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Quantification of Capacity and Transmission Delay for Mobile Ad Hoc Networks (MANET)

Authors:

Abstract

The capacity of mobile ad hoc network (MANET) is typically determined by the size of network, routing protocol, mobility and the interactions that occur between the nodes. Moreover, these critical parameters cause the loss rate that has severed impact on the performance of the MANET. This situation even becomes worst when these critical parameters are chosen inappropriately. This paper presents an analytical model that incorporates most of the critical parameters that can influence the capacity of MANET. Based on the analytical model, an efficient 3-phase algorithm is designed to optimize the performance of MANET in terms of increased capacity and reduced transmission delay. The proposed 3-pahse algorithm considers both delay-tolerant and delay-sensitive network traffics. In addition, the 3-phase algorithm can be used to approximate both the best and worst case capacities of MANET with the relaying and non-relaying nodes.
Abstract-The capacity of mobile ad hoc network (MANET) is
typically determined by the size of network, routing protocol,
mobility and the interactions that occur between the nodes.
Moreover, these critical parameters cause the loss rate that has
severed impact on the performance of the MANET. This
situation even becomes worst when these critical parameters are
chosen inappropriately. This paper presents an analytical model
that incorporates most of the critical parameters that can
influence the capacity of MANET. Based on the analytical
model, an efficient 3-phase algorithm is designed to optimize the
performance of MANET in terms of increased capacity and
reduced transmission delay. The proposed 3-pahse algorithm
considers both delay-tolerant and delay-sensitive network
traffics. In addition, the 3-phase algorithm can be used to
approximate both the best and worst case capacities of MANET
with the relaying and non-relaying nodes.
Keywords Ad Hoc networks, capacity analysis,
transmission delay, and bandwidth
I. INTRODUCTION
Much research has already been done for improving the
performance of MANET [1, 2, 5]. The capacity of a fixed
wireless network decreases as the number of nodes increases
when all the nodes share a common wireless channel [1]. This
scheme was shown to increase the capacity of the MANET in
such a way that it remains constant as the total number of
nodes increases in the system. More recently, [3] has proposed
a two phase packet relaying technique. The main intention of
this technique was to reduce the overall packet transmission
delay. However, the delay experienced by packets under this
strategy was shown to be large and it can be even infinite for a
fixed number of nodes in the system, which has prompted
more recent work presenting analysis of capacity and delay
tradeoffs. However, the proposed 3-phase technique is highly
efficient in such a way that it shows that the capacity of
1
Contact author: srizvi@bridgeport.edu
MANET can be increased at the expense of comparatively
small increased in the transmission delay.
According to the analysis of Gupta and Kumar [1], the
capacity region of network is defined as n(n-1) where n
represents the number of nodes. Two types of capacities are
typically measured: transport and throughput. The transport
capacity is determined by multiplying bits and the distance per
second where as the throughput capacity is expressed simply
by bits per second. In a MANET, the transport capacity is
approximated as O(n) bit-meter per second whereas the
throughput capacity of each node is O(1/n) bit per second.
However, this analysis does not include the mobility of nodes.
The proposed analytical model and 3-phase algorithm not only
accounts the transport and throughput capacities of MANET
but also considers the node mobility at one specific point. Our
numerical and simulation analysis demonstrates that the
capacity of MANET can be improved significantly if the
critical parameters are set intelligently.
II. ANALYTICAL MODEL FOR CAPACITY ANALYSIS AND
TRANSMISSION DELAY
Our proposed analytical model is based on the method
proposed by Gupta and Kumar [1]. They considered a static
model where all nodes are fixed and relaying is an allowable
property of MANET. The node positions Xi are independent
and identically-distributed in the open disk of a unit area. The
destinations are chosen independently and the destination for
each source node is chosen with respect to the node closest to
a randomly chosen point on the disk. For such a static model,
the upper and lower bounds on the asymptotically feasible
throughput reaches to infinity for each pair of source and
destination (S-D) [1]. However, the capacity of mobile nodes
without relaying can also be computed [5]. This requires
considering a model that consists of n nodes in an open disk of
unit area where the radius can be approximated as 1/√π.
Although, [3, 4] proved that the capacity of MANET is
constant, but they did not determine the particular capacity at
one certain point of time. In other words, the proposed
algorithm considers the transmission time which involves one
Quantification of Capacity and Transmission
Delay for Mobile Ad Hoc Networks (MANET)
1
Syed S. Rizvi,
2
Aasia Riasat, and
3
Khaled M. Elleithy
1, 3
Computer Science and Engineering Department, University of Bridgeport, Bridgeport CT, 06601
2
Department of Computer Science, Institute of Business Management, Karachi, Pakistan
{srizvi
1
, elleithy
3
}@bridgeport.edu, aasia.riasat@cbm.edu.pk
2
particular pair of S-D. However, we use these 2 basic models
to develop the proposed algorithm that considers both the
delay time and the broadcasting between the nodes of
MANET.
A. Framework for a 3-Phase Algorithm
We use special scheduling policy [3], called as π,” for our
3- phase transmission algorithm. This scheduling policy (π)
selects S-D pairs randomly in each time slot t. Our
transmission algorism is divided into three phases. In the first
phase, the transmission occurs only between the sender that
has packets for transmission and the relay nodes as shown in
Fig. 1. The relay nodes might have some part of packets which
must be sent to the destination or between sender and
destination if the nearest node of destination is sender node. In
the second phase, these nodes move around in unit circle
whose radius is 1/√π. During the second phase, no
transmission is carried out among mobile nodes until the relay
nodes approach an appropriate destination node. Even though,
this mobility of nodes may cause a delay time, this can not be
influenced to the total throughput. Lastly, the processing of
third phases begins when the location of mobile relay nodes is
near the destination node as shown in Fig. 2. In such a case,
the transmission can occur immediately between the relay and
the destination nodes or between the S-D pair. It should be
noted in Fig. 2 that the first and the last phases of the
proposed algorithm are interleaved in a sense that the
processing of first phase occurs in even time slots where as the
processing of the last phase occurs in odd time slots.
B. Implementation of the Proposed 3-Phase Algorithm
In order to implement the proposed algorithm, we use
scheduling model (π) that selects only one sender node which
has 3 packets for transmission with one destination node
within the unit circle which consists of n mobile nodes.
Moreover, we assume that there are three mobile nodes which
are located within the close proximity of the sender node. In
other words, this second assumption implies that the
transmissions can occurs at distance of order of 1/n. In first
phase, sender distributes each packet to 10 mobile nodes, so
each mobile node (relay node) has a part of the sender packets.
In the second phase, these mobile nodes move around the unit
circle. If some relay node(s) which has the part of the sender’s
packet enters within the close proximity of destination node,
the transmission occurs immediately. Finally, in the third
phase, the relay node(s) transmits the part of the sender’s
packet to the appropriate destination node. Both second and
the third phases of the proposed algorithm are repeated until
the destination receives the entire packets.
III. ANALYSIS OF BEST AND WORST CASE CAPACITIES FOR
MANET
In this section, we present the analysis of the best and the
worst case capacities for a MANET. Specifically, we show
that how the proposed 3-phase algorithm can be implanted in
order to compute the capacities for a MANET.
A. The Worst Case Capacity
For the worst cast capacity, it is assumed that the
transmission occurs for the largest time. Also, we assume that
Fig. 2. Processing of the first and the third phase. The parameter L
p
is set to 2, L
Tt
is the transmission-time 2 packets, M is set to 3, P
0
is set to 2, P
1
is set to 1, P
2
is set to 2, and T
t0
, T
t1
,
T
t2
represents
the required time to transmit 2, 1, 2 packets to the destination
,
respectively.
Fig. 1. Processing of the first phase. The biggest rectangle is
unit
rectangle which is 1. S
nodes can communicate. This model has 12 mobile nodes and 3 relay
nodes
P
i
is the maximum number of packets that can be transmitted
from the ith source node to a destination. The size of a
transmitted packet between each pair of S-D can not exceed to
L
P
. In the given scenario, each relay nodes may start
transmission at different time. The packet transmission in
MANET can be estimated as:
1
0
2
M
Tra nsmission
P i P
i
S D L P L
=
+
A
Property (1)
where, M represents the number of relay nodes.
Moreover, if relay nodes transmission occurs at different
times, then
Ti
L
represents the transmission time between the
ith source and the other relay nodes. In addition, the source
and the relay nodes are assumed to have the largest number of
packets for transmission. Based on the above argument, the
total transmission time can be approximated as follows:
1
0
M
Tt Ti
i
Transmission Time L T
=
= +
Property (2)
Using (1) and (2), we can derive a closed form expression
for estimating the worst case capacity (WC
capacity
) such as:
1
0
2
M
capacity P Tt Ti
i
WC L L L
=
+
A
Property (3)
where the total delay time is set to 0
B. The Best Case Capacity
For the best case capacity, we consider the shortest
transmission time between a pair of S-D. The shortest time is
generated when the transmission starts simultaneously
between the relay nodes and the destination node. This
transmission time can be considered as a time in which the
relay node has the largest packet size for transmission towards
a destination. This time is the same as the transmission time
between the source node and the relay node. This leads us to
the following expression for the best case capacity: L
P
/L
Ti
Finally, we can combine the result of worst and the best
case capacities. When the characteristics of property (3) are
true, the total transmission throughput reaches to O(1)
between node i and j at distance of order 1/n. We also
assume that there is no direct transmission exists between the
source and the destination system. Taking this into account,
one can approximate the best and the worst case capacities
such as:
( )
1
0
lim 2 ( )
M
P Tt ti P Tt
t
i
L L T t L L
λ
−>
=
+
Property (4)
where )(t
λ
is the throughput with respect to the transmission
time.
C. Reducing Delay Time
The delay time is always generated with a certain
probability with respect to a certain complexity such as of
O(1/n). In the given scenario, when the transmission occurs,
relay nodes approach to appropriate destinations. The second
phase of the proposed algorithm (see Fig. 2) can be effectively
used to reduce the delay time by improving the probability (see
Fig. 3 for delay reduction). We have shown that the second
phase of the proposed algorithm improves this probability by
asymmetrically distributing the packets that each relay node is
supposed to transmit to other nodes. Based on the proposed
approach, as the number of relay node increases that carry the
identical packets, the probability of constructing the pairs of
relay nodes and the destination nodes also increases. The
improvement in the probability is in the order of O (c/n), c >
0.
D. Numerical and Simulation Results
Before we discuss the simulation results, it is worth
Fig. 3. This picture shows the improvement to reduce
the overall
delay time. The biggest rectangle is a unit rectangle (1)
where as
the small circle re
presents the distance at which nodes can
communicate. This model has 12 mobile nodes,
3 relay nodes and 3
reproduced relay nodes.
TABLE I
THE RESULT OF RELAY MOBILE NETWORK WITHOUT REPRODUCTION
NRN Ttime (sec) Delay (sec) Throughput
1 3 0.0112 3406232 14285.70
2 4 0.0096 5056653 16666.66
3 3 0.0112 3442331 14285.70
4 3 0.012 3515001 13333.32
5 5 0.0096 4160049 16666.66
6 8 0.0096 4758960 16666.66
7 6 0.012 5544597 13333.32
8 2 0.012 1378757 13333.32
NRN = THE NUMBER OF RELAY NODE, T
TIME
= TRANSMISSION TIME, DELAY =
DELAY TIME
mentioning some of our key assumptions. We assume that the
location of a mobile node may change randomly as shown in
Fig. 4. In addition, each node has enough buffer size with the
maximum capacity of 80 kbps. We also assume that the packet
size is typically 8 bits. For the sake of simulation, we consider
a network that consists of 100 nodes where each node may
transmit 10 packets. The simulation is run over a long period
of time and the results are presented in Table I. It should be
noted in Table I that the achievable throughput exists between
the best and the worst case capacities. The proposed algorithm
provides reduced delay time as shown in Table I.
IV. CONCLUSION
This paper presented an analytical model that uses special
scheduling policy for the random selection of the S-D pairs.
Based on the analytical model, we designed an efficient 3-
pahse algorithm that can be effectively used to analyze the
capacities of MANET. The proposed algorithm considers the
random selection of S-D pair which is essential in order to
produce the correct approximation of best and worst case
capacities. Our results have shown that the capacity of
MANET can be improved by using the proposed algorithm.
Also, the numerical results suggest that the transmission delay
can be reduced even in the presence of node mobility.
REFERENCES
[1] Piyush Gupta and P.Kumar, “The capacity of wireless
networks,” IEEE Transactions on Information Theory, Vol. 46,
pp. 388-404, 2000.
[2] L. Jinyang, C. Blake, S. Douglas, D. Couto, I. Lee, and R.
Morris, “Capacity of Ad Hoc Wireless Networks,” In the
proceedings of the 7
th
ACM International Conference on Mobile
Computing and Networking, pp. 61 69, Rome, Italy, July
2001.
[3] M. Grossglauser and T. David, “Mobility increases the capacity
of Ad-hoc wireless networks, IEEE/ACM Transactions on
Networking, Vol.10, no. 4, pp. 477 – 486, 2002.
[4] C. Schindelhauer, T. Lukovszki, S. Rührup, K. Volbert, “Worst
case mobility in Ad Hoc networks,“ Proceedings of the fifteenth
annual ACM symposium on Parallel algorithms and
architectures, pp. 230 – 239, 2003.
[5] C.-K. Toh, Maximum Battery Life Routing to Support
Ubiquitous Mobile Computing in Wireless Ad Hoc Networks,
IEEE Communications Magazine, Vol. 39, no. 6, pp. 138 - 147
June 2001.
[6] A.J. Goldsmith and S.B. Wicker, "Design challenge for energy
constrained ad-hoc wireless networks," IEEE Wireless,
Communication, vol.4, pp.8–9, Aug. 2002.
Authors Biographies
SYED S. RIZVI is a Ph.D. student of
Computer Engineering at University of
Bridgeport. He received a B.S. in
Computer Engineering from Sir Syed
University of Engineering and
Technology and an M.S. in Computer
Engineering from Old Dominion
University in 2001 and 2005 respectively.
In the past, he has done research on
bioinformatics projects where he
investigated the use of Linux based cluster search engines for finding
the desired proteins in input and outputs sequences from multiple
databases. For last one year, his research focused primarily on the
modeling and simulation of wide range parallel/distributed systems
and the web based training applications. Syed Rizvi is the author of
75 scholarly publications in various areas. His current research
focuses on the design, implementation and comparisons of
algorithms in the areas of multiuser communications, multipath
signals detection, multi-access interference estimation,
computational complexity and combinatorial optimization of
multiuser receivers, peer-to-peer networking, and reconfigurable
coprocessor and FPGA based architectures.
AASIA RIASAT is an Associate
Professor of Computer Science at
Collage of Business Management
(CBM) since May 2006. She received
an M.S.C. in Computer Science from
the University of Sindh, and an M.S in
Computer Science from Old Dominion
University in 2005. For last one year,
she is working as one of the active
members of the wireless and mobile communications (WMC) lab
research group of University of Bridgeport, Bridgeport CT. In WMC
research group, she is mainly responsible for simulation design for
all the research work. Aasia Riasat is the author or co-author of
several scholarly publications in various areas. Her research interests
Fig. 4. This picture shows the location of mob
ile nodes in the
simulation. The unit rectangle is 1. The red, blue, and green
nodes represent the source, destination, and the relay node
,
respectively. Simulation consists of 3 relay nodes
and 100 regular
nodes
include modeling and simulation, web-based visualization, virtual
reality, data compression, and algorithms optimization.
KHALED ELLEITHY received the
B.Sc. degree in computer science and
automatic control from Alexandria
University in 1983, the MS Degree in
computer networks from the same
university in 1986, and the MS and Ph.D.
degrees in computer science from The
Center for Advanced Computer Studies at
the University of Louisiana at Lafayette
in 1988 and 1990, respectively. From 1983 to 1986, he was with the
Computer Science Department, Alexandria University, Egypt, as a
lecturer. From September 1990 to May 1995 he worked as an
assistant professor at the Department of Computer Engineering, King
Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.
From May 1995 to December 2000, he has worked as an Associate
Professor in the same department. In January 2000, Dr. Elleithy has
joined the Department of Computer Science and Engineering in
University.
... The end to end packet delay in mobile ad-hoc network is complex because it depends on many influential factors as path length from source to destination, average neighbours of intermediate hops and interference. [5] [6] On the basis of available papers, it has been review in [7] that delay is a dynamic metric which is built upon the following factors multi-hop nature of network, Mobility, path length, Dynamic topology, Link-Breakage, limited battery life, bandwidth issues and Selfish behaviour of nodes. And in a dense network these factors show their affect even more than in a sparce network. ...
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Capacity of Ad Hoc Wireless Networks
  • L Jinyang
  • C Blake
  • S Douglas
  • D Couto
  • I Lee
  • R Morris
L. Jinyang, C. Blake, S. Douglas, D. Couto, I. Lee, and R. Morris, "Capacity of Ad Hoc Wireless Networks," In the proceedings of the 7 th ACM International Conference on Mobile Computing and Networking, pp. 61-69, Rome, Italy, July 2001.