Conference PaperPDF Available

The Worst and Best Case Capacity Analysis of Mobile Ad Hoc Networks (MANET) Using a 3-Phase Algorithm

Authors:

Abstract and Figures

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 an increased capacity and the reduced transmission delay. The proposed 3-phase 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.
No caption available
… 
Content may be subject to copyright.
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 an increased capacity and the 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
.
I. I
NTRODUCTION
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
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. P
ROPOSED ANALYTICAL MODEL AND THE 3-PHASE
ALGORITHM
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
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. Proposed 3-Phase Algorithm
We use special scheduling policy [3], called asπ,” 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 may have some part of packets which
must be sent to the destination or between sender and
The Worst and Best Case Capacity Analysis of
Mobile Ad Hoc Networks (MANET) Using a 3-
Phase Algorithm
Syed S. Rizvi
1
, Aasia Riasat
2
, Mustafa A. Khan
3
, and Khaled Elleithy
4
Computer Science and Engineering Department, University of Bridgeport
1,
3, 4
, Bridgeport CT, 06604
Department of Computer Science, Institute of Business Management
2
, Karachi, Pakistan
{
1
srizvi,
3
mustafak,
4
elleithy}@bridgeport.edu,
2
aasia.riasat@iobm.edu.pk
594978-1-4244-1777-3/08/$25.00 ©2008 IEEE
Authorized licensed use limited to: University of Bridgeport. Downloaded on February 24,2010 at 12:05:57 EST from IEEE Xplore. Restrictions apply.
destination if the nearest node of destination is sender node. In
the second phase, these nodes move around in unit circle area
with the radius of 1/√π. During the second phase, no
transmission is carried out among mobile nodes until the relay
nodes approach an appropriate destination node. Although, this
mobility of nodes may increase 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. It should be noted
in Fig. 2 that the first and the third phases of the proposed
algorithm are interleaved since the processing of first phase
occurs in even time slots whereas the processing of the third
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 randomly selects one sender node
that has packets for transmission with one destination node that
exists within the unit circle area of n mobile nodes. Moreover,
we assume that there are two or more mobile nodes which are
located within the close proximity of the sender node. This
second assumption implies that the transmissions can occurs at
a 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 packet.
III. T
HE 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 using the proposed 3-
phase algorithm.
A. The Worst Case Capacity
For the worst cast capacity, we assume that the transmission
occurs for the largest time. Also, we assume that P
i
is the
maximum number of packets that can be transmitted from the
ith source node to a destination node. The size of a transmitted
packet between each pair of S-D can not exceed to L
P
. In the
given scenario, each relay node may start transmission at
different time. Based on the above assumptions, the packet
transmission in MANET can be estimated as:
1
0
2
M
Transmission
P
iP
i
SD L P L
=
−⎯ +
(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:
Transmission Time
1
0
M
Tt Ti
i
L
T
=
=+
(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
=
⎛⎞
+
⎜⎟
⎝⎠
(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 period in which the relay node
has the largest packet size for transmission towards a
destination. This leads us to an expression for the best case
capacity:
capacity
BC =
PTt
L
L . Finally, we can combine the
result of worst and the best case capacities. When the
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 transmission time
Fig.1. Processing of the first phase. The biggest rectangle is unit rectangle
which is 1. Small circle presents the distance at which nodes ca
n
communicate. This model has 12 mobile nodes and 3 relay nodes
595
Authorized licensed use limited to: University of Bridgeport. Downloaded on February 24,2010 at 12:05:57 EST from IEEE Xplore. Restrictions apply.
characteristics of property (3) are true, the total transmission
throughput reaches to
()
i
Oj between node i and j at distance
of order 1/n. One can approximate the best and the worst case
capacities (
wb
C
) such as:
()
()
()
1
0
lim 2 ( )
ti
M
Tt PTt
wb
t
i
CLLTtLL
λ
−>∞
=
⎛⎞
=+
⎜⎟
⎝⎠
(4)
where
)(t
λ
is the throughput
C. Reducing Delay Time
The delay time is always generated with a certain probability
with respect to a certain complexity such as 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).
It is observed that the second phase of the proposed algorithm
improves this probability by asymmetrically distributing the
packets that each relay node may transmit. As the number of
relay node increases that carry the identical packets, the
probability of constructing the pairs of S-D nodes also
increases. The improvement in the probability is in the order of
O (c/n), where c > 0.
D. Numerical and Simulation Results
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
where as the packet size is 8 bits. For the sake of simulation,
we consider a network of 100 nodes where each node may
transmit 10 packets per second. The simulation is setup in ns-2
and the results are presented in Table I. The proposed
algorithm reduced the over all delay time as shown in Table I.
IV. C
ONCLUSION
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.
R
EFERENCES
[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 Wirel. Commun., vol.4,
pp.8–9, Aug. 2002.
Fig.3. Biggest rectangle is a unit rectangle (1) and the small circle re
p
resents
the distance at which nodes can communicate. This model has 12 mobile nodes,
3 relay nodes and 3 reproduced relay nodes.
Fig.4. Location of mobile nodes in the simulation. The unit rectangle is 1.
The red, blue, and green nodes represent the source, destination, and the rela
y
node, respectively. Simulation consists of 3 relay nodes and 100 regular nodes
TABLE I
T
HE 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
596
Authorized licensed use limited to: University of Bridgeport. Downloaded on February 24,2010 at 12:05:57 EST from IEEE Xplore. Restrictions apply.
Conference Paper
Mathematical modeling for energy consumption of MANETs considering the impact of different layers in the protocol stack in addition to that of different network parameters remains unexplored till now even though such modeling is considered as the fastest and the most cost-effective tool for evaluating the performance of a network. Therefore, in this paper, we attempt to develop a mathematical model for energy consumption of MANETs considering both of the aspects. In addition, we also focus on developing mathematical models for end-to-end delay, this metric limits the maximum throughput of a network. In our analysis, we perform rigorous simulation utilizing ns-2 to capture the performance of MANETs under diversified settings. Our rigorous empirical study reveals that we need to develop cross-layer mathematical models for energy consumption and delay to represent the performance of MANETs and such mathematical models need to resolve higher-order polynomial equations. Consequently, our study uncovers a key finding that mathematical modeling of MANETs considering variations in all parameters is not feasible.
Conference Paper
Full-text available
We investigate distributed algorithms for mobile ad hoc networks for moving radio stations with adjustable transmission power in a worst case scenario. We consider two models to find a reasonable restriction on the worst-case mobility. In the pedestrian model we assume a maximum speed vmax of the radio stations, while in the vehicular model we assume a maximum acceleration amax of the points.Our goal is to maintain persistent routes with nice communication network properties like hop distance, energy-consumption, congestion and number of interferences. A route is persistent, if we can guarantee that all edges of this route can be uphold for a given time span Δ, which is a parameter denoting the minimum time the mobile network needs to adopt changes, i.e. update routing tables, change directory entries, etc. This Δ can be used as the length of an update interval for a proactive routing scheme.We extend some known notions such as transmission range, interferences, spanner, power spanner and congestion to both mobility models and introduce a new parameter called crowdedness that states a lower bound on the number of radio interferences. Then we prove that a mobile spanner hosts a path system that polylogarithmically approximates the optimal congestion.We present distributed algorithms based on a grid clustering technique and a high-dimensional representation of the dynamical start situation which construct mobile spanners with low congestion, low interference number, low energy-consumption, and low degree. We measure the optimality of the output of our algorithm by comparing it with the optimal choice of persistent routes under the same circumstances with respect to pedestrian or vehicular worst-case movements. Finally, we present solutions for dynamic position information management under our mobility models.
Article
The capacity of ad hoc wireless networks is constrained by the mutual interference of concurrent transmissions between nodes. We study a model of an ad hoc network where n nodes communicate in random source-destination pairs. These nodes are assumed to be mobile. We examine the per-session throughput for applications with loose delay constraints, such that the topology changes over the time-scale of packet delivery. Under this assumption, the per-user throughput can increase dramatically when nodes are mobile rather than fixed. This improvement can be achieved by exploiting a form of multiuser diversity via packet relaying.
Conference Paper
The capacity of ad-hoc wireless networks is constrained by the mutual interference of concurrent transmissions between nodes. We study a model of an ad-hoc network where n nodes communicate in random source-destination pairs. These nodes are assumed to be mobile. We examine the per-session throughput for applications with loose delay constraints, such that the topology changes over the time-scale of packet delivery. Under this assumption, the per-user throughput can increase dramatically when the nodes are mobile rather than fixed. This improvement can be achieved by exploiting node mobility as a type of multiuser diversity
Article
Ad hoc wireless networks enable new and exciting applications, but also pose significant technical challenges. In this article we give a brief overview of ad hoc wireless networks and their applications with a particular emphasis on energy constraints. We then discuss advances in the link, multiple access, network, and application protocols for these networks. We show that cross-layer design of these protocols is imperative to meet emerging application requirements, particularly when energy is a limited resource.
Article
Most ad hoc mobile devices today operate on batteries. Hence, power consumption becomes an important issue. To maximize the lifetime of ad hoc mobile networks, the power consumption rate of each node must be evenly distributed, and the overall transmission power for each connection request must be minimized. These two objectives cannot be satisfied simultaneously by employing routing algorithms proposed in previous work. We present a new power-aware routing protocol to satisfy these two constraints simultaneously; we also compare the performance of different types of power-related routing algorithms via simulation. Simulation results confirm the need to strike a balance in attaining service availability performance of the whole network vs. the lifetime of ad hoc mobile devices
Article
When n identical randomly located nodes, each capable of transmitting at W bits per second and using a fixed range, form a wireless network, the throughput λ(n) obtainable by each node for a randomly chosen destination is Θ(W/√(nlogn)) bits per second under a noninterference protocol. If the nodes are optimally placed in a disk of unit area, traffic patterns are optimally assigned, and each transmission's range is optimally chosen, the bit-distance product that can be transported by the network per second is Θ(W√An) bit-meters per second. Thus even under optimal circumstances, the throughput is only Θ(W/√n) bits per second for each node for a destination nonvanishingly far away. Similar results also hold under an alternate physical model where a required signal-to-interference ratio is specified for successful receptions. Fundamentally, it is the need for every node all over the domain to share whatever portion of the channel it is utilizing with nodes in its local neighborhood that is the reason for the constriction in capacity. Splitting the channel into several subchannels does not change any of the results. Some implications may be worth considering by designers. Since the throughput furnished to each user diminishes to zero as the number of users is increased, perhaps networks connecting smaller numbers of users, or featuring connections mostly with nearby neighbors, may be more likely to be find acceptance
Article
Early simulation experience with wireless ad hoc networks suggests that their capacity can be surprisingly low, due to the requirement that nodes forward each others' packets. The achievable capacity depends on network size, traffic patterns, and detailed local radio interactions. This paper examines these factors alone and in combination, using simulation and analysis from first principles. Our results include both specific constants and general scaling relationships helpful in understanding the limitations of wireless ad hoc networks.
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.