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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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ii
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
iii
iv
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:
v
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-
vi
vii
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
viii
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-
ix
x
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.
xi
• 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
xii
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
xvi
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
xvii
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
3.5 Sample nodes placement. . . . . . . . . . . . . . . . 45
3.6 Receivers Connected Topologies . . . . . . . . . . . 47
3.7 Symmetric Not Connected Topologies . . . . . . . . 48
3.8 Sample nodes placement. . . . . . . . . . . . . . . . 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
xx
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
CHAPTER 1. INTRODUCTION 3
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
CHAPTER 1. INTRODUCTION 4
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
CHAPTER 1. INTRODUCTION 5
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
CHAPTER 1. INTRODUCTION 6
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.
CHAPTER 1. INTRODUCTION 7
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.
CHAPTER 1. INTRODUCTION 8
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
CHAPTER 1. INTRODUCTION 9
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
CHAPTER 1. INTRODUCTION 10
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-
CHAPTER 1. INTRODUCTION 11
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
CHAPTER 1. INTRODUCTION 12
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-
CHAPTER 1. INTRODUCTION 13
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
CHAPTER 1. INTRODUCTION 14
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
CHAPTER 1. INTRODUCTION 15
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
CHAPTER 1. INTRODUCTION 16
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-
CHAPTER 1. INTRODUCTION 17
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-
CHAPTER 2. LITERATURE REVIEW 20
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
CHAPTER 2. LITERATURE REVIEW 21
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].
CHAPTER 2. LITERATURE REVIEW 22
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-
CHAPTER 2. LITERATURE REVIEW 23
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-
CHAPTER 2. LITERATURE REVIEW 24
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
CHAPTER 2. LITERATURE REVIEW 25
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
CHAPTER 2. LITERATURE REVIEW 26
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-
CHAPTER 2. LITERATURE REVIEW 27
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.
CHAPTER 2. LITERATURE REVIEW 28
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
CHAPTER 2. LITERATURE REVIEW 29
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-
CHAPTER 2. LITERATURE REVIEW 30
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
CHAPTER 2. LITERATURE REVIEW 31
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
CHAPTER 2. LITERATURE REVIEW 32
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
CHAPTER 2. LITERATURE REVIEW 33
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
CHAPTER 2. LITERATURE REVIEW 34
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
CHAPTER 2. LITERATURE REVIEW 35
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
CHAPTER 2. LITERATURE REVIEW 36
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
CHAPTER 2. LITERATURE REVIEW 37
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].
CHAPTER 2. LITERATURE REVIEW 38
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
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY41
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
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY42
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
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY43
(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
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY44
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.
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY45
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
Figure 3.5: Sample nodes placement.
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY46
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
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY47
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
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY48
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
Figure 3.8: Sample nodes placement.
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY49
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
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY50
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-
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY51
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
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY52
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 .
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY53
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 .
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY54
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
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY55
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.
CHAPTER 3. TWO FLOW CLASSIFICATION AND OCCURRENCE PROBABILITY56
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 59
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 60
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.
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 61
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 62
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 63
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 64
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-
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 65
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-
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 66
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.
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 67
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 68
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 69
A RTS (A) CTS (a) ACK (a) DIFS
a RTS (A) CTS (a) ACK (a) DIFS
B f
Receiver b RTS (A)
Channel sensed idle Channel busy Signalextension & SIFS
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 70
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)
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 71
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-
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 72
200 400 600 800 1000 12002
3
4
5
6
7
8
Data Payload Size (bytes)
Thr
ough
put (
Mbp
s)
model flow Aopnet flow Amodel flow Bopnet flow B
(a) SSRC
200 400 600 800 1000 12000
5
10
15
Data Payload Size (bytes)
Thr
ough
put (
Mbp
s)
model flow Aopnet flow Amodel flow Bopnet flow B
(b) ASRC
200 400 600 800 1000 12002
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
Data Payload Size (bytes)
Thr
ough
put (
Mbp
s)
model flow Aopnet flow Amodel flow Bopnet flow B
(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-
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 73
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-
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 74
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 75
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 76
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 77
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 78
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 79
200 300 400 500 600 700 800 900 1000 11002
3
4
5
6
7
8
Data Payload Size (bytes)
Thr
ough
put (
Mbp
s)
model flow Aopnet flow Amodel flow Bopnet flow B
(a) SNC per flow throughput
40 45 50 55 60 654
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
Distance (meters)
Thr
ough
put (
Mbp
s)
model flow Aopnet flow A
(b) SNC per flow throughput with increasing distance d(A, B)
Figure 4.6: Per flow throughput of SNC
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 80
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 81
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-
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 82
A RTS (A) CTS (a) ACK (a) DIFS
a RTS (A) CTS (a) ACK (a) DIFS
B
Receiver b
Channel sensed idle Channel busy Signalextension & SIFS
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
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 83
200 300 400 500 600 700 800 900 1000 11000
2
4
6
8
10
12
14
16
Data Payload Size (bytes)
Thr
ough
put (
Mbp
s)
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
40 45 50 55 60 654
5
6
7
8
9
10
Distance (meters)
Thr
ough
put (
Mbp
s)
model flow Aopnet flow Amodel flow Bopnet flow B
(b) Per flow throughput for ANC with increasing distance d(A, b)
Figure 4.8: Per flow throughput of ANC
CHAPTER 4. INTERFERENCE AND THROUGHPUT ANALYSIS 84
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 87
[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-
CHAPTER 5. THROUGHPUT MODELING IN WMN 88
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 89
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.
CHAPTER 5. THROUGHPUT MODELING IN WMN 90
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-
CHAPTER 5. THROUGHPUT MODELING IN WMN 91
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 92
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 93
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)
CHAPTER 5. THROUGHPUT MODELING IN WMN 94
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 95
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 96
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-
CHAPTER 5. THROUGHPUT MODELING IN WMN 97
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-
CHAPTER 5. THROUGHPUT MODELING IN WMN 98
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 99
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 100
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-
CHAPTER 5. THROUGHPUT MODELING IN WMN 101
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
13: for ∀u ∈ U do . for all virtual nodes in U
14: GU ← GU + gu
15: end for
16: while i ≤ n do . for all stations
17: λidle (i)← GU
18: end while
19: while i ≤ n do . for all stations
20: T idle(i)← 1λidle(i)
21: end while
CHAPTER 5. THROUGHPUT MODELING IN WMN 102
Compute average duration of a busy period of i
22: while i ≤ n do . for all stations
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
25: for ∀u ∈ U do . for all virtual nodes in U
26: λU ← λU + λu
27: end for
28: while i ≤ n do . for all stations
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
31: while i ≤ n do . for all stations
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 103
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 104
(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).
CHAPTER 5. THROUGHPUT MODELING IN WMN 105
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 106
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:
CHAPTER 5. THROUGHPUT MODELING IN WMN 107
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-
CHAPTER 5. THROUGHPUT MODELING IN WMN 108
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.
CHAPTER 5. THROUGHPUT MODELING IN WMN 109
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-
CHAPTER 5. THROUGHPUT MODELING IN WMN 110
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 111
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
CHAPTER 5. THROUGHPUT MODELING IN WMN 112
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.
CHAPTER 5. THROUGHPUT MODELING IN WMN 113
(a) Flow topology
(b) Connectivity graph
Figure 5.3: Network topology and connectivity graph
CHAPTER 5. THROUGHPUT MODELING IN WMN 114
Figure 5.4: Analytical comparison of busy time probability
CHAPTER 5. THROUGHPUT MODELING IN WMN 115
Figure 5.5: Analytical comparison of conditional packet loss probability
CHAPTER 5. THROUGHPUT MODELING IN WMN 116
Figure 5.6: Contribution of packet loss probability due to information asymmetry
CHAPTER 5. THROUGHPUT MODELING IN WMN 117
Figure 5.7: Comparison between analytical transmission probabilities
CHAPTER 5. THROUGHPUT MODELING IN WMN 118
Figure 5.8: Analytical comparison of throughput
CHAPTER 5. THROUGHPUT MODELING IN WMN 119
Figure 5.9: Comparison between analytical normalized throughput
CHAPTER 5. THROUGHPUT MODELING IN WMN 120
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-
CHAPTER 6. CONCLUSION 123
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
CHAPTER 6. CONCLUSION 124
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-
CHAPTER 6. CONCLUSION 125
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.
CHAPTER 6. CONCLUSION 126
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
CHAPTER 6. CONCLUSION 127
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.
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