UNIVERSITY OF CINCINNATI
Date:______
I, ______, hereby submit this work as part of the requirements for the degree of: in:
It is entitled:
This work and its defense approved by:
Chair: ______
Modeling and Performance Analysis of Mobile Ad Hoc Networks
A dissertation submitted to the
Division of Graduate Studies and Research of The University of Cincinnati
In partial fulfillment of the requirements for the degree of
DOCTOR OF PHILOSOPHY
In the Department of Electrical & Computer Engineering and Computer Science of the College of Engineering by Xiaolong Li M.E., (EE), Huazhong University of Science & Technology, China, 2002. B.E., (EE), Huazhong University of Science & Technology, China, 1999.
Thesis Advisor and Committee Chair: Dr. Qing-An Zeng
February 23, 2006 Abstract
Ad hoc networks are gaining increasing popularity in recent years because of their ease of deployment. No wired base station or infrastructure is supported, and each host communicates one another via packet radios. In ad hoc networks, nodes are mobile which bring many challenges, such as network connectivity, topology change, link characteristic, and etc. In this research work, a novel model to analyze the link stability in mobile ad hoc networks is proposed. In the proposed analytical model, between each communicating pair, one node is considered to be stationary while the other moves relative to it. With this method, the mobility models defined in this dissertation can be approximated as a fluid flow model. Using the result of the fluid flow model, the analytical model for the link duration is obtained, which is used to obtain the link holding time and the link breaking probability of a communicating pair. The distribution of a routing path duration and the routing path breaking probability are also obtained by extending the models of the link duration and the link breaking probability. These results of link and routing path stabilities are serviced as ground knowledge to obtain the performance of medium access control (MAC) protocol considering node mobility.
1 MAC protocols are a fundamental element that determines the efficiency in sharing the limited communication bandwidth of wireless channels. IEEE 802.11 distributed coordination function (DCF) MAC protocol is the most widely used
MAC protocol in ad hoc networks due to its compatibility with the IEEE 802 protocol suite. Since the release of the IEEE 802.11 standard, many research efforts have been devoted to modeling the performance of this protocol. However, most of studies are confined to the stationary performance where the nodes are immobile. In this research work, we employ the link and routing path stability models to analyze the performance of the IEEE 802.11 DCF MAC protocol in dynamic environment. To the best of our knowledge, this is the first time to evaluate the performance of this protocol with mobility.
Another contribution of this research work is to analyze the performance of the
IEEE 802.11 DCF MAC protocol with capture effect. Currently, most analytical models assume that all received packets at the receiver have the same physical conditions (same power, same coding, etc), so when two or more nodes transmit their packets at the same time, the collision happens and all packets involved are destroyed, which may not be the case in reality due to capture effect. In this research work, we provide an analytical model to obtain the probability of capture effect. We use this probability of capture effect to analyze the throughput of the IEEE 802.11 DCF MAC protocol in ad hoc networks considering path loss, multipath fading, and shadowing.
Wireless channel is time-varying and error prone. The packet transmission can be failed due to transmission errors. In this research work, a refined analytical
2 model is presented to evaluate the performance of the IEEE 802.11 DCF MAC protocol with time-varying wireless channel. In the proposed model, the time- varying wireless channel is modeled by a finite-state Markov (FSM) chain. In each channel state, the operation of the IEEE 802.11 DCF MAC protocol is modeled by an embedded Markov chain. Using this model, the throughput of the DCF protocol can be theoretically calculated. The results show that the performance of the DCF protocol strongly depends on the network size, the incoming traffic loads, and the bit error rate (BER). When the incoming traffic load is light, the throughput increases when the network size grows. When the network works under heavy
(saturated) condition, the throughput decreases when the network size grows. The throughput always degrades when increasing BER regardless the network size and the traffic load.
3
Acknowledgements
I am most grateful and indebted to my advisor, Professor Qing-An Zeng, for the large doses of guidance, patience, and encouragement he has shown me during my time here at The University of Cincinnati. He always found time whenever I needed an intelligent discussion. It is a pleasure, as well as a honor, to work with him. I am also grateful and indebted to Professor Dharma Agrawal, for inspiration and enlightening discussions on a wide variety of topics. I thank my other committee members, Professor Anca Ralescu, Professor James Caffery, and Professor Heng
Wei, for their insightful commentary on my work.
Also, I would like to extend my gratitude to the department staff members.
My special thanks to Julie Muenchen and Teresa Hamad for making sure I stay out of trouble.
Finally, I would like to express my deepest gratitude to my family and friends.
I thank Duojia Zhu, my wife, who has been an endless source of encouragement and support through the most trying of times. I would like to extend my endless gratitude and love to my parents, without whom I would never have been able to think of embarking on such a journey.
i Table of Contents
1 Introduction 1
1.1 Background and Motivation ...... 1
1.1.1 Wireless Local Area Networks ...... 1
1.1.2 Challenges in Ad Hoc Networks ...... 3
1.2 Contributions ...... 7
1.3 Organization of the dissertation ...... 8
1.4 Summary ...... 8
2 Overview of Mobility Models and MAC Protocols 9
2.1 Introduction ...... 9
2.2 Mobility Models ...... 10
2.2.1 Independent Mobility Models ...... 10
2.2.2 Group Mobility Models ...... 14
2.2.3 Other Mobility Parameters ...... 15
2.3 MAC Protocols ...... 15
2.3.1 Carrier Sense Multiple Access ...... 16
2.3.2 Multiple Access with Collision Avoidance ...... 16
ii 2.3.3 Floor Acquisition Multiple Access ...... 17
2.3.4 IEEE 802.11 Distributed Coordination Function ...... 18
2.4 Summary ...... 20
3 Link and Routing Path Stabilities in Mobile Ad Hoc Networks 21
3.1 Introduction ...... 21
3.2 System Model ...... 23
3.3 Analysis of Node Motion ...... 25
3.4 Analysis of Link Characteristics ...... 26
3.4.1 Link Duration ...... 27
3.4.2 Link Holding Time ...... 29
3.4.3 Link Breaking Probability ...... 30
3.5 Simulations and Discussions ...... 32
3.6 Summary ...... 39
4 Performance Analysis of MAC Protocol in Mobile Ad Hoc Net-
works 41
4.1 Introduction ...... 41
4.2 Single-hop Ad Hoc Networks ...... 43
4.2.1 System Model ...... 43
4.2.2 Performance Analysis ...... 44
4.3 Multi-hop Ad Hoc Networks ...... 52
4.3.1 System Model ...... 52
4.3.2 Performance Analysis ...... 53
iii 4.4 Simulations and Discussions ...... 59
4.5 Summary ...... 61
5 Impact of Capture Effect on the Performance of MAC Protocol 63
5.1 Introduction ...... 63
5.2 Channel Model ...... 65
5.3 Capture Model ...... 67
5.4 Analytical Model ...... 70
5.5 Numerical Results and Discussions ...... 72
5.6 Summary ...... 76
6 Influence of Time-varying Channel on the Performance of MAC
Protocol 79
6.1 Introduction ...... 79
6.2 Wireless Channel Model ...... 81
6.3 Analytical Model ...... 84
6.4 Numerical Results and Discussions ...... 89
6.5 Summary ...... 91
7 Conclusions and Future Work 94
7.1 Conclusions ...... 94
7.2 Future Work ...... 97
iv List of Figures
2.1 Illustration of hidden node problem ...... 17
2.2 Illustration of exposed node problem ...... 18
2.3 Basic CSMA/CA Protocol ...... 20
2.4 CSMA/CA with RTS/CTS protocol ...... 20
3.1 System model ...... 24
3.2 pdfs of link duration ...... 34
3.3 pdfs of routing path duration ...... 35
3.4 pdfs of link holding time ...... 37
3.5 Link breaking probability versus average virtual packet transmission
time ...... 38
3.6 Routing path breaking probability versus average speed ...... 40
4.1 Embedded slots ...... 46
4.2 Markov chain model for the entire network ...... 46
4.3 Structure of time Tv ...... 51
4.4 System model ...... 53
4.5 Illustration of hidden area ...... 54
v 4.6 Throughput of CSMA/CA protocol ...... 60
4.7 Throughput for basic CSMA/CA ...... 61
4.8 Throughput for CSMA/CA with RTS/CTS ...... 61
5.1 Spatial distribution of two arbitrary nodes in ad hoc networks . . . 66
5.2 pdf of distance R between any two nodes in ad hoc networks . . . . 67
5.3 Capture probability in infrastructure mode (σs = 1.35) ...... 73
5.4 Capture probability in ad hoc mode (σs = 1.35) ...... 73
5.5 Capture probability in infrastructure mode (σs = 1.35) ...... 74
5.6 Capture probability in an ad hoc mode (σs = 1.35) ...... 74
5.7 Throughput of basic CSMA/CA versus traffic load G with capture
model of the first category ...... 75
5.8 Throughput of CSMA/CA with RTS/CTS versus traffic load G with
capture model of the first category ...... 76
5.9 Throughput of basic CSMA/CA versus traffic load G with capture
model of the second category ...... 77
5.10 Throughput of CSMA/CA with RTS/CTS versus traffic load G with
capture model of the second category ...... 78
vi List of Tables
6.1 ek and χk in 4-state and 7-state FSM channel models ...... 90
6.2 Throughput of IEEE 802.11 DCF versus traffic load G ...... 91
6.3 Throughput of IEEE 802.11 DCF versus number of stations (G = 0.2) 92
6.4 Throughput of IEEE 802.11 DCF versus number of stations (G = 2.2) 93
vii List of Abbreviations
MAC Medium access control
IEEE Institute of Electrical and Electronics Engineers
DCF Distributed coordination function
PCF Point coordination function
FSM Finite state Markov
BER Bit error rate
WLAN Wireless local area network
CSMA/CA Carrier sense multiple access with collision avoidance
CSMA Carrier sense multiple access
MACA Multiple access with collision avoidance
FAMA Floor acquisition multiple access
FAMANTR Floor acquisition multiple access with non-persistent transmit request
RTS Ready to send
CTS Clear to send
ACK Acknowledgment
DIFS Distributed interframe space
SIFS Short interframe space
viii CW Contention window pdf Probability density function
CDF Cumulative distribution function
DSR Dynamic source routing
AODV Ad hoc on-demand distance routing
BSS Basic service set
FSK Frequency shift keying
NCFSK Non-coherent frequency shift keying
BPSK Binary phase shift keying
π/4-DQPSK π/4 differential quadrature phase shift keying
SNR Signal to noise ratio
BSC Binary symmetric channel
TDD Time division duplex
QoS Quality of service
ix Chapter 1
Introduction
1.1 Background and Motivation
1.1.1 Wireless Local Area Networks
In recent years, the continuing advances in communications and networks and the ever-increasing demand for mobility of users, have been fueling the interest in wireless communications. Mobility, broadband, installation speed, simplicity, scal- ability, and less vulnerability to point-of-break problem, make wireless local area networks (WLANs) a good candidate for providing wireless services [1]. WLANs utilize electromagnetic waves, particularly spread-spectrum technology based on radio waves, to transfer information between devices (nodes) in a limited area.
There are two types of WLANs, infrastructure WLANs and independent WLANs.
Infrastructure WLANs, where the wireless network is linked to a wired network, are more commonly deployed today. In an infrastructure WLAN, the wireless network
1 is connected to a wired network such as Ethernet, via access points, which possesses both Ethernet links and antennas to send signals. These signals span microcells, or circular coverage areas (depending on walls and other physical obstructions), in which nodes can communicate with the access points, and through these, with the wired network. The independent WLAN is a peer-to-peer network, which is dynamically created and maintained by the individual nodes. The independent
WLAN is usually called ad hoc network, which does not require a pre-existing architecture for communication purposes and does not rely on any type of wired infrastructure. Nodes forward packets to or from each other via a common wireless channel. The nature of ad hoc network makes them suitable for applications from military use in battlefields and personnel coordinate tools in emergency disaster relief, to sensor networks which have many applications themselves.
Two different architectures exist for ad hoc networks: flat and hierarchical [2].
The flat network is the simplest because all mobile nodes are equal in this network.
The flat network requires each mobile node to participate in the forwarding and receiving of packets depending on the implemented routing scheme. A hierarchical network uses a tiered approach and consists of two or more tiers. The bottom tier consists of mobile nodes grouped into several smaller networks. A single member from each of these groups acts as a gateway or cluster head to the next higher tier.
Together, the gateways or cluster heads create the next higher tier. When a mobile node belonging to a group wants to interact with another mobile node located in the same group, routing is the same as in a flat ad hoc network. However, for example, if a mobile node in group A wants to communicate with another mobile
2 node in group B, more advanced routing techniques incorporating the higher tiers must be implemented. In this research work, we assume that the flat ad hoc network is used.
1.1.2 Challenges in Ad Hoc Networks
Although ad hoc networks are treated with little difference in the IEEE standards for wireless networks as a whole, some unique features make ad hoc networks distinct from other types of wireless networks such as wireless cellular networks.
These unique features also bring some new challenges compared with other type of wireless networks.
The first unique feature is infrastructureless. Ad hoc networks are usually deployed in emergent and temporary situations such as accidents or public gath- erings, where mobile nodes may join the network at will, move around, or become disconnected at any time. The node mobility generates rapid changes in network connectivity and link characteristics. In ad hoc networks, some research work has been done in this area to analyze the link characteristics either via simulations [3]
- [5] or analytical models [6] [7]. These research work has their own restrictions.
[3] - [5] only provided the simulation results. [6] and [7] analyzed the link and path availabilities with two different mobility models. However, these studies are not enough to describe the link status in ad hoc networks. In our research work, we propose an analytical model to study the link stability using more metrics, i.e., link duration, link holding time, and link breaking probability. Our model can be
3 easily extended to describe a routing path stability.
Because of the above-mentioned feature, the state of ad hoc networks is far less predictable than that of other networks and it is quite natural for individual nodes to share a common wireless channel via distributed mechanisms. Thus, how the medium access control (MAC) protocol is designed to allocate the communi- cation resources efficiently and fairly of ad hoc networks largely determines the network performance, which can be measured in term of throughput, transmission delay, and fairness etc. In the literature, the IEEE 802.11 MAC protocol has been widely used due to its compatibility with the IEEE 802 MAC protocol suite [9].
The IEEE 802.11 MAC protocol has defined two fundamental medium access con- trol methods: the contention-based distributed coordination function (DCF) and contention-free based point coordination function (PCF). The IEEE 802.11 DCF, which provides a controlled access method to the shared wireless media called
Carrier-Sense Multiple Access with Collision Avoidance (CSMA/CA), is the most popular MAC protocol used in both infrastructure WLAN and ad hoc networks.
Therefore, in this research work, we focus our analysis on the performance of DCF mechanism. Since the release of the IEEE 802.11 standard, many research efforts have been devoted to modeling the performance of the IEEE 802.11 DCF medium access method. In [10], Bianchi used Markov chain model to analyze DCF opera- tion and provided a close-form to calculate the saturated throughput of the IEEE
802.11 DCF protocol. In particular, Bianchi modeled the idealistic assumption of only collision errors, that packet retransmissions are unlimited and a packet is be- ing transmitted continuously until its successful reception. [11] extended Bianchi’s
4 model to include the finite retry limits as defined in the IEEE 802.11 standard.
[12] analyzed the channel capacity - i.e., maximum throughput - when using the basic CSMA/CA protocol. In [13], although the authors tried to analyze the per- formance of CSMA/CA, the analysis is only based on p-persistent CSMA, not the exact CSMA/CA. All these papers are restricted to the analysis in single-hop ad hoc networks. [14] used a linear feedback model to evaluate the performance of the IEEE 802.11 DCF protocol without assuming the traffic to be in a saturated state. However, the nodes in all above studies are stationary without mobility. In this study, we take the mobility effect into account to study the performance of the
IEEE 802.11 DCF protocol with a general traffic load (from light traffic to heavy traffic) in dynamic environment.
In mobile ad hoc network, it is unrealistic to expect such a network to be fully connected, in which a mobile node can communicate directly with every other nodes in the network via wireless channels. As a result, another important feature emerges - multi-hop communication. Each node in the network has to take the responsibility of relaying packets for its peers and a packet may traverse multiple nodes before it reaches the destination. Two typical problems, namely hidden node and exposed node problems, come along with multi-hop communication. The work from [15] analyzed the impact of hidden node problem and obtained the saturated throughput of CSMA/CA with RTS/CTS in a two-hop ad hoc networks. A simple model to derive the saturated throughput of collision avoidance protocols based on a RTS/CTS handshake in a two-hop ad hoc networks is presented in [16].
Up to now, the studies mainly focus on the saturated throughput in fixed ad
5 hoc networks. In our research work, we release these restrictions and analyze the throughput of CSMA/CA protocol in dynamic ad hoc networks with general traffic load.
In classical analysis of MAC protocols, it is assumed that all packets involved in collision are destroyed. This is somewhat unrealistic assumption in mobile networks because of the difference in power levels of the transmitted packets at the receiver introduced by multipath fading, shadowing, and path loss. In ad hoc networks, a packet with the strongest received power might be successfully decoded at the receiver even in presence of simultaneous transmissions of multiple packets. This phenomena is called capture effect. Although there are many studies to analyze the performance of MAC protocols [10] - [14], few consider the capture effect [17] [18]. Their models essentially rely on the p-persistent CSMA protocol, which differ from the standard protocol in the selection of the backoff interval. In our research work, by using the probability and statistical methods, we calculate the probability of capture effect. We take this capture effect into account and theoretically predict the performance of CSMA/CA protocol in an ad hoc network considering path loss, multipath fading, and shadowing.
Wireless channels are severely affected by time-varying losses due to path loss, shadowing, and multipath fading. While the variation in the losses due to path loss and shadowing is relatively slow, the variation due to multipath fading is quite fast.
The fading envelope due to multipath fading often follows a Rayleigh distribution, so that the envelope squared has an exponential distribution. Most notably, the correlation in the multipath fading behavior and its effect on the performance of
6 MAC protocols have not been adequately addressed in the literature so far. The primary focus of chapter 6 is to address this void. In this chapter, the influence of time-varying channel on the performance of CSMA/CA protocol is analyzed.
1.2 Contributions
Our accomplishments, which are elaborated throughout of this research, can be broadly listed as follows:
• Model and analyze the impact of node mobility on the link and routing path
stabilities. The link and routing path stabilities include link and routing
path durations, link holding time, link breaking probability, and routing
path breaking probability.
• Study and compare the performance of the IEEE 802.11 MAC protocol in
stationary and dynamic ad hoc networks. Our research work is the first to
perform an analytical study of the IEEE 802.11 MAC protocol in dynamic
ad hoc network environment.
• Study and compare the performance of the IEEE 802.11 MAC protocol with
different capture models. Our research work is the first to perform an ana-
lytical model of this protocols with various capture models under a general
traffic load.
• Obtain an analytical model of the performance of the IEEE 802.11 MAC
protocol with time-varying wireless channel environments. Our proposed
7 model takes into account various incoming traffic load, network size, and bit
error rate (BER).
1.3 Organization of the dissertation
The rest of this dissertation is organized as follows: Mobility models and MAC protocols are introduced in the next Chapter. The impact of node mobility on link and routing path stabilities are discussed in Chapter 3. The performance of the IEEE 802.11 DCF MAC protocols in stationary and dynamic ad hoc network environments is provided in Chapter 4. Chapter 5 analyzes the capture effect and its impact on the IEEE 802.11 DCF MAC performance in WLANs with path loss,
Rayleigh fading, and shadowing. In Chapter 6, influence of time-varying channel on the performance of the IEEE 802.11 MAC protocol is analyzed. Finally, we make conclusions and discuss our future work in Chapter 7.
1.4 Summary
In this chapter, we introduced the concepts of ad hoc networks and looked into the challenging issues that have to be considered while designing ad hoc networks. We summarized our contributions and presented an organizational overview of how the dissertation is organized.
8 Chapter 2
Overview of Mobility Models and
MAC Protocols
2.1 Introduction
Obviously, nodes in ad hoc networks are mobile and may move from one loca- tion to another. However, finding ways to model these movements is not obvious.
Since a real movement pattern is difficult to obtain, a common approach is to use synthetic mobility models, which represent the behavior of a real mobile scenario.
These mobility models are used to determine whether the proposed protocols will be useful when implemented. Therefore, the mobility models play a very important role when evaluating the performance of mobile ad hoc networks. The mobility models used in mobile ad hoc networks can be roughly divided into two categories: independent and group. The independent mobility models are usually used to describe the mobility of an individual node in which the movement of each node
9 is modeled independently of any other nodes. While the group mobility models are used to describe the aggregate pattern of all nodes where there are some re- lationships among the nodes and their movements. In this chapter, we survey a number of synthetic independent and group mobility models used in mobile ad hoc networks.
In ad hoc networks, how the MAC protocol is designed to allocate the communi- cation resources efficiently and fairly largely determines the network performance.
In the literature, many researchers have proposed a lot of MAC protocols [19] - [22].
In this chapter, we introduce these MAC protocols which are the basic knowledge of our dissertation.
2.2 Mobility Models
2.2.1 Independent Mobility Models
In this section, we present several independent mobility models proposed for the simulation and analysis of mobile ad hoc networks.
• Fluid flow model [23]
The fluid flow model has been used to model the mobility of vehicular on
highways and other similar situations with a constant flow of mobile nodes.
It requires a continuous movement without stop-and-go interruption.
• Random walk model [8] [24]
The simplest mobility model used in ad hoc networks is known as the ran-
10 dom walk model, which is sometimes referred as to Brownian motion. In
this model, a mobile node moves from its current location to a new location
by randomly choosing its moving speed and moving direction in which to
travel. The new moving speed and moving direction are both chosen from
pre-determined range [Vmin,Vmax] of moving speed and range [0, 2π) of mov-
ing direction, respectively. Each movement in this model occurs in either
a constant time interval or a constant distance, at the end of which a new
moving speed and a new moving direction are generated.
The random walk model is memoryless since it does not use the past in-
formation when generating new moving speed and moving direction. This
characteristic can generate sudden stops and sharp turns. Another charac-
teristic of this mobility model is that it will not change the distribution of
mobile nodes if the initial distribution of mobile nodes is uniform. (other
models, such as the random waypoint model, which will be discussed in the
following section, changes the distribution of mobile nodes). In its use, the
model is sometimes modified. For example, the moving speed in [8] is a ran-
dom variable with mean µi and variance σi for mobile node i. Mobile node
changes its moving speed and moving direction after an interval τi, where τi
is exponentially distributed with rate 1/E[τi].
• Random waypoint model [25]
In ad hoc network literature, the random waypoint model is probably the
most widely used mobility model. In this model, a mobile node chooses
11 uniformly a destination in the service area and travels toward the destination
with a moving speed chosen uniformly in the interval [Vmin,Vmax] of moving
speed. Once the mobile node reaches the destination, it pauses for a specified
time period according to some random variable before starting the process
again. Recently, a study of this model has revealed that the random waypoint
model does not lead to a uniform distribution of mobile nodes if the mobile
nodes are initially distributed uniformly around the simulation area [26]. It
has a border effect which results in fewer mobile nodes around the border.
The border effect can be overcame by a boundless mobility model in which
a node that reaches one side of the simulation area continues to travel and
reappears on the opposite side of the simulation area [2]. A recent study
[27] of random waypoint model also found that even though the speed of a
mobile node is chosen uniformly at random from a given interval, the speed of
a mobile node in a steady state is not necessarily from the same distribution.
• Gauss-Markov model [28]
The Gauss-Markov mobility model was originally proposed in [28] to adapt
to different levels of randomness via one tuning parameter. In this model, a
mobile node is initially assigned a moving speed V0 and a moving direction
Θ0. The values of moving speed Vm and moving direction Θm at the time
interval m are updated as follows:
p 2 Vm = γVm−1 + (1 − γ)V + 1 − γ Xm−1 (2.1)
12 and
p 2 Θm = γΘm−1 + (1 − γ)Θ + 1 − γ Ym−1, (2.2)
where γ (0 ≤ γ ≤ 1) is the tuning parameter used to vary the randomness,
V and Θ are mean values of moving speed and moving direction when m
approaches infinity, and Xm−1 and Ym−1 are random variables from Gaussian
process with zero mean.
The Gauss-Markov model can eliminate the sudden stops and sharp turns
encountered in the random walk mobility model by allowing past moving
speeds and moving directions to influence future moving speeds and moving
directions. The Gauss-Markov mobility model represents a wide range of
mobility models, including the fluid flow model (γ = 1) and the random
walk-based model (γ = 0).
• Manhattan grid model [29]
In this model, a grid is placed to model the streets. Each mobile node
moves along the paths, changes its moving speed and moving direction with
a certain probability at the intersections of grid.
A slight modification to the Manhattan grid model is the shortest path model
[29]. In this modified model, each mobile node follows the shortest path
from current position to the next position, which is chosen uniformly in the
simulation area. At each intersection, the mobile node makes a decision
to proceed to any of the neighboring paths such that the shortest distance
assumption is maintained. It means that mobile nodes can only go straight
13 or make a left or right turn at an intersection. Furthermore, mobile nodes
cannot make two consecutive left turns or right turns.
2.2.2 Group Mobility Models
So far we have presented several independent mobility models whose mobile nodes are completely independent of each other. However, in many situations such as conference seminar sessions, conventional events, or military scenarios, the mobile nodes are often involved in team activities and exhibit collaborative mobility. In order to model such situations, group mobility models are needed. Researchers have previously proposed several group mobility models for the purpose of simu- lating ad hoc networks with group movements [30] [31].
• Reference point group mobility model (RPGM) The RPGM model
was developed by Hong et al in [31] to represent the group mobility behav-
ior of mobile nodes. For each mobility group, the model defines a logical
reference center whose movement is followed by all mobile nodes within the
group. First, the location RP (t) of the group reference center is updated
via a group motion vector, GM~ . Then each individual mobile node within
a group updates its location by adding a random motion vector RM~ to the
new reference location RP (t). The vector RM~ has its length uniformly dis-
tributed within a certain radius centered at the reference point RP (t) and
its direction is uniformly distributed between 0 and 2π. This random vector
RM~ is independent from the node’s previous location.
14 • Other group mobility models[32]
The other group mobility models, such as column mobility model, nomadic
community mobility model, and pursue mobility model , can be implemented
as the special cases of the RPGM model.
2.2.3 Other Mobility Parameters
While not relevant to all mobility models, there are other factors that relate to the simulation of node mobility. Various parameters relating to the field itself may influence mobility. By applying constraints to the paths that mobile nodes may follow, the simulation and analysis may be radically affected. For example, the obstacle mobility model in [33] limits the mobile nodes movement due to the objects such as buildings and other structures.
Another consideration that affects the mobility model is the border of simu- lation area. In the real world, there may be no effective of border effect or stay within a very big area (city, campus, etc.). However, in the synthetic model, the border effect has a great effect on the distribution of mobile node, such as the border effect on random waypoint model.
2.3 MAC Protocols
In the following part of this chapter, we briefly introduce several selected MAC protocols which represent a progression in protocol development. Each one builds upon the previous one through the addition of either carrier sensing or control
15 overhead in order to achieve better network performance.
2.3.1 Carrier Sense Multiple Access
The carrier sense multiple access (CSMA) [19] protocol is the most primitive of the MAC protocol utilized in this study. The CSMA version used is non-persistent
CSMA. In this protocol, a node senses the channel for ongoing transmission before sending a packet. If the channel is already in use, the node sets a random timer and then waits this period of time before re-attempting the transmission. On the other hand, if the channel is not currently in use, the node begins transmission.
2.3.2 Multiple Access with Collision Avoidance
The multiple access with collision avoidance (MACA) protocol [20] improves upon
CSMA by taking steps toward the avoidance of the hidden node problem. Fig.
2.1 illustrates this problem. Node A starts its transmission to node S. Node C does not catch the transmission of A and starts its transmission to node D. The two transmissions collide at node S. The MACA protocol defines request-to-send
(RTS) and clear-to-send (CTS) control packets to solve this problem. A node wishing to send a data packet broadcasts a RTS message containing the length of the data packet that will follow. Upon receiving the RTS, the receiver responds by broadcasting a CTS packet which also contains the length of the upcoming data packet. Any node hearing either of these two control packets must be silent long enough for the data packet to be transmitted. In this way, neighboring nodes will
16 not transmit during the data transmission period, and the number of collisions is
reduced. For example, when node A wants to communicates with node S, it broad-
casts the RTS message; both nodes B and D receive the RTS message and delay
their transmission attempts. Similarly, when node S responds with a CTS, nodes
C and D also receive the CTS message and are silent during the data transmission.
In the event that two nodes send simultaneous RTS messages to the same node,
the RTS transmissions collide and are lost. If this occurs, the nodes which sent the
unsuccessful RTS messages sets a random timer utilizing the binary exponential
backoff algorithm for the next transmission attempt.
B
D C A S
Figure 2.1: Illustration of hidden node problem
The other problem is the exposed node problem. In Fig. 2.2, node D defers its transmission to node C because it hears transmission of node S to node A, even if there would be no collision at node C.
2.3.3 Floor Acquisition Multiple Access
The floor acquisition multiple access (FAMA) variant introduced here is FAMA-
NTR (Non-persistent Transmit Request) [21]. FAMA-NTR builds upon the MACA
17 B
D C A S
Figure 2.2: Illustration of exposed node problem protocol by adding non-persistent carrier sensing to the RTS/CTS exchange. Be- fore transmitting a RTS frame, a node first listens to the channel to determine if it is already in use. If the channel is busy, the node calculates a random backoff period to wait before sensing the channel again. The addition of this carrier sense to the control packet exchange aids in the prevention of control packet collisions.
2.3.4 IEEE 802.11 Distributed Coordination Function
The IEEE 802.11 MAC protocol [9] specifies a distributed coordination function
(DCF) which is based on the same RTS/CTS message exchange for unicast data transmission as the previous MACA protocol. Where the IEEE 802.11 differs, however, is its use of collision avoidance before RTS transmission, and its require- ment of an acknowledgment (ACK) transmission by the receiver after the successful reception of the data packet. The inclusion of the ACK allows immediate retrans- mission if necessary by verifying that the data packet was successfully received. In the case of node mobility, the ACK may also aid in the detection of hidden-node interference that was not detectable when the CTS message was sent.
18 In the IEEE 802.11 specification [9], there are two access protocols, namely, basic CSMA/CA and CSMA/CA with RTS/CTS. With the basic CSMA/CA pro- tocol (see Fig. 2.3), a node, before initiating a transmission, senses the medium to determine if any other node is transmitting. The node proceeds with its transmis- sion if the medium is idle for an interval that exceeds the distributed interframe space (DIFS). If the medium is busy, the node will defer its transmission until the end of the current transmission. Prior to transmission again, the node will initiate a backoff interval, a random interval being selected from [0, CW] (CW is the contention window) to initiate the backoff timer. The backoff timer is decre- mented only when the medium is idle, and it is frozen when the medium becomes busy. After a busy period, the backoff time resumes only after the medium is idle longer than DIFS. A node initiates a transmission when the backoff timer reaches zero. If the packet is successfully received at destination, the receiver will send an
ACK back to the sender after a short interframe space (SIFS). In CSMA/CA with
RTS/CTS (see Fig. 2.4), whenever a node wishes to send a data packet, it will broadcast a short RTS containing the length of the data packet that will follow.
Upon receiving the RTS, the destination responds by broadcasting a CTS packet which also contains the length of the upcoming data frame. Any node hearing ei- ther of these two control packets must be silent long enough for the data packet to be transmitted. After this exchange, the transmitter will begin the packet trans- mission. This signaling packet exchange reduces the hidden node problem. The problem is not completely solved since the RTS and CTS messages are sent with
CSMA. Thus, they are still suffer hidden node problem. But they are very short
19 packets: collision only occurs few times.
DIFS
DATA Source SIFS
ACK Destination DIFS CW
Other Defer access Backoff after defer
Figure 2.3: Basic CSMA/CA Protocol
SIFS DIFS RTS DATA Source SIFS SIFS
CTS ACK Destination DIFS NAV(RTS) CW Other NAV(CTS) Defer access Backoff after defer
Figure 2.4: CSMA/CA with RTS/CTS protocol
2.4 Summary
In this chapter, we introduced some basic knowledge which will be used in our later research. We summarized the current mobility models used in ad hoc networks.
And we also presented several MAC protocols.
20 Chapter 3
Link and Routing Path Stabilities in Mobile Ad Hoc Networks
3.1 Introduction
In this chapter, we model the link and routing path stabilities and compare the ana- lytical results with the simulation results including the probability density function
(pdf) of link duration, the pdf of link holding time, and the link breaking prob- ability with different mobility models. We believe these results are very helpful when modeling analytical models for MAC and routing protocols in mobile ad hoc networks. However, such a thought was inspired by other pioneering work done in ad hoc networks. In this section, a detailed related work is summarized and discussed.
Since ad hoc networks are still in their developing stage, not many ad hoc networks have been deployed yet. Thus, most of research work in these fields is
21 simulation-based [3] - [5]. The statistics of link duration and residual link lifetime
under several different mobility models were examined in [4]. The persistence of
a routing path under various mobility models is studied in [5] where the authors
found that the routing path persistence declines with increasing network density
and network size. [3] gave a detailed statistical results of link and routing path
durations across a set of mobility models and found that at moderate and high
velocities the exponential distribution with appropriate parameter is a good ap-
proximation of the distribution of the routing path duration.
Apart from simulation-based studies, there is some research work on analytical
model of mobility and its impact on communication links in mobile ad hoc networks
[6] [7] [34]. An analytical model of a link or a routing path availability was derived
in [6]. In this study, the authors assumed that the mobile nodes keep their velocity
(i.e., moving speed and moving direction) unchanged during the whole period.
[7] used a random walk-based mobility model and derived an expression for the
probability that a link exists at time t2, in case the link existed at the time t0.
When dealing with a joint node mobility, the authors used a transform method which was accomplished by logically treating one of the nodes to be stationary, while the other moves with an equivalent mobility vector. However, their model does not ensure, that the link exists at time t1 with t0 < t1 < t2. Therefore, no forecasts about the link duration in which the link uninterruptedly exists can be made. An analytical model on link duration in a two-hop scenario with two stationary nodes as source and destination and one node in motion as relay was provided by [34]. They found that the distribution of link duration appears to
22 be exponential. However, this model can only be used in a very special scenario, which is not a traditional ad hoc network. The exponential distribution of link duration also comes up in the analysis of routing path with DSR (dynamic source routing) in [35]. In [42], the authors provided an approximate framework to prove that under a set of mild conditions, when the number of hops becomes large, the distribution of routing path duration can indeed be accurately approximated by an exponential distribution. However, it was left open on how to derive the rates of exponential distributions for link and routing path durations. Inspired by these studies, in this chapter, we model the stability of a link using parameters of link duration, link holding time, and link breaking probability. We also find that the routing path durations can be approximated by exponential distributions when the number of links is greater than 3 or 4.
3.2 System Model
A real ad hoc network is affected by many factors, such as the distribution of mobile nodes, transmission power, irregular terrain, and etc. To simplify our analysis, we make some reasonable assumptions before starting the analysis. Although in ad hoc networks the node distribution usually exhibits some random processes, to simply our analysis, we assume that the nodes are distributed uniformly over a
flat circular area with radius R0 at the beginning. Their positions and velocities are given by the mobility models described below. We assume that all nodes have the same fixed transmission power and are equipped with omni-directional
23 antenna. Therefore, all nodes have an equal radio transmission range R. The proposed system model is shown in Figure 3.1.
Node 3
V2
Θ 2 V1 Θ 1 Node 2
Node 1 R R '
Node 4 Node M
Figure 3.1: System model
Let N = {1, 2, ..., M} denote the set of mobile nodes. In order to keep the net- work connectivity, the density of mobile nodes is large enough and keeps constant.
Each mobile node moves around the circular area independently according to our mobility models described below. In this chapter, we define two random walk- based mobility models, namely, mobility model I and mobility model II, where each mobile node moves at randomly chosen velocity.
Mobility model I: at the beginning, mobile node i (i = 1, 2, ..., M) chooses its moving speed Vi (random variable) with a pdf fV (v) in the interval [Vmin,Vmax] and moving direction Θi (random variable) with a pdf fΘ(θ) in the interval [0, 2π).
The moving speed and moving direction of a mobile node are independent and unchanged.
Mobility model II: mobile node i (i = 1, 2, ..., M) picks a moving direction Θi with a pdf fΘ(θ) in the interval [0, 2π) and moves in that direction for a specified
24 time period τi, at speed Vi, where τi is a random variable with an exponential
distribution and the moving speed Vi is a random variable with a pdf fV (v) in the interval [Vmin,Vmax]. The moving speed and moving direction of a mobile node are independent. The process repeats when the mobile node spends time period τi in the direction Θi.
3.3 Analysis of Node Motion
→ We assume that node 1 moves with a velocity V1 and node 2 moves with a velocity
→ → V2 (see Figure 3.1). The relative velocity V of node 2 to node 1 is given by
→ → → V =V2 − V1 . (3.1)
→ Thus, the magnitude of the relative velocity V is given by
q 2 2 V = V1 + V2 − 2V1V2cos(Θ1 − Θ2), (3.2)
→ → where V1 and V2 are the magnitudes of V1 and V2.
The mean value of V is given by
R Vmax R Vmax R 2πR 2πp 2 2 E[V ] = v + v − 2v1v2cos (θ1 − θ2) Vmin Vmin 0 0 1 2
·fV1,V2,Θ1,Θ2 (v1, v2, θ1, θ2)dθ1dθ2dv1dv2, (3.3)
where fV1,V2,Θ1,Θ2 (v1, v2, θ1, θ2) is the joint pdf of the random variables V1, V2,Θ1,
and Θ2, Vmin and Vmax are the minimum and maximum moving speeds, the symbol
E[X] is used to represent an average value of a random variable X throughout this
dissertation. Since the moving speeds V1 and V2 and moving directions Θ1 and Θ2
25 of nodes 1 and 2 are independent, Equation (3.3) can be simplified as
R Vmax R Vmax R 2πR 2πp 2 2 E[V ] = v + v − 2v1v2cos (θ1 − θ2) Vmin Vmin 0 0 1 2
·fV (v1)fV (v2)fΘ(θ1)fΘ(θ2)dθ1dθ2dv1dv2. (3.4)
If Θ1 and Θ2 are uniformly distributed in [0, 2π), Equation (3.4) can be further rewritten as
√ 1 R Vmax R Vmax 2 v1v2 E[V ] = 2 (v1 + v2)Fe( )fV (v1)fV (v2)dv1dv2, (3.5) π Vmin Vmin v1+v2
R 1 q 1−k2t2 where Fe(k) = 0 1−t2 dt is a complete elliptic integral of the second kind.
Therefore, in the following analysis, we can consider that node 1 is at rest, and
→ node 2 is moving at a relative velocity V instead of the two nodes moving with their respective velocities.
3.4 Analysis of Link Characteristics
Unlike the infrastructure networks where the base stations or access points are
fixed, all nodes including communicating pair and intermediate relay nodes in ad hoc networks are mobile. There exists relative movement among nodes, which increases the difficulty to analyze the performance. Here we transform this problem into an infrastructure network issue by considering one node to be stationary while the other moves with a relative velocity to the first one.
26 3.4.1 Link Duration
In ad hoc networks, the routing protocols have been extensively studied in the
literature [36] - [39]. The routing protocols can be broadly classified into two
categories: reactive protocol [36] - [38] and proactive protocol [39]. The proactive
protocol exchanges routing information periodically among nodes and constantly
maintains a set of available routes for all nodes. The reactive protocol, like DSR
[36] and AODV (ad hoc on-demand distance routing) [38], sets up a routing path
between a given source and destination pair upon an arrival of route request. In
this chapter, the routing protocol is assumed to be reactive protocol. Since ad hoc
networks have no fixed infrastructure and all nodes are mobile, links between nodes
are set up and torn down dynamically. We assume that a link between two nodes
i and j is set up when they are neighbors and the link is torn down at the time
when the distance between them is larger than the radio transmission range R.
The link duration Tl (random variable) is defined as the time period during which nodes i and j are within the radio transmission range of each other. Generally, the link duration is related to many factors, such as the mobility model, the range of moving speed, etc. One simple mobility model used in the infrastructure network is the fluid flow model [40], which assumes that a uniform density of mobile nodes throughout the service area and nodes are equally likely to move in arbitrary direction. In ad hoc networks, under steady-state, the system with mobility models
I or II does not favor any specific location. Hence, both mobility models I and II distribute mobile nodes uniformly everywhere. Using the transform method, [7]
27 → shows that the direction of V is distributed uniformly over [0, 2π). Therefore, we can consider that the mobility models described in this chapter are also a fluid
flow model. For a two-dimensional fluid flow model, the mean rate of crossing the boundary of radio transmission range [40] is given by
E [V ] L µ = , (3.6) c πA where A is the area of the radio transmission range and L is the perimeter of the area. Therefore, the average link duration is given by
πA E[T ] = . (3.7) l E [V ] L
As described in Section 3.1, Lots of previous research work has found that the link duration can be approximated as an exponential distribution [34] [42].
However, those papers leave it open on how to derive the mean of exponential distribution. With Equation (3.7), we can easily get this mean.
The routing path duration is significantly related to the link duration and can be easily obtained if the link duration is given. It is actually the minimum link duration along a routing path. For a routing path including k mobile nodes, the routing path duration Tp (random variable) is the minimum of the durations of the k-1 links. It can be given by
Tp = min{Ti}, 1 ≤ i ≤ k − 1. (3.8)
Since nodes move independently, two links without a shared node are independent.
In fact even for two neighboring links with a shared node, the correlation between them is very weak [42]. Therefore, we can make an assumption that all links along
28 a routing path are independent. Since all links are identical, we can easily obtain
the pdf of a routing path duration Tp as follows:
k−2 fTp (t) = (k − 1)fTl (t)[1 − FTl (t)] , (3.9)
where fTl (t) is the pdf of the link duration Tl and FTl (t) is the cumulative distri- bution function (CDF) of the link duration Tl. Therefore, if the link duration has an exponential distribution with mean 1/µc, the pdf of a routing path duration can be obtained as follows:
−(k−1)µct fTp (t) = (k − 1)µce . (3.10)
3.4.2 Link Holding Time
The time period from a packet generation to its successful transmission is defined as virtual packet transmission time Tv (random variable) in this dissertation. The packet transmission fails if the node moves out of its link partner’s radio trans- mission range before finishing the transmission. Therefore, the link holding time
Tlh (random variable) is equal to the smaller one of the link duration Tl and the virtual packet transmission time Tv. Therefore, we have
Tlh = min{Tl,Tv}. (3.11)
The virtual packet transmission time Tv is determined by the MAC protocol, traffic load, number of nodes, and etc. For example, in an ad hoc network with the IEEE
802.11 DCF protocol, the virtual packet transmission time may include the defer time, backoff time, packet transmission time, propagation delay, etc.
29 Since the link duration Tl and the virtual packet transmission time Tv are independent, we can obtain the pdf of the link holding time Tlh by
fTlh (t) = fTl (t)[1 − FTv (t)] + fTv [1 − FTl (t)], (3.12)
where fTv (t) is the pdf of the virtual packet transmission time Tv and FTv (t) is the
CDF of the virtual packet transmission time Tv.
3.4.3 Link Breaking Probability
Link breaking probability is another important statistic parameter to evaluate the link stability. The boundary crossing due to mobility while the virtual packet transmission is still in progress breaks the link. Thus, the breaking probability Plb of a link is the probability that the virtual packet transmission time exceeds the link duration. Therefore, we have
Plb = P (Tl < Tv). (3.13)
Since Tv and Tl are independent, we have
Z ∞Z t
Plb = fTv (t)fTl (u)dudt. (3.14) 0 0
As described above, the distribution of link duration can be approximated as an exponential distribution with mean rate µc. The exact distribution of the virtual packet transmission time is very difficult to find. For the sake of simplicity, we as- sume that the virtual packet transmission time also has an exponential distribution with mean rate µv. Therefore, we have
µc Plb = . (3.15) µc + µv
30 Substituting Equation (3.6) into Equation (3.15), Equation (3.15) can be rewritten as follows: E[V ]L Plb = . (3.16) µvπA + E[V ]L
The concept of link breaking probability can be extended to an entire routing path. In order to complete a successful transmission of a packet from a source node to a destination node, the links along the routing path which the packet has not traversed yet have to remain alive while it is not necessary for the links which it had already taken to stay alive. For example, a routing path is established between a source node and a destination node which comprises k links. The link duration and
the virtual packet transmission time for each link are Tlj and Tvj ,(j = 1, 2, ..., k),
respectively. The routing path will not break if Tv1 ≤ Tl1 , Tv1 + Tv2 ≤ Tl2 , ...,
and Tv1 + Tv2 + ... + Tvk ≤ Tlk . Thus, we can obtain the routing path breaking probability Ppb by
Ppb = 1 − P (Tv1 ≤ Tl1 ,Tv1 + Tv2 ≤ Tl2 , ..., Tv1 + Tv2 + ... + Tvk ≤ Tlk ). (3.17)
Since the transmissions along different links in a routing path do not overlap in the time domain, we can consider that the transmissions along different links are independent. Thus, we can simplify Equation (3.17) as follows:
k i Y X Ppb = 1 − P ( Tvj < Tlj ). (3.18) i=1 j=1
The virtual packet transmission time Tvj is a random variable and usually is not the same for different links. However, to simplify our analysis, we assume that the
Tvj is the same for a given packet. If both the virtual packet transmission time
31 and the link duration have exponential distributions with mean rates µv and µc,
we can simplify Equation (3.18) as follows:
µk P = 1 − v . (3.19) pb k Q (i × µc + µv) i=1
3.5 Simulations and Discussions
In order to verify our proposed theoretical model obtained in the previous sections,
we perform the following simulations. Without the loss of generality, we assume
that a source node is positioned in the origin. To evaluate the link stability, a
destination node is uniformly chosen within the radio transmission range of the
source node. These two nodes move around independently of each other according
to the mobility models described in Section 3.2. In the simulation, two distributions
of moving speeds of mobile nodes are simulated. One is uniform distribution and
the other is truncated normal distribution with mean µ and standard deviation σ.
Two types of mobile nodes, pedestrian and vehicle, are considered. Pedestrian is
with the following parameters: Vmin = 0 m/s, Vmax = 1 m/s, µ = 0.5 m/s, and
σ = 0.5 m/s; vehicle is with the following parameters: Vmin = 10 m/s, Vmax = 20 m/s, µ = 15 m/s, and σ = 2 m/s. The moving directions of mobile nodes are distributed uniformly in [0, 2π). The time period τi in mobility model II has an exponential distribution with mean E [τi] = 30 s. The radio transmission range is
fixed at R = 100 m.
Firstly, we evaluate the distributions of the link duration under the mobility models I and II. We assume that a link is established between a source node and
32 a destination node at the beginning of simulations. As the nodes move around during simulations, we always trace their current positions and record the time when the distance between them is greater than the radio transmission range. The time is accumulated over 5,000 simulation runs and is reported as the results of the simulations. The pdfs of link duration from the simulation and our proposed analytical model are plotted in Figure 3.2. As one can see, the analytical model of exponential distribution for link duration is an approximation of the pdfs obtained from simulations. Small fluctuations in the simulations are due to the finite number of simulation runs and the accuracy of bin size.
Similarly to the links, we record the time at which a routing path is torn down as well as the number of links in the routing path. The pdfs of routing path duration for the routing paths with 3 and 5 links and exponential distribution obtained from Equation (3.10) are plotted in Figure 3.3. Although the distribu- tion of routing path duration has small fluctuations, one can see the exponential distribution match the simulation data very well, validating our proposed model of path duration. The distribution of path duration match the analytical model better than the distribution of link duration. Our simulation results are consistent with observations made in [3] that when the number of links is larger than 3 or 4, the distribution of path duration closely resembles exponential distribution.
Secondly, to evaluate the link holding time, we need to know the distribution of the virtual packet transmission time. The actual distribution of the virtual packet transmission time is complicated and related to many factors, such as the number of mobile nodes, the traffic characteristic etc. In the simulations, we assume that the
33 −3 −3 x 10 x 10 5 6 Moving speed distributed Moving speed distributed 4 uniformly in [0, 1]m/s 5 uniformly in [10, 20]m/s 4 3 3 pdf pdf 2 2
1 1
0 0 0 500 1000 1500 0 500 1000 1500 time (seconds) time (seconds)
0.14 0.14 Moving speed distributed 0.12 Moving speed distributed 0.12 normly N(0.5,0.5) in [0,1]m/s normly N(15,2) in [10,20]m/s 0.1 0.1 pdf pdf 0.08 0.08
0.06 0.06
0.04 0.04
0.02 0.02
0 0 0 10 20 30 40 0 10 20 30 40
time (seconds) time (seconds)
(a) mobility model I
−3 −3 x 10 x 10 5 5 Moving speed distributed Moving speed distributed normaly N(0.5, 0.5) in [0,1]m/s 4 uniformly in [0, 1]m/s 4
3 3
pdf 2 2 pdf
1 1
0 0 0 200 400 600 800 1000 0 200 400 600 800 1000
time time
0.2 0.2 Moving speed distributed Moving speed distributed uniformly in [10, 20]m/s normaly N(15, 2) in [10, 20]m/s 0.15 0.15
0.1 0.1 pdf 0.05 0.05 pdf
0 0 0 10 20 30 40 0 10 20 30 40
time time
(b) mobility model II
Figure 3.2: pdfs of link duration
34 0.015 0.5
moving speed distributed moving speed distributed uniformly in [0, 1]m/s 0.4 uniformly in [10, 20]m/s 0.01 0.3 pdf pdf 0.2 0.005 0.1
0 0 0 100 200 300 0 2 4 6 8 time (seconds) time (seconds)
0.02 0.4 moving speed distributed moving speed distributed normly N(0.5,0.5) in [0, 1]m/s normly N(15,2) in [10, 20]m/s 0.015 0.3
0.01 0.2 pdf pdf
0.005 0.1
0 0 0 100 200 300 0 2 4 6 8 10 12 time (seconds) time (seconds)
(a) 3 links
0.025 0.7
moving speed distributed 0.6 moving speed distributed 0.02 uniformly in [0, 1]m/s uniformly in [10, 20]m/s 0.5
0.015 0.4 pdf pdf 0.01 0.3 0.2 0.005 0.1
0 0 0 50 100 150 200 0 2 4 6
time (seconds) time (seconds)
0.03 0.7 moving speed distributed moving speed distributed 0.025 normly N(0.5, 0.5) in [0, 1]m/s 0.6 normly N(15, 2) in [10, 20]m/s 0.5 0.02 0.4 0.015 pdf pdf 0.3 0.01 0.2
0.005 0.1
0 0 0 50 100 150 200 0 2 4 6
time (seconds) time (seconds)
(b) 5 links
Figure 3.3: pdfs of routing path duration
35 virtual packet transmission has exponential distribution with mean µv = 1/60s.
Figure 3.4 illustrates the pdfs of the link holding time obtained by simulation and Equation (3.12). The parameters used for the simulations are the standard parameters described above; we can see that the simulation results match better with the analytical model when the speed is low, which is consistent with accuracy of the analytical model of the link duration (see Figure 3.2).
Finally, we evaluate the model of the link breaking probability. Similarly as the simulation for link duration, we trace the positions of source node and destination node. If the distance between them is greater than the radio transmission range during the virtual packet transmission time period, the transmission is unsuccess- ful. The ratio of the total number of unsuccessful transmissions to the total 200,000 transmissions is reported as the results of the simulation. The link breaking prob- abilities versus the average virtual packet transmission time obtained from the simulation and Equation (3.16) are plotted in Figure 3.5. The simulation results obtained with two different distributions of moving speeds match the analytical model very well. The same results can be obtained with mobility model II, which is not included in this research. The link breaking probabilities increase with the average virtual packet transmission time. This is because the mobile node with longer virtual packet transmission time needs more time to transmit the packet and higher probability to move out of its link partner’s radio transmission range.
Figures 3.6 shows the routing path breaking probabilities versus the average virtual packet transmission time for the entire path lengths of 3 links and 5 links, respectively. The moving speeds are distributed uniformly. The routing path
36 0.04 0.5 Moving speed distributed Moving speed distributed uniformly in [0, 1]m/s 0.4 0.03 uniformly in [10, 20]m/s
0.3 0.02 pdf pdf 0.2
0.01 0.1
0 0 0 50 100 150 0 10 20 30 time (seconds) time (seconds)
0.05 0.2 Moving speed distributed Moving speed distributed 0.04 normly N(0.5,0.5) in [0, 1]m/s normly N(15,2) in [10, 20]m/s 0.15
0.03 0.1 pdf pdf 0.02
0.05 0.01
0 0 0 50 100 150 0 10 20 30 time (seconds) time (seconds)
(a) mobility model I
0.025 0.2 Moving speed distributed Moving speed distributed 0.02 uniformly in [0,1]m/s uniformly in [10,20]m/s 0.15
0.015 0.1 0.01 pdf pdf 0.05 0.005
0 0 0 50 100 150 200 250 0 10 20 30
time (second) time (second)
0.025 0.2 Moving speed distributed Moving speed distributed normaly N(0.5 0.5) in [0,1]m/s normaly N(15 2) in [10,20]m/s 0.02 0.15
0.015 0.1 0.01
0.05 0.005 pdf pdf
0 0 0 50 100 150 200 250 0 10 20 30
time (second) time (second)
(b) mobility model II
Figure 3.4: pdfs of link holding time
37 0 10 Analysis for speed in [0,1]m/s Simulation for speed in [0,1]m/s Analysis for speed in [10,20]m/s Simulation for speed in [10,20]m/s
−1 10
−2 10 Link breaking probability
−3 10
−4 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Average virtual packet transmission (seconds)
(a) uniform distribution
0 10 Analysis for speed in [0,1]m/s Simulation for speed in [0,1]m/s Analysis for speed in [10,20]m/s Simulation for speed in [10,20]m/s
−1 10
−2 10 Link breaking probability
−3 10
−4 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Average virtual packet transmission (seconds)
(b) normal distribution
Figure 3.5: Link breaking probability versus average virtual packet transmission time
38 breaking probability increases when the moving speed of mobile nodes increases.
The routing path with more than one links demonstrates convergence characteris- tics similar to those of the link breaking probability cases. The radio transmission range and the moving speed have the opposite effect on the link breaking and routing path probabilities, since scaling the radio transmission range up has the same effect of scaling the moving speed down.
3.6 Summary
In this chapter, a novel model to analyze the link stability in mobile ad hoc net- works was proposed. In the proposed analytical model, between each commu- nicating pair, one node was considered to be stationary while the other moved relative to it. With this method, the mobility models defined in this chapter can be approximated by a fluid flow model. Using the result of the fluid flow model, the analytical model for the link duration was obtained, which is used to obtain the link holding time and the link breaking probability of a communicating pair.
The distribution of a routing path duration and routing path breaking probabil- ity were also obtained by extending the models of the link duration and the link breaking probability. The accuracy of the analytical models was validated through simulations under different mobility models with various settings of the mobility parameters.
39 0 10
−1 10
−2 10 Path breaking probability Analysis for speed in [0,1]m/s Simulation for speed in [0,1]m/s Analysis for speed in [10,20]m/s Simulation for speed in [10,20]m/s
−3 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Average virtual packet transmission (seconds)
(a) 3 links
0 10
−1 10
−2 10 Path breaking probability Analysis for speed in [0,1]m/s Simulation for speed in [0,1]m/s Analysis for speed in [10,20]m/s Simulation for speed in [10,20]m/s
−3 10 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Average virtual packet transmission (seconds)
(b) 5 links
Figure 3.6: Routing path breaking probability versus average speed
40 Chapter 4
Performance Analysis of MAC
Protocol in Mobile Ad Hoc
Networks
4.1 Introduction
In mobile ad hoc networks, the MAC protocol is the main element that determines the efficiency in sharing the limited communication bandwidth of the wireless chan- nel. In the literature, researchers have proposed many MAC protocols to better support various applications [9] [19] [20] [22]. Among these protocols, the IEEE
802.11 has become the most widely used MAC protocol in ad hoc networks due to its compatibility with the IEEE 802 protocol suite. Lots of research work has been done to analyze the efficiency of the IEEE 802.11 MAC protocol. In [10], the author presented a simple analytical model to compute the saturated throughput
41 of the IEEE 802.11 DCF (basic CSMA/CA and CSMA/CA with RTS/CTS) pro- tocol. The model assumes a finite number of nodes and ideal channel conditions.
[12] analyzed the channel capacity - i.e., maximum throughput - when using the basic CSMA/CA protocol. In [13], although the authors tried to analyze the per- formance of CSMA/CA, the analysis is only based on p-persistent CSMA, not the exact CSMA/CA. All these papers are restricted to the analysis in single-hop ad hoc networks.
The hidden node and exposed node problems are two important factors which strongly influence the performance of multi-hop ad hoc networks. The performance evaluation of the IEEE 802.11 DCF protocol in multi-hop ad hoc networks has been done through either simulations [43] - [45] or through analytical models [14] - [16].
In [43], the authors investigated the performance of the IEEE 802.11 DCF protocol over multi-hop ad hoc networks and made a conclusion that the IEEE 802.11
DCF protocol is not designed for multi-hop networks. The simulation results that characterize the packet delivery ratio, goodput, delay, and capacity of multi-hop ad hoc networks are presented in [44]. [45] obtained the throughput and blocking probability behavior of an IEEE 802.11 based ad hoc network in a particular physical layout with static obstructions. However, these studies lack any analytical study and concentrate on the effect of hidden node problem on throughput through simulations only. The work from [15] analyzed the throughput of the IEEE 802.11
DCF protocol using the RTS/CTS access mechanism in multi-hop ad hoc networks.
A simple model to derive the saturated throughput of collision avoidance protocols based on an RTS/CTS handshake in multi-hop ad hoc networks was presented in
42 [16]. However, the nodes in these studies are stationary instead of moving and the
throughputs are obtained under saturated condition. [14] used a linear feedback
model to evaluate the performance for the IEEE 802.11 DCF protocol without
assuming the traffic to be in a saturated state. However, the nodes in this study
are also stationary. In this chapter, we will take the mobility effect into account
to study the performance of the IEEE 802.11 DCF protocol with a general traffic
load.
4.2 Single-hop Ad Hoc Networks
In this section, we first analyze the performance of the IEEE 802.11 DCF protocol
in stationary single-hop ad hoc networks. Later, we extend our analysis to evaluate
the performance of the IEEE 802.11 DCF protocol in dynamic environment. In a
single-hop ad hoc network, all nodes can hear each other, which means that it is a
fully connected network.
4.2.1 System Model
In a stationary single-hop ad hoc network, a finite number of nodes M are uniformly distributed in a circular area with radius R. The wireless channel in this network is assumed to be ideal, i.e., no fading and shadowing, etc. The time is slotted with a slot size α and the packets are allowed to transmit only at the beginning of a time slot. All packets are assumed to have the same length Tp. To simplify the analysis, we normalize the time by the packet length Tp. That is, the duration
43 of the packet transmission time equals to unit time and is composed of 1/α slots.
The propagation delay among all nodes is assumed to be the same and equals to a
time slot. At the end of each time slot, every node will be in either thinking state
or backlogged state. In the thinking state, each node generates a new packet with
probability g during a slot. If the transmission is successful, the node stays on the thinking state. A node is said to be in the backlogged state if its transmission is unsuccessful. No new packets are generated in the backlogged state. A backlogged node remains in the backlogged state unless it completes a successful transmission, at that time it switches to the thinking state. If we assume that the traffic arrival process is a Poisson process and denote G the number of total packets in the system during a normalized unit time period, we have Mg = Gα [13].
4.2.2 Performance Analysis
We use the linear feedback model introduced in [46] and [47] to compute the throughput for a finite number of nodes in a slotted CSMA/CA system. We assume that the channel state consists of a sequence of regeneration cycles composed of idle period I and busy period B. Let A be the time spent in useful transmission during a regeneration cycle. The throughput S is defined as the fraction of channel time occupied by a valid transmission and can be obtained by
A S = . (4.1) B + I
where A, B, and I are the average values of A, B, and I respectively.
Let X(t) be the number of nodes in the backlogged state. The random process
44 {x(t) = i} can be modeled by a homogeneous Markov chain identified by the
last slot of each idle period (see Figure 4.1). Since there are M nodes in the
system, X(t) can be 0, 1, 2..., and M. Therefore, the embedded Markov chain for
X(t) has M + 1 states as shown in Figure 4.2. Transition from state i to state j
(i ≤ j) means that there are some thinking nodes entering to the backlogged state.
Similarly, transition from state i + 1 to state i represents that there is a successful
packet transmission. It is assumed that each backlogged node has the same steady-
state probability νi to send a packet at the time slot t when X(t) equals to i. In
order to determine the probability νi, we need to know the collision probability.
In [12], an analytical model is developed to compute the collision probability pc(i),
which is given as
i−1 2[1 − 2pc(i)] 1 pc(i) = 1 − 1 − m , i > 1, (4.2) 1 − pc(i) − pc(i) [2pc(i)] W where W is the minimum contention window and m is to determine the maximum
m contention window Wmax and it satisfies Wmax = 2 W . Note that the collision probability pc(i) is the probability that more than one backlogged nodes transmit at the same time slot. This yields to
i−1 pc(i) = 1 − (1 − νi) . (4.3)
Then we can obtain the probability νi (i > 1) from Equations (4.2) and (4.3).
Obviously, ν0 = 0 and ν1 = 1/W .
lim Our goal is to obtain the stationary distribution of the chain πi =t→∞ Pr{x(t) = i}. For that purpose, we need to find the transition probability matrix P. Using the linear feedback model introduced in [46] [47], P is the product of several single
45 slot transition matrices which we will define next. We denote the transition matrix
by R for slot t1 + I and Q for all remaining slots of the busy period. Since the length of the busy period depends on the number of nodes which become ready in time slot t1 + I, we have R = U + F, where the (i, k)th elements of U and F are defined as
Embed slots B 1 I + 1 + I I + + + 1 + 1 1 t t t 1 t
I B Cycle
Figure 4.1: Embedded slots
...
0 1 2 ... M
Figure 4.2: Markov chain model for the entire network
uik = P {X(t1 + I + 1) = k and transmission is successful|X(t1 + I) = i} (4.4)
and
fik = P {X(t1 + I + 1) = k and transmission is unsuccessful|X(t1 + I) = i} .(4.5)
46 Note that U means that there is only one node ready to transmit in time slot t1 + I and F means that there are more than one nodes ready to transmit in time slot t1 + I. Q reflects the addition to the backlogged states from the M − X(t)
thinking nodes in any time slot t during a busy period. As we can see from Figures
2.3 and 2.4, if the transmission is successful, the busy period has length T s; if it
is unsuccessful, the busy period is T c. The values of T s and T c differ depending
on the access model (basic or RTS/CTS access mode). For basic CSMA/CA, it is
given s T = TDIFS + Tp + TSIFS + TACK + 2α (4.6) c T = TDIFS + Tp + TSIFS + α and CSMA/CA with RTS/CTS: s T = TDIFS + TRTS + TCTS + Tp + 3TSIFS + TACK + 4α (4.7) c T = TDIFS + TRTS + α
where TDIFS, TSIFS, and TACK are the time intervals of DIFS, SIFS, and the ACK
frame, respectively; TRTS and TCTS are the time intervals of RTS and CTS frames,
respectively.
According to [46] and [47], the transmission matrix P is expressed as
s c P = UQT J + FQT , (4.8)
where J represents the fact that a successful transmission decreases the number of
backlogged nodes by 1 and the elements of matrices U, F, Q, and J are given by
47 0, k < i, M−i i−1 (1−g) [iνi(1−νi) ] M−i , k = i, 1−(1−νi)(1−g) uik = (4.9) M−i−1 i (M−i)g(1−g) (1−νi) i M−i , k = i + 1, 1−(1−νi) (1−g) 0, k > i + 1, 0, k < i, M−i i i−1 (1−g) [1−(1−νi) −iνi(1−νi) ] M−i , k = i, 1−(1−νi)(1−g) fik = M−i−1 i (4.10) (M−i)g(1−g) [1−(1−νi) ] i M−i , k = i + 1, 1−(1−νi) (1−g) 0 1 B C B C B M − i C B C B C(1−g)M−kgk−i B C @ A k − i i M−i , k > i + 1, 1−(1−νi) (1−g) 0, k < i, qik = (4.11) M − i M−k k−i (1 − g) g , k ≥ i + 1, k − i
48 and 1, k = i − 1, jik = (4.12) 0, otherwise.
The steady-state probabilities of the Markov process are defined as a row vector
π = [π0, π1, ...πN ], which can be determined by
π = πP. (4.13)
Since the idle period is geometrically distributed [13], its expectation is given
by 1 I(i) = i M−i . (4.14) 1 − (1 − νi) (1 − g)
Let ps(i) be the probability of a successful transmission during a cycle when i nodes are in the backlogged state. During this cycle, a transmission will be successful if and only if one of i backlogged nodes transmits or one of the M − i thinking nodes transmits. Therefore, ps(i) can be obtained by
M−i−1 i i−1 M−i (M − i)g(1 − g) (1 − νi) + iνi(1 − νi) (1 − g) ps(i) = i M−i . (4.15) 1 − (1 − νi) (1 − g)
Since π is a regenerative process, the average channel throughput S is computed as the ratio of time the channel is carrying successful transmission during a cycle
(an idle period followed by a busy period) averaged over all cycles, to the average
49 cycle length [46]. Therefore, the channel throughput can be obtained by
M P πips(i)Tp S = i=0 . (4.16) M n o P s c πi I(i) + ps(i)T + [1 − ps(i)]T i=0 The mobility does affect the performance of CSMA/CA protocol. With node mobility, the transmission fails if a link breaks before the transmission is complete.
The link breaking probability can be obtained by using the Equation (3.16). In order to obtain the link breaking probability, we need to know the distributions of link duration and virtual packet transmission time. As described in the previous chapter, the distribution of link duration can be approximately as an exponential distribution and obtained given the mobility model and radio transmission range.
However, the exact distribution of virtual packet transmission is hard to obtain since it depends on the MAC protocol, traffic load, and the number of nodes in the networks. The collision and exponential backoff make it harder to find the exact distribution of virtual packet transmission. In order to simplify the analysis, we assume that the virtual packet transmission time follows an exponential distrib- ution with rate µv. Now, the question is how to obtain this rate µv. For an ad hoc network with CSMA/CA protocol, when more than one nodes are active, the virtual packet transmission time includes a successful transmission time, backoff time, and contention time i.e., a collision or transmission by another node, and it is
s Tv = Tb + Tcon + T , (4.17)
50 Backoff Backoff Backoff Successful Conention Conention transmission
Tv
Figure 4.3: Structure of time Tv
s where Tb is the length of backoff time and Tcon is the length of contention time, T is the length of successful transmission time. The average backoff time [12] is
M m X 1 − pc(i)(2pc(i)) W E[T ] = π , (4.18) b i 1 − 2p (i) 2 i=1 c
The length of contention is either equal to the length of successful packet trans-
mission or the length of collision. From the results of [12], the average number N
of contentions during a packet transmission period is obtained by
M X 2 N = π (i − 1). (4.19) 3 i i=1
M P s Thus, N ps(i)πi contentions have the length of successful transmission T and i=0 M P c N 1 − ps(i)πi contentions have the length of collision T . Thus, the average i=0
of contention time Tcon is given by
M M ! X s X c E [Tcon] = N πips(i)T + N 1 − πips(i) T . (4.20) i=0 i=0
With the above results, we can easily obtain the rate of the virtual packet transmis-
sion rate 1/E[Tv]. Given this rate, the link breaking probability is easily obtained
from the Equation (3.16). In this analysis, we made an assumption that the node
movement has zero net effect on node states. This assumption is reasonable since
we calculate the average performance in a long term. With this assumption, the
51 throughput S under the dynamic environment is given by
M P πips(i)Tp S = (1 − P ) i=0 . (4.21) lb M n o P s c πi I(i) + ps(i)T + [1 − ps(i)]T i=0
4.3 Multi-hop Ad Hoc Networks
A single-hop ad hoc network is a fully connected network which does not have hidden node problem. With multi-hop ad hoc networks, the presence of hidden node problem can significantly degrade the performance of MAC protocol. To solve this problem, the IEEE 802.11 provides an optional mechanism based on four- way handshaking technique know as CSMA/CA with RTS/CTS. In the following section, we evaluate the performance of CSMA/CA protocol by determining the impact of hidden node problem. We also include the impact of node mobility on the MAC performance.
4.3.1 System Model
A multi-hop ad hoc network has the advantage that multiple concurrent trans- mission can take place simultaneously at geographically separated locations. On the other hand, such a capacity gain may be offset by the hidden node problem and the extra hops needed for a packet to reach its destination. The latter is greatly influenced by the routing protocol adopted. In this section, we focus on the impact of the hidden node problem. To eliminate the effect of routing, all packets generated from a node are assumed to be destined for its neighbor nodes.
52 Figure 4.4 shows the network model used in the analysis. We still assume that
the transmission range is R and an average of M nodes are within this range.
Since we cannot generate an infinite network model, we just focus our attention
on the performance of the innermost M nodes. In order to make sure that all
hidden nodes of the innermost M nodes are included, the range of the service area
is chosen to be 3R. [16] found that nodes outside the concentric circles of radius
3R almost have no influence on the throughput of the innermost M nodes, i.e.,
boundary effects can be safely ignored when the circular network’s radius is 3R.
Same as the system model in 4.2.1, in this network, each thinking node generates a new packet with probability g in a time slot and each backlogged node transmits a packet with probability νi when i nodes are in the backlogged state.
R 3R
2R
Figure 4.4: System model
4.3.2 Performance Analysis
The effect of hidden node problem on the performance of multi-hop ad hoc networks
depends on the number of nodes within the radio range of senders and receivers.
53 Figure 4.5 gives the hidden area HA of the transmitting node A and the hidden area HB of the receiving node B. HA(r) has been shown to be
r H (r) = πR2 − 2R2F , (4.22) A q 2R √ 2 where Fq(t) = arccos(t) − t 1 − t .
H (r) B H A (r) r
A B R R
Figure 4.5: Illustration of hidden area
If node A chooses any one of its neighbors with equal probability and the average number of nodes within a region of radius r is proportional to r2, the pdf of the distance r is given by
2r f(r) = , 0 ≤ r ≤ R. (4.23) R2
Therefore, we can calculate the average number of hidden nodes of node A
R M Z 2r N = H (r)dr. (4.24) h πR2 R2 A 0 For basic CSMA/CA, the hidden nodes can cause collision in transmission of both data and ACK messages. First, we consider the transmission of a data packet from node A to node B. There are two cases of hidden node problem that will make this transmission fail: at least one node in the hidden area HA(r) transmits
54 the data or ACK messages during this packet transmission period. The probability of the hidden nodes to transmit the data message is equal to
N P = p (i) h , (4.25) 1 b M where p (i) = B(i) is the probability that the channel will be sensed busy when b B(i)+I(i) there are i backlogged nodes.
The alternative case that at least one node within the hidden area HA(r) trans- mits the ACK message with probability
N P = p (i)p (i) = p (i)p (i) h , (4.26) 2 s hr s b M − 1
Nh where phr(i) = pb(i) M−1 is the probability that at least one node in HA(r) receives the data and ps(i) is the probability of a successful packet transmission. This is an overestimate, since some transmissions between the nodes of the hidden area have been counted in probability P1. A better estimate is given by
N P = p (i)p (i)(1 − h ). (4.27) 2 s hr 2M
Now, we consider the transmission of ACK message when node B successfully receives the data packet from node A. According to the symmetry, we know that the number of hidden nodes of node B is the same as that of node A. After node
A finishes its transmission, all other nodes within the radio range of A should wait
DIFS period before they can sense the channel. Therefore, the exact period in which the hidden nodes of node B can cause collision is TACK + TSIFS − TDIFS.
The average number of of backlogged hidden nodes for node B is equal to Mhb(i) = i M Nh. The backlogged node will transmit a packet in a slot with probability νi
55 and the thinking node will transmit a packet with probability g. Note that a node
can start a transmission only when the channel is idle. Let TACK (i) be
I(i) TACK (i) = (TSIFS + TACK − TDIFS) . (4.28) I(i) + B(i)
Therefore, the probability that at least one hidden node in HB(r) transmits a
data packet during the period TACK (i) is given by
TACK (i)Mhb(i) TACK (i)(Nh−Mhb(i)) P3 = 1 − (1 − νi) (1 − g) . (4.29)
Because the probability that the hidden nodes of node B respond ACK during the period TACK (i) is very small, we ignore it.
Based on the above discussion, the probability that node A successfully trans- mits the data packet to node B totally degrades by
Pd = P1 + P2 + (1 − P1 − P2)P3. (4.30)
For CSMA/CA with RTS/CTS, although the RTS/CTS packet exchange re- duces the hidden node problem, the problem is not completely resolved. We still assume that at a time slot, node A is transmitting a data packet to node B, and
i nodes within the radio range of node A are backlogged. For CSMA/CA with
RTS/CTS, if any of the hidden nodes of node A is transmitting RTS or CTS mes-
sage when node A is transmitting a RTS, the transmission of node A will fail. The
corresponding P1 and P2 can be derived like basic CSMA/CA.
The collision may also happen during the data packet transmission from node
A to node B. This is because some of hidden nodes of node A will not successfully receive the CTS message and these nodes may transmit the RTS or CTS messages
56 during the data packet transmission period. The probability that the hidden nodes will not successfully receive the CTS message is the same as the probability Phri that at least one of the hidden nodes of node A receives message. Equation (4.25) gives the probability that at least one of the hidden nodes of node A transmit RTS, and equation (4.27) gives the probability that at least one of the hidden nodes of node A transmits the CTS. Therefore, the probability that the hidden nodes of node A will collide the data packet from node A to node B is given by
P3 = Phr(i)(P1 + P2) . (4.31)
The hidden nodes in hidden area HB(r) can also cause collision to the CTS and ACK messages. In fact, compared with the probability that the RTS or data packet collides, the probability that CTS or ACK collides is very small and we can ignore them.
Based on the above discussion, the probability that the node A successfully transmits a data packet to node B is totally degrades by
Pd = P1 + P2 + (1 − P1 − P2)P3. (4.32)
Let S be the throughput of the entire innermost M nodes. Based on a single station standpoint, the probability of successful data packet transmission hidden nodes is equal to
0 ps(i) = ps(i) (1 − Pd) . (4.33)
Therefore, the throughputs S for basic CSMA/CA and CSMA/CA with RTS/CTS
57 are given by M P 0 πips(i)Tp S = i=0 . (4.34) M h i P 0 s 0 c πi I(i) + ps(i)T + (1 − ps(i))T i=0 s c where Tp, I(i), T , and T are the same as those in single-hop ad hoc networks, and πi can be computed by replacing U and F with the following new values 0, k < i, M−i i−1 (1−g) [iνi(1−νi) ](1−Pd) M−i , k = i, 1−(1−νi)(1−g) uik = (4.35) M−i−1 i (M−i)g(1−g) (1−νi) (1−Pd) i M−i , k = i + 1, 1−(1−νi) (1−g) 0, k > i + 1,
0, k < i, M−i i i−1 i−1 (1−g) [1−(1−νi) −iνi(1−νi) +iνi(1−νi) Pd] M−i , k = i, 1−(1−νi)(1−g) fik = M−i−1 i i (4.36) (M−i)g(1−g) [1−(1−νi) +(1−νi) Pd] i M−i , k = i + 1, 1−(1−νi) (1−g) 0 1 B C B C B M − i C B C B C(1−g)M−kgk−i B C @ A k − i i M−i , k > i + 1, 1−(1−νi) (1−g) Since in our system model, we assume that all packets are be destined for their
neighbor nodes. It means there is only one hop for the transmission. Therefore,
58 in the analysis, we only need to know the link breaking probability instead of the path breaking probability. Similarly as in Section 4.2.2, in order to obtain the link breaking probability, we need to know the distributions of link duration and virtual packet transmission time. The link duration can be easily obtained given mobility model and radio transmission range. The virtual packet transmission time can be obtained by Equations 4.17, 4.18, and 4.20 just by replacing the π with the new values obtained above.
4.4 Simulations and Discussions
In this section, we describe our discrete event simulator which can be used to study the performance characteristics of the IEEE 802.11 DCF protocol in presence of mobility and hidden node problems. Although our interest is the performance of multi-hop ad hoc networks, it is enough to consider the innermost M nodes if we evaluate the interference from the hidden nodes. We can generalize the analysis to the whole system using the same analytical method if the system is identical and the traffic is balanced. In order to make sure that all hidden nodes of the innermost
M nodes are included, R0 is chosen to be 3R. In the simulation, the moving speed is uniformly distributed in [0 m/s, 1 m/s]. The parameters used in the simulation are defined as follows: Tp = 1 (i.e.,100 slots), α = 0.01, TDIFS = 0.03, TSIFS = 0.01,
TRTS = 0.05, TCTS = 0.05, TACK = 0.05, W = 32, CWmax = 1024, M = 15, and
R = 100 m.
Figure 4.6 shows both the analytical and simulation results for the basic CSMA/CA
59 and CSMA/CA with RTS/CTS protocols in single-hop ad hoc networks. Figures
4.7 and 4.8 show the throughputs for the basic CSMA/CA and CSMA/CA with
RTS/CTS in single-hop and multi-hop ad hoc networks. From the results, we can see that the throughput of basic CSMA/CA dramatically falls in multi-hop ad hoc networks. This is because the basic CSMA/CA has no mechanism to solve the hidden node problem. However, the throughput of CSMA/CA with RTS/CTS mechanism still degrades due to the collision caused by the hidden nodes in multi- hop ad hoc networks. No matter what mechanism is used, we can see from the
figures that the mobility does degrade the performance of mobile ad hoc networks.
From the results, it can be seen that the throughput with mobility decreases com- pared with the throughput without mobility. This is because the node’s mobility makes some nodes move out of the radio range of their partners during the virtual packet transmission period.
0.9
0.8
0.7
0.6
0.5
0.4
Throughput (S) 0.3
0.2
0.1
0 0 0.5 1 1.5 2 2.5 3 Traffic load (G)
Analysis for basic CSMA/CA without mobility Simulation for basic CSMA/CA without mobility Analysis for basic CSMA/CA with mobility Simulation for basic CSMA/CA with mobility Analysis for CSMA/CA with RTS/CTS without mobility Simulation for CSMA/CA with RTS/CTS without mobility Analysis for CSMA/CA with RTS/CTS with mobility Simulation for CSMA/CA with RTS/CTS with mobility
Figure 4.6: Throughput of CSMA/CA protocol
60 0.8
0.6
0.4
0.2 Throughput
0 0 0.4 0.8 1.2 1.6 2 Traffic load
Single-hop analysis without mobility Single-hop simulation without mobility Multi-hop analysis without mobility Multi-hop simulation without mobility Multi-hop analysis with mobility Multi-hop simulation with mobility
Figure 4.7: Throughput for basic CSMA/CA
0.8
0.6
0.4 Throughput
0.2
0 0 0.4 0.8 1.2 1.6 2 Traffic load
Single-hop analysis for CSMA/CA with RTS/CTS without mobility Multi-hop analysis for CSMA/CA with RTS/CTS without mobility Multi-hop analysis for CSMA/CA with RTS/CTS with mobility
Figure 4.8: Throughput for CSMA/CA with RTS/CTS
4.5 Summary
In this chapter, an analytical model has been provided to study the performance of the IEEE 802.11 DCF MAC protocol in a mobile ad hoc network. We use the embedded Markov chain and linear feedback method to obtain the throughput in both single-hop and multi-hop stationary ad hoc networks. In addition, we demon- strate the utility of our previous link stability model to evaluate the performance of the IEEE 802.11 DCF protocol in presence of node mobility. To the best of our knowledge, this is the first attempt to evaluate the performance of the IEEE 802.11
61 DCF protocol in dynamic ad hoc networks. Our results show that the protocol performance may degrade dramatically across mobility models. This effect can be explained by the fact that some nodes may move out of their partners’ radio transmission range during the packet transmission duration. From our results, we infer that it is highly desirable to look at methods for improving the performance of the IEEE 802.11 protocol. In our paper [48], we proposed a cross layer design method to improve its performance.
62 Chapter 5
Impact of Capture Effect on the
Performance of MAC Protocol
5.1 Introduction
In the previous chapter, we study the performance of the IEEE 802.11 DCF proto- col in ad hoc networks. The analysis assumes that the wireless channel is noiseless and all packets arrive at the receiver with the same power level. Whenever two or more packets arrive at the receiver during overlapping time, they collide and all packets involved are destroyed. This model, reasonable in some communication environments, turns out to be too pessimistic in others. In a practical wireless net- work, the transmitted packets experience not only noise but also fading, so that the receiver may fail to detect the faded packets even though there is no collision.
On the other hand, a packet can be received successfully in the presence of other overlapping packets if its power is larger than the interfering power by a certain
63 margin. The later phenomenon is called capture effect. The capture effect can
reduce the probability of collision and result in an increase of the system through-
put. Although the capture effect on the ALOHA protocols has been widely studied
[49] [50], the capture effect on the CSMA/CA protocol have not been well studied
and reported except two recent publications [17] [18] in which fading, shadowing
and path loss effect are considered. In [17], the authors analyzed the influence of
capture phenomenon over theoretical throughput and delay of a traffic-saturated
IEEE 802.11b basic service set (BSS) and ad hoc configurations based on the model
developed by Bianchi [10]. In [18], the authors assume that the CSMA/CA pro-
tocol as a hybrid protocol of slotted 1-persistent CSMA and p-persistent CSMA.
The value of p is related to the backoff delay. However, the authors leave it open on how to determine the p and they assumed some fixed values in their numeri- cal results. Moreover, the authors only discussed the performance of CSMA/CA protocol in an infrastructure network. Their model can not be used in an ad hoc network. In this chapter, we derive a relatively realistic analytical mode for the
CSMA/CA protocol operated in infrastructure network and ad hoc network, re- spectively, where fading, shadowing and path loss are considered. Unlike [17], we analyze the performance of CSMA/CA protocol with general traffic load, ranging from light traffic to heavy traffic.
64 5.2 Channel Model
The wireless channel is characterized by three nearly independent, multiplicative
propagation mechanisms, namely, path loss, fading, and shadowing. The path
loss is proportional to r−β, where β is the path loss exponent. The value of β depends on the propagation environment, typically taking values of 2 to 6, and is typically equal to 4 in land radio environment. The path loss effect gives rise to the near-far effect and determines the area mean power wa. The area mean power is the received signal power in the absence of shadowing. The shadowing is described by a log-normal distribution of the local mean wl about the area mean power wa and is assumed to be superimposed on the path loss effect. If the local mean power is expressed in nepers, it has normal distribution about the area mean, with a logarithmic standard deviation σs. The multipath reception causes
Rayleigh or Rician fading. Rayleigh fading causes the instantaneous received power to be exponentially distributed random variable. Taking Rayleigh fading, log- normal shadowing, and near-far effect into account, the uncondition pdf of the instantaneous power ws of a received packet at the receiver is given by [49],
∞ ∞ Z Z 1 w h(r) ln2(rβw ) s √ l fws (ws) = exp(− ) exp(− 2 )drdwl, (5.1) wl wl 2πσswl 2σs 0 0 where h(r) is the pdf of the distance describing the spatial distribution of the offered
packet traffic around the receiver. For example, we consider a uniform distribution
where nodes are uniformly distributed in a circle of unit radius around the access
point. In this case, the pdf is given by h(r) = 2r, r ∈ (0, 1). However, for ad hoc network, since there is no fixed access point as a receiver, every node might
65 be a receiver. This issue makes it hard to obtain a close-form of h(r) in an ad hoc network. In this chapter, we transfer this problem into a centralized issue by logically considering that the receiver in the ad hoc network is a virtual access point. With this method, we only need to find the pdf of the distance among nodes. Figure 5.1 depicts the distance L between any two arbitrary nodes. This
Node A
R1
Θ1 Θ 1 L 2
R2 Node B
Figure 5.1: Spatial distribution of two arbitrary nodes in ad hoc networks distance can be expressed as
q 2 2 L = R1 + R2 − 2R1R2cos(Θ2 − Θ1) (5.2) and, for all l ≥ 0,
2 2 2 P r[L ≤ l] = Pr[R1 + R2 − 2R1R2cos(Θ2 − Θ1) ≤ l ]. (5.3)
Therefore, if given the distributions of R1, R2,Θ1, and Θ2, we can compute the pdf of L from Equation (5.3) using Mote Carlo simulation method.
For example, nodes A and B are uniformly distributed around the center of the service area. In this case, R1 and R2 are distributed according to f(r) = 2r, r ∈
66 (0, 1), and Θ1 and Θ2 are uniformly distributed in [0, 2π), the pdf of R is shown in Figure 5.2.
0.9
0.8
0.7
0.6
0.5 pdf 0.4
0.3
0.2
0.1
0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 distance R
Figure 5.2: pdf of distance R between any two nodes in ad hoc networks
5.3 Capture Model
The instantaneous powers at the receiver for different packets will generally not be the same due to the different propagation decays. Therefore, even if there are more than two packets transmitted at the same time, one of them may still be successfully received at the receiver. This phenomenon is called capture effect in the literature. Several capture models have been provided, which can be classified into two categories. The models of the first category are based on the capture ratio z, in which only the power levels of the received packets are considered. A typical model of this category assumes that the strongest packet will be received successfully whenever its power exceeds the power sum of all other interfering
67 packets by a capture ratio z. That is,
N X w0 > z{ wi + η}, (5.4) i=1 where wi (i = 0, 1, ..., N) is received power of the ith packet and the packet with the strongest power is subscripted with 0, and η is the power of additive white Gaussian noise. It is of no significant consequence to ignore the noise since the CSMA/CA channel was principally contention limited, the same as ALOHA channel [49] [52].
Therefore, ignoring the effect of noise, the probability of capture can be expressed as N X PN+1(z) = Pr{w0 > z wi}. (5.5) i=1 In comparing power levels of different packets, it is usually assumed that the power levels remain constant during the packet reception period, i.e., the power of each bit in a packet is the same. This assumption has been used earlier [49] [50], and is considered to be accurate if nodes are stationary or are moving very slowly. If the wireless nodes move fast, the signal power may vary over the duration of a packet and all the packets received during a slot should be compared on a bit-by-bit basis.
In order to find the probability of capture, we need to know the joint pdf of the interfering packets. If the interfering power is due to incoherent accumulation of
N independently fading signals, the joint pdf is the N-fold convolution of the pdf of the individual signal power. Therefore, the probability of capture, given that
68 N+1 nodes transmit packets at the same time, can be obtained by
N X PN+1(z) = Pr{w0 > z wi} i=1 ∞ ∞ Z Z h(r) ln2(rβw ) z √ l N = exp(− 2 ) · [φ( )] drdwl, (5.6) 2πσswl 2σs wl 0 0 where φ(·) is the Laplace image of the pdf of one single interferer. Using (5.1),
φ(·) can be expressed as
∞ ∞ Z Z 1 h(r) ln2(rβw ) √ l φ(s) = exp(− 2 )drdwl. (5.7) 1 + swl 2πσswl 2σs 0 0 The models of the second category are bit decision process under interfering
packets and noise, and relates to the type of demodulation and the coding scheme.
The bit decision process determines whether the individual bits are correctly re-
ceived or not. In these models, the capture effect occurs if and only if there is no
bit error of a packet.
H PN+1(z) = (1 − Pb(z)) , (5.8)
where H denotes packet size (bits) and Pb(z) is the bit error rate (BER). The
BER depends on the type of demodulation, the coding scheme, and the signal-to-
interfering ratio. Therefore, these models are more accurate and convincing. In
the case of non-coherent FSK demodulation (NCFSK) without any coding scheme,
if the sum of the interfering signals is assumed to be Gaussian distributed and
independent from bit to bit, the BER Pb(z) is equal to [53]
1 P (z) = e−z/2. (5.9) b 2
If we combine these two categories together, capture effect happens when the
power level of the strongest packet to the power sum of all other interfering packets
69 by a capture ratio z and the detected bit sequence is identical to the bit sequence of the wanted packet. Thus, we have
∞ N X H X PN+1(z) = (1 − Pb(z)) Pr{w0 = z wi}, (5.10) z=1 i=1
The right part of the above equation can be obtained numerically from Equations
(5.6) and (5.9).
In above models, the probability that one out of N+1 packets is successfully received is given by
qN+1 = (N + 1)PN+1(z). (5.11)
5.4 Analytical Model
In the following, we consider the basic CSMA/CA and CSMA/CA with RTS/CTS protocols, and calculate the throughputs of these protocols under the impact of capture effect. Since the objective of this chapter is to investigate the effect of capture effect, we assume that there is no hidden node problem in the networks.
Therefore, we can use the same system model described in Section 4.2.1.
Adopting the Markov chain model introduced in the previous chapter, we present an analytical model of the performance of basic CSMA/CA and CSMA/CA with RTS/CTS protocols in the presence of path loss, shadowing, and Rayleigh fading. With the capture effect, the packet transmission is successful if only one node is ready to transmit or the packet captures the receiver if more than one nodes are ready to transmit. Therefore, we need to modify the Equations (4.10)
70 as follows 0, k < i, 2 0 1 3 6 B C 7 6 B C 7 6 Pi B i C 7 M−i6 i−1 B C j i−j 7 (1−g) 6iνi(1−νi) + B Cνi (1−νi) qi7 6 j=2B C 7 4 @ A 5 j i M−i , k = i, 1−(12−νi) (1−g) 0 1 3 6 B C 7 6 B C 7 u = 6 Pi B i C 7 (5.12) ik M−i−16 i B C j i−j 7 (M−i)g(1−g) 6(1−νi) + B Cν (1−νi) qi+17 6 B C i 7 4 j=1@ A 5 j i M−i , k = i + 1, 0 1 1−(1−νi) 2(1−g0) 1 3 B C 6 B C 7 B C 6 B C 7 B M − i C 6 Pi B i C 7 B C M−k k−i6 B C j i−j 7 B C(1−g) g 6 B Cν (1−νi) qk+j−i7 B C 6 B C i 7 @ A 4j=0@ A 5 k − i j i M−i , k > i + 1. 1−(1−νi) (1−g) Similarly, the transmission is unsuccessful if and only if there are more than one
nodes transmit their packets at the same time and no one captures the receiver.
Thus the Equation (4.9) is modified as 0, k < i, 2 0 1 3 6 B C 7 6 B C 7 6 Pi B i C 7 M−i6 B C j i−j 7 (1−g) 6 B Cνi (1−νi) (1−qi)7 6j=2B C 7 4 @ A 5 j i M−i , k = i, 1−(1−νi)2(1−0g) 1 3 6 B C 7 6 B C 7 f = 6 Pi B i C 7 ik M−i−16 B C j i−j 7 (M−i)g(1−g) 6 B Cν (1−νi) (1−qi+1)7 6 B C i 7 4j=1@ A 5 j i M−i , k = i + 1, 0 1 1−(1−νi) (12−g) 0 1 3 B C 6 B C 7 B C 6 B C 7 B M − i C 6 Pi B i C 7 B C M−k k−i6 B C j i−j 7 B C(1−g) g 6 B Cν (1−νi) (1−qk+j−i)7 B C 6 B C i 7 @ A 4j=0@ A 5 k − i j i M−i , k > i + 1. 1−(1−νi) (1−g) (5.13)
The stationary probability πi that i nodes are in backlogged state can be obtained from the Equation (4.13) by replacing the U and F in Equation (4.8) with the
71 above new values.
The probability of successful transmission ps(i) when X(t) equals to i is given by M X ps(i) = uik. (5.14) k=0
Substituting the new πi and ps(i) into the Equation (4.16), we can obtain the throughput of CSMA/CA protocol in presence of fading, shadowing, and path loss
s c effect. The other parameters Tp, I(i), T , and T are the same as chapter 4.
5.5 Numerical Results and Discussions
Numerical results are computed in this section based on the analytical model pre-
sented in the previous section. In all plots, the following parameters are assumed:
a) the path loss exponent β = 4; b) the nodes are uniformly distributed in a
circular area with radius 1 (i.e., f(r) = 2r, r ∈ (0, 1]).
The capture probability for the model of the first category can be obtained from the Equation (5.6) using the Gauss-Hermite quadrature [54]. Figures 5.3 and
5.4 show the capture probabilities versus the number of contending nodes, for some values of capture ratio z in infrastructure mode and ad hoc mode, respectively. The number of nodes plays an important role in determining the capture probability.
The behavior of Figures 5.3 and 5.4 show that the capture probability decreases significantly as the number of contending nodes increase. One can also observe that an increase of successful capture probability occurs when z decreases. Lower
value of z means more powerful receiver detection probability. On the other hand,
72 the increase of transmission power should be limited due to the power control and battery requirement.
0.8 z=5 z=10 z=15 0.7
0.6 N
0.5
0.4 Capture probability q
0.3
0.2
0.1 0 5 10 15 20 25 Number of conteding nodes N
Figure 5.3: Capture probability in infrastructure mode (σs = 1.35)
0.45 z=5 z=10 z=15 0.4
0.35
N 0.3
0.25
Capture probability q 0.2
0.15
0.1
0.05 0 5 10 15 20 25 Number of conteding nodes N
Figure 5.4: Capture probability in ad hoc mode (σs = 1.35)
The capture probability for the model of the second category can be obtained from the Equation (5.10). Figures 5.5 and 5.6 plot the capture probabilities versus the number of contending nodes under infrastructure mode and ad hoc mode with different packet sizes. From the figures, we know that the packet size is another important factor to determine the capture probability. Shorter packets have larger
73 capture probability, while longer packets have higher probability of being lost due to channel fading. The capture probability in the infrastructure mode is higher than the capture probability in the ad hoc mode if nodes are uniformly distributed in a circular area. This is due to the fact that nodes are closer to the receiver in ad hoc mode than in infrastructure mode (see Figure 5.2).
0.8 L=100 L=200 L=500 0.7 L=1000
0.6 N
0.5
0.4 Capture Probability q
0.3
0.2
0.1 0 5 10 15 20 25 Number of contending nodes N
Figure 5.5: Capture probability in infrastructure mode (σs = 1.35)
0.55 L=100 L=200 0.5 L=500 L=1000
0.45
0.4 N 0.35
0.3
0.25 Capture probability q
0.2
0.15
0.1
0.05 0 5 10 15 20 25 Number of contending nodes N
Figure 5.6: Capture probability in an ad hoc mode (σs = 1.35)
The impact of capture effect on the performance of CSMA/CA protocol is shown in the following figures. The other parameters for this performance evalua-
74 tion are defined as follows: M = 15, Tp = 1 (i.e.,100 slots), α = 0.01, TDIFS = 0.03,
TSIFS = 0.01, TRTS = 0.05, TCTS = 0.05, TACK = 0.05, W = 32, and Wmax =
1024. Figures 5.7 and 5.8 show the throughputs of CSMA/CA protocol versus the offered load G for infrastructure mode and ad hoc mode with capture model of the
first category respectively. If the basic CSMA/CA is used, it is obvious that the presence of capture effect generates significant throughput improvement as traffic load G increases. For example, given G = 3.0, the throughput with capture effect is estimated to be 0.82 for infrastructure mode when z equals to 10 as opposed to
0.73 in the absence of capture effect. However, for CSMA/CA with RTS/CTS, the exchange of RTS and CTS before the actual transmission significantly reduces the likeliness of simultaneous transmission and packet capture.
0.9
0.8
0.7
0.6
0.5 Throughput S 0.4
0.3
basic CSMA/CA: no capture effect 0.2 basic CSMA/CA: z=5 for ad hoc mode basic CSMA/CA: z=10 for ad hoc mode basic CSMA/CA: z=5 for for infrastructure mode basic CSMA/CA: z=10 for for infrastructure mode 0.1 0 0.5 1 1.5 2 2.5 3 Traffic load G
Figure 5.7: Throughput of basic CSMA/CA versus traffic load G with capture
model of the first category
The throughputs of CSMA/CA protocol with capture model of the second
category are shown in Figures 5.9 and 5.10. They have similar behavior as the
throughput with capture model of the first category. These results are consistent
75 0.8
0.7
0.6
0.5
Throughput S 0.4
0.3
CSMA/CA with RTS/CTS: no capture effect 0.2 CSMA/CA wtih RTS/CTS: z=5 for ad hoc mode CSMA/CA with RTS/CTS: z=10 for ad hoc mode CSMA/CA with RTS/CTS: z=5 for infrastructure mode CSMA/CA with RTS/CTS: z=10 for infrastructure mode 0.1 0 0.5 1 1.5 2 2.5 3 Traffic load G
Figure 5.8: Throughput of CSMA/CA with RTS/CTS versus traffic load G with capture model of the first category the behavior of capture probabilities shown in Figures 5.3, 5.4, 5.5, and 5.6. More- over, we note that the throughput of CSMA/CA protocol in the fading channel is not much different compared with that in the perfect channel model when the traffic is low. This is because we ignore the noise and assume that the transmission is always successful if only one node transmits its packet. In fact, this assumption is not totally correct. The exact throughput of CSMA/CA protocol with fading should be less than our results when traffic load is low. We add this analysis and provide more accurate results in the next chapter.
5.6 Summary
In this chapter, we have presented two categories of capture models in a wireless communication network. We observed that these capture models have similar behavior and have no significant difference. However, for all models, the capture
76 0.9
0.8
0.7
0.6
0.5 Throughput S 0.4
0.3
basic CSMA/CA: no capture effect 0.2 basic CSMA/CA: L=100 for ad hoc mode basic CSMA/CA: L=1000 for ad hoc mode basic CSMA/CA: L=100 for infrastructure mode basic CSMA/CA: L=1000 for infrastructure mode 0.1 0 0.5 1 1.5 2 2.5 3 Traffic load G
Figure 5.9: Throughput of basic CSMA/CA versus traffic load G with capture model of the second category probabilities are sensitive to the number of contending nodes and the distance between the receiver and the transmitters. The impact of capture effect on the throughput of CSMA/CA protocol was also analyzed in this paper. The results show that path loss, shadowing, and fading make the capture effect possible and provide the CSMA/CA protocol with substantial improvement of the throughput.
The basic CSMA/CA has higher improvement of its throughput than CSMA/CA with RTS/CTS. This is due to the fact that the exchange of RTS and CTS before actual transmission significantly reduces the likeliness of simultaneous transmission and packet capture. In this chapter, in order to simplify our analysis, we made some assumptions: 1) a packet is always successfully received if only one transmitter sends its packet, and 2) only a single packet is captured at one time. The first assumption can be released by considering the packet error rate in fading channel, which will be discussed in the next chapter. The second assumption is certainly correct in infrastructure mode. However, in ad hoc mode, the simultaneous capture
77 0.8
0.7
0.6
0.5
Throughput S 0.4
0.3
CSMA/CA with RTS/CTS: no capture effect 0.2 CSMA/CA wtih RTS/CTS: L=100 for ad hoc mode CSMA/CA with RTS/CTS: L=1000 for ad hoc mode CSMA/CA with RTS/CTS: L=100 for infrastructure mode CSMA/CA with RTS/CTS: L=1000 for infrastructure mode 0.1 0 0.5 1 1.5 2 2.5 3 Traffic load G
Figure 5.10: Throughput of CSMA/CA with RTS/CTS versus traffic load G with capture model of the second category of multiple packets is feasible. These issue will be addressed in our future work.
78 Chapter 6
Influence of Time-varying
Channel on the Performance of
MAC Protocol
6.1 Introduction
In the previous chapter, we discussed the capture effect considering the path loss, shadowing, and multipath fading. The wireless channel are severely affected by the time-varying losses due to path loss, shadowing, and multipath fading. While the variation in the losses due to path loss and shadowing is relatively slow, the variation due to multipath fading is quite fast. The fading envelope due to mul- tipath fading follows a Rayleigh distribution, so that the envelope squared (i.e., the power) has an exponential distribution. Most notably, the correlation in the multipath fading behavior and its effect on the performance of the IEEE 802.11
79 MAC protocols have not been adequately addressed in the literature so far. The primary focus of this chapter is to address this void.
In the past, most of models [10] [12] [14] assumes that the transmission is always successful if there is only one node sending its packet. This may not be the case in reality since there are bit errors in transmission due to the wireless channel variation. In the literature, the only studies that take the packet transmission errors into account are [55] and [59], where the analysis, however, are based on the saturated condition. Moreover, the networks in their models are stationary.
To the best of the authors’ knowledge, there is no analytical model that considers the packet transmission error conditions in the unsaturated performance analysis for the IEEE 802.11 DCF MAC protocol with time-varying channel environment.
Because a wireless channel generally varies with time, it is desirable to consider a time-varying channel environment for accurate analysis. In this chapter, we provide a redefined analytical model to evaluate the performance of the IEEE 802.11 DCF with time-varying channel environment. In the proposed model, a time-varying channel is modeled by a finite-state Markov (FSM) model, and therefore the bit error rate (BER) can be changed according to the channel state [60]. In this study, we also consider the impact of different factors together, including the binary exponential backoff mechanism, various incoming traffic loads, network size, and packet transmission errors.
80 6.2 Wireless Channel Model
In order to analyze the performance of the IEEE 802.11 DCF with time-varying environment, we need to model the wireless channel. Due to the random move- ment of the mobile nodes, the wireless channel exhibits a time-variant behavior and correlation over consecutive packet period. A natural way to model a corre- lated channel is to approximate it by means of Markov model. In most studies, the two-state Markov channel is assumed [61] [62] to approximate Rayleigh fading channels. In this model, each state corresponds to a specific channel quality which is either noiseless or totally noisy. In some cases, modeling a wireless communica- tion channel as a two-state Markov model is not adequate when the channel quality varies dramatically. Thus, the authors in [60] proposed a FSM channel model to better describe the time-varying wireless channel. In this model, the time-varying channel is defined by its channel state set C = {c0, c1, ..., ck−1} and its K ×K state transition probability matrix T . The channel state ck represents the BER of the channel. The average BER e of the FSM channel is given by
K−1 X e = χk · ek, (6.1) k=0 where χk and ek are the steady state probability and the BER of the channel state ck.
Note that χk and ek can be obtained from the wireless characteristics and the coding scheme. In this paper, we consider a Rayleigh fading channel. Let A denote the received signal to noise ratio (SNR) which is proportional to the square of the
81 signal envelope. The pdf of A is exponential and can be obtained by
1 a p (a) = exp − , fora ≥ 0, (6.2) A ρ ρ where ρ = E[A].
The fading characteristics of the signal envelope are determined by the Doppler
frequency due to the motion of a mobile node. Let fD = v/λ is the maximum
Doppler frequency (v is the moving speed of mobile node and λ is the carrier wavelength). Now consider the level crossing rate of the instantaneous SNR process
A. It is the expected number of times per second that the received SNR A passes downward a given level am. For a random distribution of direction of motion providing a maximum Doppler frequency fD, we can show, as in [63], that the level crossing rate of level am for SNR process, in the positive direction only (or in the negative direction only), is
r2πa a N(a ) = m f exp − m . (6.3) m ρ D ρ
It is noted that any partition of the received SNR into a finite number of
intervals forms a finite state channel model. Let 0 = A0 < A1 < A2 < ... < AK =
∞ be the thresholds of the received SNR. Then the Rayleigh fading channel is
said to be in state ck(k = 0, 1, ..., K − 1), if the received SNR is in the interval
[Ak,Ak+1). Associated with each state, there is a binary symmetric channel (BSC)
with BER ek. The states are thus ordered with decreasing average BER values.
For a packet transmission system, we assume that a one-step transition in the model corresponds to the channel state transition after one packet time period Tp.
A received packet is said to be in channel state ck(k = 0, 2, ..., K − 1), if the SNR
82 values in the packet are located in the range [Ak,Ak+1). We allow the transition
from given state to its two adjacent states only.
Tk,i = 0, if |k − i| > 1. (6.4)
With the assumption of discrete channel structure, modulation and demodula-
tion are considered as an inherent part of the channel. Given a specific modulation
scheme, the average error probability is a function of SNR. For example, if the bi-
nary phase shift keying (BPSK) is assumed with coherent demodulation, the error
probability as a function of the received SNR a can be written as
√ em(a) = 1 − F ( 2a), (6.5)
where
Z a 1 x2 F (a) = exp − dx. (6.6) −∞ 2π 2
Thus, the steady state probability and the BER of each state of the Rayleigh
channel are
Z Ak+1 1 a Ak Ak+1 χk = exp{− }da = exp − − exp − , (6.7) Ak ρ ρ ρ ρ and n o √ R Ak+1 1 exp − a (1 − F ( 2a))da Ak ρ ρ ek = n o . (6.8) R Ak+1 1 exp − a da Ak ρ ρ Substituting Equations (6.7) and (6.8) into (6.1) , the average error probability e for Rayleigh channel in FSM model is
1 r ρ e = 1 − . (6.9) 2 ρ + 1
83 The transition probability from state ck to state ck+1, Tk,k+1, can be approx- imated by the ratio of the level crossing rate at threshold Ak+1 and the average number of packets per second staying in state ck. Similarly, the transition probabil- ity Tk,k−1 is approximated by the ratio of the level crossing rate at threshold Ak and the number of packets per second staying in state ck. The transition probabilities can be approximated as [60]
N (Ak+1) N (Ak+1) Tp Tk,k+1 ≈ = , k = 1, 2, ...K − 1 (6.10) Rtχk χk
N (Ak) N (Ak) Tp Tk,k−1 ≈ = , k = 2, 3, ...K, (6.11) Rtχk χk where Rt = 1/Tp is the transmission rate.
6.3 Analytical Model
In this section, we use the approach described in our previous research work [58] to evaluate the throughput for a finite number of nodes in a slotted CSMA/CA system with the wireless channel model described above. Since our objective of this chapter is to investigate the effect of transmission errors, we assume that there is no hidden node problem in the networks and the nodes are immobile.
Therefore, we can use the same system model as described in Section 4.2.1. In this chapter, we assume that the average channel state duration time is greater than the packet transmission time. Therefore, errors caused by channel transitions during the packet transmission are neglected. We assume that each channel state
84 ck consists of a sequence of regeneration cycles composed of idle period Ik and busy
period Bk. Let Uk be the time spent in useful transmission for channel state ck.
The throughput Sk for channel state ck is defined as the fraction of channel time
occupied by a valid transmission and can be obtained by
Uk Sk = , k = 0, 1, ..., K − 1, (6.12) Bk + Ik
where Uk, Bk, and Ik are the average time of useful transmission, busy period, and
idle period.
Let Xk(t) be the number of nodes in the backlogged state for the channel state
ck. The random process {xk(t) = i} can be modeled by a homogeneous Markov
chain identified by the last slot of each idle period (see Figure 4.1). Since there
are M nodes in the system, Xk(t) can be 0, 1, 2..., M. Thus the embedded Markov chain for Xk(t) has M +1 states as shown in Figure 4.2. Transition from state i to j
(i ≤ j) means that there are some thinking nodes entering to the backlogged state.
Similarly, transition from state i+1 to i represents that there is a successful packet transmission. It is assumed that each backlogged node has the same steady-state probability νi to send a packet at the time slot t when Xk(t) equals to i. In order to determine the probability νi, we need to know the collision probability. In [12], an analytical model is developed to compute the collision probability pc(i), which is given as
2 [1 − 2pc(i)] 1 i−1 pc(i) = 1 − {1 − m } , i > 1, (6.13) 1 − pc(i) − pc(i) [2pc(i)] W
where W is the minimum contention window and m is to determine the maximum
m contention window Wmax and it satisfies Wmax = 2 W . Note that the collision
85 probability pc(i) is the probability that more than one backlogged nodes transmit
at the same slot. This yields to
i−1 pc(i) = 1 − (1 − νi) . (6.14)
Then we can get the probability νi (i > 1) from equations (6.13) and (6.14).
Obviously, ν0 = 0 and ν1 = 1/W .
lim Our goal is to obtain the stationary distribution of the chain πki =t→∞ Pr{xk(t) = i}. For that purpose, we need to find the transition probability matrix Pk. Using the linear feedback model introduced by Tobagi and Kleinrock [46] [47], Pk is the product of several single slot transition matrices which we will define next. We denote the transition matrix by Rk for slot t1 + I and Qk for all remaining slots of the busy period. Since the length of the busy period depends on the number of nodes which become ready in slot t1 + I, we have Rk = Uk + Fk, where the (i, j)th elements of Uk and Fk are defined as
uk(i, j) = P r(xk(t1 + I + 1) = j and transmission is successful|xk(t1 + I) = i)(6.15)
and
fk(i, j) = P r(xk(t1 + I + 1) = j andtransmission is unsuccessful|xk(t1 + I) = i(6.16)).
Note that Uk is the probability that there is only one node ready to trans- mit and there is no bit error in the transmission. Fk is the probability that a transmitted packet is in a collision or error with the channel state ck. In this
86 study, we assume a packet transmission error occurs if any one bit in the packet is not correctly received. Qk reflects the addition to the backlogged state from the
M − Xk(t) thinking nodes in any slot t during the busy period.
s c Tk and Tk are the average time intervals for which the medium is sensed to be busy due to successful transmission and unsuccessful transmission (collision or
c error transmission under the channel state ck), respectively. Of these, only Tk
s varies with the channel state, which is describe below. The Tk is given by
s Tk = TDIFS + Tp + TSIFS + TACK + 2α, (6.17)
Because only the nodes with unsuccessful transmission should wait for the ACK timeout intervals, and the remaining nodes should continue to decrease their back- off timers after DIFS, the probability of unsuccessful transmission fk is multiplied
c by the ACK timeout interval, and the Tk is given by
c Tk = (1 − fk) × TDIFS + Tp + fk × TACKtimeout , (6.18)
where TACKtimeout is the time interval of the ACK timeout.
According to [46] and [47], the transmission matrix Pk is expressed as
s c Tk Tk Pk = UkQk Hk + FkQk , (6.19)
where Hk represents the fact that a successful transmission decreases the number of backlogged nodes by 1 and the elements of matrices Uk, Fk, Qk, and Hk are given by
87 0, j < i, M−i i−1 Tp (1−g) [iνi(1−νi) ](1−ek) i M−i , j = i, 1−(1−νi) (1−g) uk(i, j) = (6.20) M−i−1 i Tp (M−i)g(1−g) (1−νi) (1−ek) i M−i , j = i + 1, 1−(1−νi) (1−g) 0, j > i + 1.
0, j < i, M−i i i−1 Tp (1−g) [1−(1−νi) −iνi(1−νi) (1−ek) ] i M−i , j = i, 1−(1−νi) (1−g) M−i−1 i Tp (M−i)g(1−g) [1−(1−νi) (1−ek) ] i M−i , j = i + 1, fk(i, j) = 0 1−1(1−νi) (1−g) (6.21) B C B C B M − i C B C B C(1−g)M−j gj−i B C @ A j − i i M−i , j > i + 1. 1−(1−νi) (1−g)
0, j < i, qk(i, j) = M − i (6.22) M−j j−i (1 − g) g , j ≥ i + 1, j − i
1, j = i − 1, hk(i, j) = (6.23) 0, otherwise.
The steady-state probabilities of the Markov process are defined as a row vector
πk = [πk(0), πk(1), ..., πk(N)], which can be determined by πk = πkPk.
88 Since the idle period Ik(i) is geometrically distributed [13], its expectation is
given by 1 Ik(i) = i M−i . (6.24) 1 − (1 − νi) (1 − g)
s The probability of successful transmission pk(i) for channel state ck when Xk(t) equals to i is given by M X pk(i) = uk(i, j). (6.25) j=0
Therefore, the throughput Sk for the channel state ck can be obtained by
PM i=0 πk(i)pk(i)Tp Sk = . (6.26) PM s c i=0 πk(i){Ik(i) + pk(i)Tk + [1 − pk(i)]Tk }
The throughput S of the IEEE 802.11 DCF protocol with the time-varying
wireless channel is
K−1 X S = χk · Sk. (6.27) k=0
6.4 Numerical Results and Discussions
In this section, we apply our proposed model to theoretically predict the through-
put performance of the IEEE 802.11 DCF under different traffic load and packet
transmission error conditions through numerical analysis. All numerical results are
obtained with Matlab.
First, it is essential to determine the characteristics of wireless channels. In
[60], the choice of number of states and SNR partitions was somewhat arbitrary.
Therefore, we adopt the methodology of [64], in which the received SNR values
are partitioned into a finite number of states according to a criterion based on the
89 average duration of each state. In the numerical analysis, π/4-DQPSK modulation
with coherent detection was used. Table 6.1 shows the BER ek and steady state
probability χk in 4-state and 7-state FSM channel models.
Table 6.1: ek and χk in 4-state and 7-state FSM channel models
state ek χk ek χk
index ρ = 15dB ρ = 15dB ρ = 10dB ρ = 10dB
1 2.96·10−1 1.97·10−3 5.57 · 10−1 6.22 · 10−3
2 9.77·10−3 5.91 · 10−3 1.31 · 10−1 1.85 · 10−2
3 9.98·10−6 9.84 · 10−3 9.90 · 10−3 3.02 · 10−2
4 2.464·10−10 9.823 · 10−1 2.43 · 10−4 4.12 · 10−2
5 - - 1.81 · 10−6 5.11 · 10−2
6 - - 3.78 · 10−9 5.96 · 10−2
7 - - 2.00 · 10−12 7.93 · 10−1
The numerical results of the performance of the IEEE 802.11 DCF under the
error-free and time-varying channels are provided in Table 6.2. Due to limited
space, we only provided a part of values in this table. In the analysis, we let
the packet arrival to any node be a Poisson process. The offered traffic load G varies from light condition to heavy (saturated) condition. The other parameters are defined as follows: M = 15, Tp = 1 (i.e.,100 slots), α = 0.01, TDIFS = 0.03,
TSIFS = 0.01, TACK = 0.05, TACKtimeout = 0.06, W = 32, and Wmax = 1024. It can
be observed that, when BER increases, the throughput always degrades.
Tables 6.3 and 6.4 depict that the throughput are highly dependent on the
90 Table 6.2: Throughput of IEEE 802.11 DCF versus traffic load G
G 0.2 0.6 1.0 1.4 1.8 2.2
S 0.1962 0.5492 0.7516 0.7657 0.7509 0.7415
(no BER)
S 0.1958 0.5466 0.7472 0.7611 0.7464 0.7371
(ρ = 15dB)
S 0.1910 0.52757 0.7311 0.7171 0.7025 0.6990
(ρ = 10dB) number of contending nodes and incoming traffic loads. When the incoming traffic load is light, the throughput increases when the network size grows. When the net- work works under heavy (saturated) condition, the throughput decreases when the network size grows. This phenomenon is primarily because the collision becomes larger with the increase of network size. The other result showed in Tables III and
IV is that increasing BER always results in throughput decreases regardless the network size and the incoming traffic load.
6.5 Summary
In this chapter, we developed a new analytical model using Markov chains to evaluate the performance of the IEEE 802.11 DCF in time-varying channels, in which packet transmission can be failed due to transmission errors. In the proposed model, the time-varying wireless channel was modeled by a finite-state Markov
91 Table 6.3: Throughput of IEEE 802.11 DCF versus number of stations (G = 0.2)
Number of 5 10 15 20 25 30
station
S 0.1901 0.1946 0.1962 0.1970 0.19754 0.1979
(no BER)
S 0.1895 0.1941 0.1958 0.1966 0.1971 0.1974
(ρ = 15dB)
S 0.1846 0.1893 0.1910 0.1919 0.1924 0.1927
(ρ = 10dB) chain. In each channel state, the operation of the IEEE 802.11 DCF was modeled by an embedded Markov chain. Using these two Markov chains, the throughput of the IEEE 802.11 DCF can be theoretically calculated. The results show that the protocol strongly depends on the network size, the incoming traffic loads, and the
BER. When the incoming traffic load is light, the throughput increases when the network size grows. When the network works under heavy (saturated) condition, the throughput decreases when the network size grows. The performance always degrades when increasing BER regardless the network size and the traffic load.
92 Table 6.4: Throughput of IEEE 802.11 DCF versus number of stations (G = 2.2)
Number of 5 10 15 20 25 30
station
S 0.7938 0.7689 0.7415 0.7182 0.6995 0.6851
(no BER)
S 0.7892 0.7643 0.7371 0.7139 0.6954 0.6810
(ρ = 15dB)
S 0.7584 0.7344 0.7025 0.6860 0.6681 0.6543
(ρ = 10dB)
93 Chapter 7
Conclusions and Future Work
7.1 Conclusions
In this research work, firstly, we proposed a novel model to analyze the link and routing path stabilities in mobile ad hoc networks. In our proposed analytical model, between each communicating pair, one node was considered to be station- ary while the other moved relative to it. With this method, the mobility models defined in this dissertation were approximated as a fluid flow model. Using the re- sult of the fluid flow model, the analytical model for the link duration was obtained, which was used to obtain the link holding time and the link breaking probability of a communicating pair. The distribution of a routing path duration and the rout- ing path breaking probability were also obtained by extending the models of the link duration and the link breaking probability. Our results showed that the link duration and routing path duration can be approximated as exponential distribu- tions. Specially, when the number of links is larger than 3 or 4, the distribution
94 of routing path duration closely resembles exponential distribution. For the link and routing path breaking probability, if the MAC protocol and traffic load are
fixed, they are depends on the moving speed and radio transmission range. The radio transmission range and the moving speed have the opposite effect on the link breaking and routing path probabilities, since scaling the radio transmission range up has the same effect of scaling the moving speed down. For nodes with high moving speed, it was better to have a larger radio transmission range to low the link and routing path breaking probabilities. However, the radio transmission range was limited by the power of wireless device. The proposed analytical model obtained in this section can serve as the ground knowledge for the performance analysis of MAC protocols in mobile ad hoc networks.
In mobile ad hoc networks, the MAC protocol is the main element that de- termines the efficiency in sharing the limited communication bandwidth of the wireless channel. In order to adjust system parameters to obtain high channel uti- lization or fulfill specific needs, a mathematical description of the MAC protocol turns to be a lot helpful in observing the trend of any parameter changes made.
In this research work, we provided a model to analyze the performance of MAC protocol in dynamic environment where all nodes are mobile. In our study, we have observed that the node mobility does affect the MAC protocol performance.
This conclusion is consistent with previous studies. Unlike previous studies that is simulation-based, our study provided an analytical model. Moreover, we observe that the mobility influenced the link stability that in turn influenced the MAC protocol performance. Therefore, in our work [48], we proposed a scheme, which
95 used the cross layer information, to improve the performance of the IEEE 802.11
DCF protocol in dynamic environment.
Most performance analysis of MAC protocol assumes that the wireless chan- nel is noiseless and all packets arrive at the receiver with the same power level.
Whenever two or more packets arrive at the receiver during overlapping time, they collide and all packets involved were destroyed. This model, reasonable in some communication environment, turns out to be too pessimistic in others. In a prac- tical wireless network, the transmitted packets experience not only noise but also fading, so that the receiver may fail to detect the faded packets even though there is no collision. On the other hand, a packet can be received successfully in the presence of other overlapping packets if its power is larger than the interfering power by a certain margin. The later phenomenon is called capture effect. The capture effect will bring the performance improvement. Our third contribution is to provide an analytical model to obtain the throughput of CSMA/CA protocol in the presence of fading, shadowing, and path loss. Our results showed that he throughput improvement is significant compared to the model without capture effect. However, for CSMA/CA with RTS/CTS, the exchange of RTS and CTS before actual transmission reduces the likeliness of simultaneous transmission and packet capture.
Due to the random movement of the mobile nodes, the wireless channel in mo- bile ad hoc networks exhibits a time-variant behavior. The wireless channel are severely affected by the time-varying losses due to path loss, shadowing, and mul- tipath fading. While the variation in the losses due to path loss and shadowing is
96 relatively slow, the variation due to multipath fading is quite fast. The fading en- velope due to multipath fading follows a Rayleigh distribution, so that the envelope squared (i.e., the power) has an exponential distribution. Most notably, the cor- relation in the multipath fading behavior and its effect on the performance of the
IEEE 802.11 MAC protocols have not been adequately addressed in the literature so far. The primary focus of Chapter 6 is to address this void. In the Chapter, the time-varying wireless channel was modeled by a finite-state Markov chain. In each channel state, the operation of the IEEE 802.11 DCF MAC protocol was modeled by an embedded Markov chain. Using these two Markov chains, the throughput of the IEEE 802.11 DCF can be very accurately calculated. The results showed that the protocol strongly depends on the network size, the incoming traffic loads, and the BER. When the incoming traffic load is light, the throughput increases when the network size grows. When the network works under heavy (saturated) condition, the throughput decreases when the network size grows. The perfor- mance always degrades when increasing BER regardless the network size and the incoming traffic load.
7.2 Future Work
So far we have modeled and analyzed the performance of the IEEE 802.11 MAC protocols in different environments. These analysis mainly focus on the modeling and performance analysis of MAC protocols with omni-directional antennas. In our future work, we plan to propose a new MAC protocols for mobile ad hoc networks
97 using smart antennas. We also want to use our current model and analytical method to model the performance of our new MAC protocols.
• New MAC protocol for mobile ad hoc networks with smart anten-
nas: We plan to design a transmitter-initiated MAC protocol for use with
smart antennas, which allows a node with separate antenna entities to receive
and transmit, and that mutually exclusive directions are used for transmis-
sion and reception at any given time instant. In order that two separate
systems for reception and transmission are not required, we plan to explore
the use of a time division duplex (TDD) MAC scheme between transmission
and reception. At the same time, it should harness parallelism as far as
possible in the transmission and reception process. A balanced MAC pro-
tocol for smart antennas should, therefore, maximizes the parallelism while
maintaining TDD between transmission and reception.
• Performance analysis of MAC protocol with smart antennas: The
performance of MAC protocols needs to be examined carefully with simula-
tions as well as analytical models in order to design a robust MAC protocol
for use with smart antennas. We have obtained the analytical results in
mobile ad hoc networks with omni-directional antennas under different en-
vironments. We will use the similar analytical method to the networks with
smart antennas. In fact, we can model each beam as a sub-channel with a
succession of regeneration cycles. Each cycle is comprised of an idle period
and busy period. In idle period, there is no nodes that have packets to trans-
98 mit. In busy period, one or more nodes have a packet to transmit. Now considering that N nodes are uniformly distributed around the receiver that is capable of forming M non-overlapping beams. Then each beam has the
N same average number of nodes n = M . This assumption ensures that the throughput achieved by each beam is identically distributed over the load.
Therefore, throughputs and transmission delays of new MAC protocols can be obtained with the same method as our previous work. The impact of other parameters, such as beam width, density of nodes, transmission power, etc., on the throughput and average transmission delay will also be examined.
Using smart antennas, dramatic improvements in the network performance can be obtained and to cross the frontier of multiple access in space for ad hoc networks. There is a promising aspect of providing QoS for real-time services using smart antennas. We intend to explore this possibility and provide substantial results in this direction at the disposal of the research community.
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