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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

mall circle presents the distance at which

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.