005.

[52] Giusi Alfano, Michele Garetto, and Emilio Leonardi. New in-

sights into the stochastic geometry analysis of dense csma net-

works. In INFOCOM, 2011 Proceedings IEEE, pages 2642–

2650. IEEE, 2011.

[53] Beakcheol Jang and Mihail L Sichitiu. Ieee 802.11 satura-

tion throughput analysis in the presence of hidden terminals.

IEEE/ACM Transactions on Networking (TON), 20(2):557–

570, 2012.

[54] Bruno Nardelli and Edward W Knightly. Closed-form through-

put expressions for csma networks with collisions and hid-

den terminals. In INFOCOM, 2012 Proceedings IEEE, pages

2309–2317. IEEE, 2012.

BIBLIOGRAPHY 139

[55] Thomas Begin, Bruno Baynat, Isabelle Guerin-Lassous, and

Thiago Abreu. Performance analysis of multi-hop flows in ieee

802.11 networks: A flexible and accurate modeling framework.

Performance Evaluation, 2016.

[56] Michele Garetto, Paolo Giaccone, and Emilio Leonardi. Ca-

pacity scaling in delay tolerant networks with heterogeneous

mobile nodes. In Proceedings of the 8th ACM international

symposium on Mobile ad hoc networking and computing, pages

41–50. ACM, 2007.

[57] Michele Garetto, Paolo Giaccone, and Emilio Leonardi. Ca-

pacity scaling in ad hoc networks with heterogeneous mobile

nodes: The subcritical regime. IEEE/ACM Transactions on

Networking (TON), 17(6):1888–1901, 2009.

[58] Delia Ciullo, Valentina Martina, Michele Garetto, and Emilio

Leonardi. Impact of correlated mobility on delay-throughput

performance in mobile ad hoc networks. IEEE/ACM Transac-

tions on Networking (TON), 19(6):1745–1758, 2011.

[59] Ilenia Tinnirello, Giuseppe Bianchi, Pierluigi Gallo, Domenico

Garlisi, Francesco Giuliano, and Francesco Gringoli. Wire-

less mac processors: Programming mac protocols on commod-

BIBLIOGRAPHY 140

ity hardware. In INFOCOM, 2012 Proceedings IEEE, pages

1269–1277. IEEE, 2012.

[60] Giuseppe Bianchi, Pierluigi Gallo, Domenico Garlisi, Fabrizio

Giuliano, Francesco Gringoli, and Ilenia Tinnirello. Maclets:

active mac protocols over hard-coded devices. In Proceedings

of the 8th international conference on Emerging networking

experiments and technologies, pages 229–240. ACM, 2012.

[61] Giuseppe Bianchi and Ilenia Tinnirello. One size hardly fits all:

towards context-specific wireless mac protocol deployment. In

Proceedings of the 8th ACM international workshop on Wire-

less network testbeds, experimental evaluation & characteriza-

tion, pages 1–8. ACM, 2013.

[62] M. LI, H. Liu, et al. Performance and interference analysis of

802.11g wireless network. International Journal of Wireless

and Mobile Networks (IJWMN), pages 165–177, 2013.

[63] Michael Dinitz. Distributed algorithms for approximating

wireless network capacity. In INFOCOM, 2010 Proceedings

IEEE, pages 1–9. IEEE, 2010.

[64] Santosh Kawade, Terry G Hodgkinson, and V Abhayaward-

hana. Interference analysis of 802.11 b and 802.11 g wire-

BIBLIOGRAPHY 141

less systems. In Vehicular Technology Conference, 2007. VTC-

2007 Fall. 2007 IEEE 66th, pages 787–791. IEEE, 2007.

[65] Santosh Kawade and Terry G Hodgkinson. Analysis of inter-

ference effects between co-existent 802.11 b and 802.11 g wi-

fi systems. In Vehicular Technology Conference, 2008. VTC

Spring 2008. IEEE, pages 1881–1885. IEEE, 2008.

[66] Steven Weber, Jeffrey G Andrews, and Nihar Jindal. An

overview of the transmission capacity of wireless networks.

Communications, IEEE Transactions on, 58(12):3593–3604,

2010.

[67] Liqun Fu, Soung Chang Liew, and Jianwei Huang. Effective

carrier sensing in csma networks under cumulative interfer-

ence. Mobile Computing, IEEE Transactions on, 12(4):748–

760, 2013.

[68] Stefano Vitturi, Lucia Seno, Federico Tramarin, and Matteo

Bertocco. On the rate adaptation techniques of ieee 802.11 net-

works for industrial applications. Industrial Informatics, IEEE

Transactions on, 9(1):198–208, 2013.

[69] Daji Qiao, Sunghyun Choi, and Kang G Shin. Interference

analysis and transmit power control in ieee 802.11 a/h wire-

BIBLIOGRAPHY 142

less lans. IEEE/ACM Transactions on Networking (TON),

15(5):1007–1020, 2007.

[70] Eiman Alotaibi, Vishwanath Ramamurthi, Marwan Batayneh,

and Biswanath Mukherjee. Interference-aware routing for

multi-hop wireless mesh networks. Computer Communica-

tions, 33(16):1961–1971, 2010.

[71] Qin Liu, Xiaohua Jia, and Yuan Zhou. Topology control for

multi-channel multi-radio wireless mesh networks using direc-

tional antennas. Wireless Networks, 17(1):41–51, 2011.

[72] Neeraj Kumar, Manoj Kumar, and RB Patel. Capacity and in-

terference aware link scheduling with channel assignment in

wireless mesh networks. Journal of Network and Computer

Applications, 34(1):30–38, 2011.

[73] Anurag Kumar, Eitan Altman, Daniele Miorandi, and Munish

Goyal. New insights from a fixed point analysis of single cell

ieee 802.11 wlans. In INFOCOM 2005. 24th Annual Joint Con-

ference of the IEEE Computer and Communications Societies.

Proceedings IEEE, volume 3, pages 1550–1561. IEEE, 2005.

[74] Wikipedia. Friis transmission equation — wikipedia, the free

encyclopedia, 2015. [Online; accessed 21-August-2015].

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