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How the density of nodes in ad hoc networks
affects the overall network performance.
Student Name: Daniel Harvey
Supervisor Name: Matthew Johnson
Submitted as part of the degree of Daniel Harvey to the
Board of Examiners in the Department of Computer Science, Durham University.

Abstract
Background
An ad hoc network is a collection of wireless nodes with a dynamically changing topology. Data is
sent through the network in packets which are routed by algorithms in the routing layer and are
transmitted between nodes through broadcast channels in the physical layer. Broadcasts at high
densities interfere by causing deterioration in network performance. At low densities, a failure of
transmissions increases with range and there are fewer neighbours, both decreasing performance.
Aims
This paper will investigate how the density of nodes in an ad hoc network affects the overall
performance by focusing on problems in the physical and network layers. The results will be used to
predict network performance trends with respect to the density of nodes.
Method
A simulation framework was built around ns-2 to test ad hoc networks in topologies of varying
density using different routing algorithms. Measurable properties from simulations were analysed to
find relations to performance related properties. Trends in these properties were then used with further
analysis to explain the effects of density of nodes on the network performance.
Results
Peak performance for static nodes at lower densities occurred at the equilibrium point of two physical
layer properties, and for higher densities the throughput was inversely proportional to the density at
the expense of increased delay. Mobile nodes had no common trend between the routing protocols.
AODV had the same trend as static nodes but DSR and DSDV were found to differ, due to being less
effective at highly dynamic routing.
Conclusions
The density of both static and mobile nodes was found to be related to the network performance.
Due to disconnected networks at low densities, the peak performance found had no direct application.
Further research would be needed to find common trends for mobile nodes and quantify the
relationships found.

Keywords – Density of nodes, ad hoc network, wireless network, physical layer, routing layer, routing
algorithms.
I.INTRODUCTION
A. Background
The problem of optimally configuring the topology of data networks has existed ever since
their introduction. These networks typically consist of several layers, each focusing on one
objective, which are all affected by the topology in different ways depending on the
application. An ad hoc network is a collection of mobile nodes with a dynamic topology that
form a network based upon the interconnections between nodes [1]; this is shown in Figure 1.

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Each node can transmit packets to those within range, which are its neighbours, and route
packets to them for other nodes out of range. With a completely mobile infrastructure, the
extra degrees of freedom for each node make many more permutations of the topology as it
evolves through time. This makes optimisation of the topology from the perspective of the
physical and routing layers a hard problem.

Research in ad hoc networks started in the 1970s with the DARPA packet radio network
projects [2], and in the last 30 years has rapidly grown to cover many diverse academic areas
and applications. The core properties of ad hoc networks are that there is no fixed central
infrastructure and the configuration and repair is completely autonomous, making the
network as a whole very reliable.
The properties of ad hoc networks make using a data network viable in many cases where
it had not been possible before, and this has lead to a wide range of innovative uses and
solutions to problems. One of the most well-know are mesh networks that use static ad hoc
networks to provide internet access to remote and rural villages around the world. Others also
range from vehicular hazard warning and information networks [3] to reinventing education
with collaborative learning in rural and developing regions [4], and scientific sensor networks
in extreme environments [5]. All of these uses would benefit from an optimised topology to
allow for increased reliability and maximal performance.
The two main network layers that make an ad hoc network are the physical layer and the
routing layer. Depending on the networking layer specification used, these may have different
labels and meanings. For this paper, the physical layer is the communication between radio
hardware in nodes, and the routing layer is the computation of paths for packets to travel
between nodes in the physical layer.
B. Physical Layer
There are many different types of wireless physical layer protocols; some of these are
specifically designed for ad hoc networks such as ZigBee and 6lowpan while others are more
general but have an ad hoc functioning mode such as Bluetooth and 802.11.
Common to all wireless protocols is the use of a broadcast channel to transmit data
between nodes; as such the broadcasts can be received by any node in range. When multiple
nodes are in range they are susceptible to interference problems from using the same channel
at once due to simultaneous transmissions. The medium access control (MAC) layer is a sub
layer of the physical layer that tries to solve this problem with the use of algorithms to
allocate time to broadcast on the single channel, decreasing the chance of interference [6 p.
251]. A related issue is the hidden terminal problem where two nodes that are out of range of
each other try and communicate with a third of which they are both in range [6 p. 296]. These
problems both cause a reduction in the total capacity of the channel for each node [7].
Figure 1. Two visualisations of an ad hoc network at an instance in time. This
shows how ad hoc networks can be visualised as a graph, allowing them to be
described in a formal way and analysed mathemat ically through graph theory.

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Transmissions over a wireless medium also suffer from attenuation as they propagate
away from the source. This implies that the probability of a failed transmission is
proportional to the distance between the source and the destination, causing a larger
proportion to fail at greater distances. The total capacity of the broadcast channel between
two nodes also decreases as this is inversely proportional to the probability of a failed
transmission.
The dependence of the physical layer on the density is now obvious. At higher densities
there will be more nodes in range of the same broadcast channel causing interference with
each other. At lower densities, there will be a larger probability of a failed transmission as
nodes are further apart. Different densities and topologies of nodes will therefore all have
different trends and relationships with network and graph theory properties.
C. Routing Layer
To allow nodes in the ad hoc network to send packets to one another with no fixed central
infrastructure requires routing algorithms, or protocols, which can find and maintain routes
through the nodes. The primary goal of these algorithms is a correct and efficient route
establishment between a pair of nodes, so that packets can be delivered with minimal latency
[1]. Ad hoc routing protocols can be split into two groups depending on whether they use a
reactive or proactive algorithm. Reactive algorithms are those where routes to all the
destinations are determined when the network is created and are maintained by using a
periodic route update process, whereas in a proactive protocol, routes are determined when a
packet needs to be sent by the source using a route discovery process [8]. The ad hoc routing
algorithms used in this investigation are outlined below.
Destination Sequenced Distance Vector routing (DSDV) is a proactive routing algorithm
based upon the Bellman-Ford routing mechanism, with the main improvement being freedom
from loops in the routing table [9]. Each node stores a routing table with an entry for every
node in the network. To create and update this table, each node sends its routing table to other
nodes by broadcasting either a full dump, or an update of changes on a regular basis.
Dynamic Source Routing (DSR) is a reactive source routing based algorithm. Source
routing is a routing technique in which the sender of a packet determines the complete
sequence of nodes through which to forward the packet [10]. DSR extends this base
definition with route caching for individual nodes and maintenance procedures for finding
and repairing broken routes when the network changes.
Ad hoc On demand Distance Vector (AODV) routing is a reactive routing algorithm that
was designed as an improvement to the performance characteristics of DSDV [1]. The main
difference is that routes are only created when needed, as opposed to DSDV where routes are
created for every pair of nodes in the network as it changes all the time. There are additional
maintenance features that are able to detect when nodes are no longer available and notify all
dependent nodes.
D. Objectives
There are many different variables which define the topology that can be optimised to
improve the overall performance of ad hoc networks. The aim of this paper is to find out how
the density of nodes affects the overall performance. This would allow ad hoc networks to be
better designed for solving or limiting problems with more intelligent algorithms in the
physical and routing layers.
This required looking at simulations of various ad hoc networks over a variety of
densities to gather data from measurable network and graph theory properties. The measured

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data was analysed to find relationships to desired network and graph theory properties and
find their optimal values. Both, mobile and static, topologies along with different routing
algorithms were used to try and find any generalised results which can be applied to many
diverse applications.
II.RELATED WORK
Since the advent of ad hoc networks, researchers have been interested in finding an optimal
topology for maximum performance. In [11], Kleinrock and Silvester looked into the
optimum transmission radius for nodes in an ad hoc network. This was done from a
completely theoretical point of view and no simulations where carried out. The network that
was analysed used slotted ALOHA to share the broadcast channel between nodes and any
routing algorithm that had the affect of allowing packets to be sent from the source to the
destination. By taking into account the probability of obtaining a successful transmission for
one hop, and then expanding this for multi-hop paths in the network, equations relating to the
variables were found. The result was finding the optimum number of neighbours for a node to
obtain the maximum network throughput. It was found that the optimal number of neighbours
was approximately 6, which lead to the maximal theoretical throughput of n0.976 per node,
where n is the total number of nodes.
This was one of the first papers that looked into the topology of ad hoc networks, and at
the time, in 1978, the theoretical model was the only way of looking at it due to the expense
of hardware and computer resources required for simulations. The theoretical model uses
quite a few assumptions. To make sure that the network was connected, the transmission
radius was required to be sufficiently large so that the probability of not being connected was
low. This prevents an analysis of the optimum communication radius, as the title suggests,
and causes the number of neighbours for each node to be found instead. This is still a useful
analysis but does not directly implicate relations to physical density, as any given degree of
neighbours can be reached with a varying transmission radius. All the nodes are assumed to
be identical, having the same density, traffic flow and transmission probability. This is quite
unrealistic, as every node will be different throughout the network, but will allow an upper
bound to be found on the theoretical throughput, and a lower bound on the number of
neighbours.
Another theoretical analysis using graph theory was done more recently by Bettstetter
[12]. A simple model for the transmission of packets between nodes was used where the
received power decreased as a fraction 1/r of the transmitted power; any packets below the
threshold power level were dropped. This was then used to find the minimum topology
density or transmission radius for the entire graph to be k-connected for static nodes. The
implications of introducing a mobile model were also briefly discussed. The theoretical
findings were validated by running simulations of the same networks theorised to compare
with. They found that the theoretical model matches the simulation results qualitative ly but
were different quantitatively, due to the simulations having bounding on the topology size
and the theoretical models having infinite bounds.
The analysis by Bettstetter has also taken several assumptions. There was no MAC
protocol used as the physical layer was not taken into account. This means the results are not
the most accurate predictions but can be used to come up with a lower bound on values to be
considered for the transmission radius and node density. In validating the theoretical model,
the simulations are not detailed with what or how they were conducted, so the validation is
hard to discuss and compare to other papers.

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Related to this is the work done by Sánchez, Manzoni and Haas in [13]. Their paper
focused on the dependence of throughput on transmission range and the variation of this and
node connectivity in different mobility models. This was analysed by creating a mathemat ical
model from a graph of the network which was simulated in Java using the Simjava library.
The simulation was needed because there were randomised variables inside the model they
used. The model was constructed by taking the direct neighbours of nodes in the network as a
graph in which where the edges were weighted by the Euclidean distance between them.
Loops were then removed from the graph using the minimum spanning tree algorithm so that
only the shortest path between nodes remained; this was defined as the critical transmission
range. For the position of nodes in the simulations, two different mobility models where used
for comparison, namely random way point and random Gauss-Markov. The Dual Busy Tone
Multiple Access (DBTMA) scheme was modelled as the MAC for nodes; and a simple model
of fixed sized packets with a variable transmission rate was used to vary the throughput.
It was concluded that there was no strong dependence on the different mobility models
used on either the critical transmission range or node connectivity, but that the throughput
was dependent on the transmission range. This was a rather weak conclusion, as only the
dependences found were stated and no relations were given to describe them. This was
because the models were not quantised to give a magnitude to the results, but allowed the
dependences to be seen. The dependences from the conclusion do provide areas that can be
analysed and investigated further.
Royer, Melliar-Smith and Moser [14] analysed the optimum node density for ad hoc
mobile networks. The simulations were run using the GloMoSim network simulator, which is
based upon the parsec parallel discrete event simulator. The networks consisted of 802.11
hardware nodes and the AODV routing algorithm, which Royer developed along with Perkins
[15]. Both mobile and static nodes were investigated and run with varying topology density.
The performance of the network was measured by its average throughput which was
calculated by the number of successful transmissions divided by the average path length.
The aim of the paper was to find the optimum number of neighbours for static and mobile
topologies. It was found that there was no global optimum for the mobile topologies but that,
as the velocity increased, for a given density, the transmission range must increase to keep the
performance the same. At very low densities the network was also found to no longer be
connected. For static topologies, an optimum was found between 7 to 8 nodes, which is
higher than the 6 that Kleinrock and Silvester found in [11].
Even though the simulations in the paper where quite thorough, only one routing
algorithm was used and there was no evidence to the statement that the results could be
generalised for other routing algorithms. They also investigated the optimum number of
neighbours as opposed to the physical density of nodes; and although these are related by the
transmission radius, there is no proof of this relationship in the paper.
In [16], Nilsson also investigated how ad hoc networks reacted to different network loads
and node densities. Simulations were run on the GloMoSim network simulator with nodes
using an 802.11 MAC and both the AODV and OSLR routing algorithms. The modified
random direction mobility model was used as in [14] on an area of 1000m2 for 300 seconds.
The delivery ratio was used to measure how reliably packets were transmitted between the
source and destination to compare AODV and OSLR. To find relationships for network
properties, the packet loads and node densities were varied alternately. The node densities
were varied by changing the transmission range that changed the average number of
neighbours. The packet loads were varied by using a constant sized packet and by varying the
rate at which they were sent.
It was found that for an increased node density and transmission range, the delivery rate
increased. Looking at the number of collisions in the MAC layer during the simulations, it

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was found that this also increases as the node density and transmission range increased. So
the delivery rate could be maximised at the expense of a higher number of collisions, which
is noted as a problem for nodes trying to minimise power usage. The paper concludes that in
order to predict the behaviour, capacity and performance in an ad hoc network, you need to
take both, the expected network load and node density, into account. The paper concludes
what it set out to find well; although it does not find a quantitative relationship, it highlights
the dependency between the network load and node density that needs to be taken into
account in further research. Both, proactive and reactive routing algorithms were used; thus,
the assumption by Royer, Melliar-Smith and Moser [14] has been partially validated but
needs more investigation for the validation to be complete.
III.SOLUTION
This section looks at the experimental setup used to gather data for analysis. A simulator was
controlled from within a framework that allowed the experiments to run over a wide range of
different variables in the ad hoc networks. The analytical methods used are then discussed,
followed by an outline of the experiments that were run.
A. Simulator
There are various network simulators that can simulate wireless ad hoc networks which have
the features needed for this investigation. An open source simulator was used so that, if
limiting problems were found, they could be fixed and also so that it would be possible to see
what was happening underneath the API. The network simulator 2 (ns-2) was chosen for
these experiments because of its mature code, extensive documentation and a large user base
in academia. ns-2 is a discrete event simulator which is written at the core in C++ for the
event scheduler and processor intensive code, and oTcl for the scripts that set up the
environment and define the simulation to be run. This separation means that it is easy to
create dynamic simulations in oTcl, yet have them run quickly with the C++ core.
Each node in the ns-2 wireless model has a MAC level protocol and a routing agent. The
routing agent has three inbuilt routing protocols, i.e. DSR, AODV and DSDV, which were all
used for comparison. The 802.11 MAC protocol was chosen as it is the most used and
abundant in networks today. This protocol has four main parameters that can be adjusted to
make the simulations more realistic: the data rate, request to send threshold, short preamble,
and packet size. The data rate and packet size are related, as for a given packet size the data
rate controls the number of packets of this size transmitted per second. The request to send
(RTS) threshold is the minimum size of a packet with which the MAC protocol will transmit
a request to other nodes before transmitting the packet; this increases latency due to waiting
before sending packets. The preamble is a known pattern of data the MAC protocol uses to
lock on to a signal; it is transmitted at the base rate of 1mpbs and can be either set to a short
or long size, with the shorter taking less time to transmit, thus decreasing latency. As the
ability of electronics has increased, most 802.11 hardware now has RTS turned off by default,
and the preamble is set to short. Simulations with two nodes were run to find the best value
for each of these parameters, giving the highest and most consistent value of the throughput
to make the final results more reliable. Table 1 lists the results that were found and would be
used in later simulations.
In order to control how transmissions between nodes are affected by their location, ns-2
uses a propagation model to simulate the transmission behaviour over distance. Three
different models are built into ns-2, which are the free space, two-ray ground reflection and
shadowing models. The free space model calculates the signal strength based upon the line of

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sight path between two points; if the signal strength is below a given threshold, then it is too
weak to be received and the packet is dropped. The two-ray ground reflection model adds to
the free space model with the superposition of the line of sight path and a ground reflection
path to calculate the signal strength between two points. The free space and two-ray
reflection are deterministic models and effectively create a circular perimeter around a node
in which other nodes can receive transmissions. The shadowing model adds a probability
based variance to the deterministic signal strength which is dependent on the path length; this
causes the model to be probabilistic and the transmission range to be no longer a fixed
circular perimeter. The two-ray ground reflection model was chosen as it gives a constant
transmission radius to simplify the analysis and took less simulation time compared with the
shadowing model, but was more realistic than the free space model.

The random waypoint model was used as the mobility model which randomly selects a
location inside a fixed size box and moves towards it with a fixed velocity. A new location
was selected after the time it took to travel the width of the box to make sure that on average
over the simulation the nodes were not stationary for long. This model was used to test the
network in an environment where the nodes were constantly moving with random velocities.
The density of nodes in this model was not consistent throughout the topology, but was
constant on average over the whole box. For static simulations, it was initially thought that
using a grid layout between nodes would work, but it was found that this gave flat areas of
equal performance in the network performance as quantised groups of nodes came in and out
of range together. A similar model to the mobility model was used in which the position of
each node was only randomly selected once and did not change; this gave a more even
distribution of neighbours.
Traffic flows were used to put a load onto the network in order to test its performance.
From preliminary simulations it was found that the maximum network throughput was
achieved when the links between nodes were saturated. This was done using the UDP
transport layer protocol, as it has a lower overhead and a constant bit rate source using fixed
sized packets, which is the upper limit of the physical layer in the simulation. The traffic
flows were added to the simulation by randomly picking a set number of pairs of nodes and
assigning one as the source and one as the sink for the UDP streams.
The parameters for hardware and the physical environment inbuilt into ns-2 are used to
initialise the simulation in the oTcl script; algorithms for the mobility model and traffic flows
were then implemented in oTcl as well to extend ns-2 as the experiment required. To record
data for analysis, ns-2 was configured to log every routed packet in the network which was
parsed after the simulation to find the average throughput, delay and drop ratio for the
network as a whole and between each pair of nodes.
TABLE 1. PARAMETERS FOR 802.11 HARDWARE SIMULATIONS IN NS-2.
Parameter Value
Data Rate 11 Mbps
RTS Threshold 3000 bytes (above the maximum packet size)
Short Preamble 75 bytes (short)
Packet size 2000 bytes

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B. Framework
The oTcl script for ns-2 defines a single simulation, but analysis required many different
simulations to be run over a range of parameters multiple times to gather the amount of data
needed, to create redundancy in the results, and to check for anomalous values. Each
simulation also produced around 500Mb of data that needed processing and archiving. To
automate these tasks, a framework to run the simulations and processes was created; this is
shown in Figure 2.
The framework requires a simulation script that can be varied by a single value; this was
given in the oTcl script which takes a variable to adjust parts of the simulation as the
experiment requires. Some parts of the simulation required random variables, so the oTcl
script was also given a seed which was used to set internal pseudo random number
generators; the seed was then recorded in the report so that the simulations could be recreated
if it was needed. The list of variables to run the simulation script over were included in the
XML file along with details of the experiment so that it could be referenced later, including a
reference to the oTcl script for the experiment.
A list of commands was created by the framework for each parameter and iteration of the
simulation to be run. It also created the list of random seeds to be used for each of the
iterations. ns-2 was then run for each command as a separate process and the output was
piped back to the framework to be processed. Each trace line output by ns-2 was first logged
to a gzip compressed archive and then parsed to gather the desired data. The parser creates
average statistics for the throughput, delay and drop ratio from each simulation, which the
framework stores in arrays to create the report. The locations of the nodes were also used to
create a graph of the network for each instance that was recorded. Each node was a vertex,
Figure 2. Architecture and workflow of the simulation framework. This shows the
different parts of the framework, their input and output, and how they interact. Each
instance is a single experiment which consists of multip le simulations varying by one
parameter.

Load parameters.
Generate random seed
for each iterat ion.
Create simulation
definit ion for each
parameter and iteration.
Gzip and arch ive
raw traces.
ns-2 Simulat ion.
Output raw traces.
oTcl Script
XML File
Create graphs and html reports.
Output files.
HTML Graphs
2. Control & Processing
1. Input
3. Simulator
4. Reports & Arch ive

Process traces to generate statistics.
Store statistics from each simulat ion.

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and edges were added when two nodes were in range of each other based upon the distance
between them. The average degree and number of components in each graph were stored so
that they could also be used in the report.
The output of the framework was an HTML document with graph plots. The values from
each simulation were used to create a mean value and standard deviation for each parameter.
These were plotted on three graphs against the parameter and value, and the standard
deviation was shown as the error bar for each point. The HTML document contained the
details of the experiment, a reference for each experiment, and the tables of statistics along
with the related graphs. A second document was also created with tables summarising the
values for each data flow in the simulation.
It was decided that the framework would be written in Python; this was due to it having a
large number of libraries and bindings which were needed. The ns-2 traces were parsed by
ns2stats; graphs were produced by Gnuplot with the Python bindings; Numpy was used to
process the numeric arrays and SimpleXMLParse was used to load the XML file. For further
analysis of the data, Gnumeric was used to create more detailed graphs and to find regression
equations for relations along with the Persons correlation coefficient to show their
significance. Maple was also used to analyse the relation equations found.
IV.RESULTS
A. Experimental Setup
The framework now allowed many different experiments to be run and summarised quickly.
Before the different routing protocols could be compared from simulations, the exact
configuration of the network that had to be tested needed to be determined to be able to
provide useful results. The configurations used must allow a large enough range of
throughput, delay and drop ratio to provide sufficient resolution for analysis and for finding
out how long the network would take to warm up. These were found by running initial
simulations using the framework. The AODV routing protocol was used for these
simulations, as the configuration of the network only needed to be known to an approximate
value so differences in network performance would be seen. The flows used a constant bit
rate source of 2 Mbps with 2000 byte packets. Table 2 below shows the initial parameters that
were picked by intuition, then varied one at a time over the range specified to find an
appropriate value to use in later simulations. The initial values for a parameter were used in
the simulations where it was not being varied.
To investigate the density of nodes, the width of the square topology for both static and
mobile scenarios was varied between 10m and 240m in units of 10m; this parameter is
inversely proportional to the density. The nodes were given a range of 40m, so this covered
the range outside of 5 nodes in a line communicating up to high densities. These
configurations will be run with the DSDV, DSR and AODV routing protocols.
TABLE 2. INITIAL, RANGE, AND FINAL PARAMETERS FOR SIMULATIONS.
Parameter Initial Range Final
Number of nodes 25 2 to 10 squared 25
Number of flows 15 10 to 30, units of 2 21
Duration (seconds) 80 20 to 120, units of 20 60

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B. Static Nodes
The average throughput for the static scenario for all three routing protocols had two seperate
regions which varied differently with the topology size; this is shown in Figure 3. In the
upper region, the average throuput increased to a peak, then dropped off to around the same
level again. The location of the peaks were found by calculating the second order polynomial
regression on the data range which produced a quadratic equation that was solved to find the
maximum value. For the lower region, the average throughput increased until it flattened off
at very high densities.
There are some anomalous values from all three routing protocols, which were mostly
due to the fact that the simulation contained random variables in the model; the anomalies
were therefore expected. The regression will take these into account as it smoothes out all the
values in the range, providing the correct type of regression is used. All three protocols have a
coefficient of determination above 0.68, which means that the regression used for each data
set explains a majority of the data in it. AODV parted from the lower range at very high
densities, as it dropped again as opposed to leveling off. Further experiments would be
needed to establish a reason for this, as there is not enough evidance to show that it is an
anomaolous value or not.
The drop ratio results have not been shown as they were found to be inversely
proportional to the average thoughput; thus they would not add information to the analysis of
the simulations.


Figure 3. The average throughput against the topology size for static nodes. The dotted
lines show the seperation of the lower and upper regions of the average throughput. The
dashed lines show the positions of the peaks in the upper region from regression.
The characteristic points and regions described for the relationship between the topology
size and throughput were all relative with respect to each of the three routing protocols. This
shows that they all had the same relationship, which was defined by physical layer properties.
Routing protocol properties modified the magnitude of the values measured, but did not
affect the relationship.
DSR peaked at the highest throughput and lowest density, with DSDV and AODV being
lower respectivly, as shown in Table 3. At these peaks the number of neighbours on average

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for each node was around 3. Since above 150m, the network in the simulation had more than
one component, the avaliable neighbours of each component will only be a subset of the total
nodes.
All the routing protocols again follow a very similar trend for the average delay,
remaining relatively flat as the density increases and then rapidly increasing to a high level
for very high densities that can be seen in Figure 4. The point at which the average delay
starts to rapidly increase was the same as the point at which the two regions were separated in
Figure 3. The trend and rapid increase was due to the number of neighbours, which was
proportional to the delay and can be clearly seen in Figure 4. The number of neighbours was
also proportional to the density of nodes, i.e. when the nodes were closer together, more were
in range. When there were more neighbours, the probability of simultaneous transmissions
increased, leading to more retransmissions and an increased delay. At very high densities
AODV levels out at a lower value, this could be due to it needing to send more packets for
the routing algorithm. AODV also has an anomalous value at the same point as the average
throughput.


Figure 4. The average delay against topology size fo r static nodes. The dotted lines show
the division of the lower and upper regions of the average throughput as in Figure 3.
The upper region was explained by the equlibrium of the two problems in the physica l
layer, as mentioned in the introduction. At the start of the region there was more interference,
due to a higher density of nodes, and at the end of the region each node had fewer neighbours
and thus less capacity in the overall network. As the topology size changes, these two
TABLE 3. ANALYSIS AT THE PEAK VALUES FOR DSR, DSDV AND AODV FOR STATIC NODES.
Routing Protocol Topology Size (m) Throughput (MBps) Neighbours Network Components
DSR 174 0.743 3 2.5
DSDV 162 0.730 3.2 2.3
AODV 150 0.715 3.8 1.4

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problems decrease and increase oppositely, the peak in the middle occurs when both are
balanced so that the maximum throughput was obtained.
The lower region does not follow the same trend. This was due to the fact that as the
density increases so does the proportion of nodes that are in range of each other. As they can
communicate directly, there was no need for multiple hops which use the capacity of other
nodes, so there would be more capacity available to each node. The routing protocols all give
the same results as they are not being used to calculate routes a t such high densities. When
this happens, there will be increased interference as only one of the nodes in the
neighbourhood can communicate at a time, causing retransmissions; this will also increase
the delay in sending packets. As the retransmission of packets is outweighed by the increased
capacity, the throughput of the network increases until all of the nodes are in a range where it
levels off. This increase in delay is shown in Figure 4, linking the trend of the throughput and
delay.
C. Mobile Nodes
When mobile nodes were used, there were large differences in the trends between the average
throughput and the topology size over the routing protocols, this can be seen in Figure 5.
AODV had the same trend as with static nodes but peaked at a lower average throughput.
DSR differed from this by not having a peak at lower densities but levelling out as it did for
higher densities; this showed that only the interference problem from the physical layer
appeared to affect the throughput, with the fewer neighbours at the lower densities not having
any effect. The average throughput with DSDV showed a trend that was proportional to the
density, which means that the physical layer problems did not appear to affect the network
properties as with static nodes. The differences in the trends for DSR and DSDV from the
static scenario could have been due to the routing protocol not being as effective at
calculating routes with a rapidly changing topology; as fewer routes were needed to be found
at higher densities, the network performance would increase until it was level with the static
nodes.


Figure 5. The average throughput against the topology size for mobile nodes. The dotted
lines show the troughs of the trends. The dashed lines show the peak of the trends.

13
The characteristics of the routing protocols are quite different from one another, so their peak
performance was difficult to quantify comparably. Only AODV and DSR had equilibrium
points at low densities, as DSDV only dropped as the density decreased; these points are
shown in Table 4. All routing protocols are on average lower than for static nodes. AODV
peaks at the highest throughput but with a larger number of neighbours than for static nodes,
it is also very likely to be connected at this density. DSR peaks at a lower throughput at a far
lower density where it is mostly likely split into three components.
The average delay from each routing protocol showed similar trends as with the static nodes,
which is shown in Figure 6. This was because the delay was found to depend only
proportionally on the number of neighbours and hence inversely on the density of nodes.
There was a change in the rate of increase, for all routing protocols, at the same point as
before; this was where the density increased more rapidly to where all nodes were in range.
DSR and DSDV both showed a flatter increase at the point of change from before, as
indicated on Figure 6. This could be due to the fact that fewer routes were successfully
calculated in a highly dynamic topology, as was found with the throughput. The rate of
change of AODV is still sharp as with static nodes, as this was the only routing protocol
found to still be effective at calculating routes with dynamic topologies.


Figure 6. A graph of the average delay against the topology size for mobile nodes. The
dotted lines show the position of the trough from trends in the average throughput as in
Figure 5.
TABLE 4. ANALYSIS OF THE PEAKS FOR AODV AND DSR WITH VARYING TOPOLOGY SIZE FOR
MOBILE NODES.
Routing Protocol Topology Size (m) Throughput (MBps) Average Neighbours Average Components
AODV 145 0.68 5.5 1.2
DSR 200 0.49 3.4 2.6

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D. Summary
Static nodes showed similar trends for all three routing protocols, and so the relationships
found were from properties in the common physical layer as opposed to the routing layer. At
lower densities, there was an optimal performance point where the affects of attenuation,
number of neighbours and interference, were minimised. At higher densities, the throughput
increased to another peak at the decline of the delay; this change was found to occur at the
same point with both properties and was due to all the nodes being in range of each other.
There was no common trend of throughput for mobile nodes between the three routing
protocols, so their characteristics rather affected the relationships, along with the physical
layer properties. The difference from trends with static nodes appeared to be from how
effectively the routing protocol could create routes in a highly dynamic topology. The delay
was found to be proportional to the number of neighbours for all three routing protocols.
V.EVALUATION
As the simulator and frameworks played a large role in the results of this investigation, these
are evaluated first, followed by the algorithms used in the simulation scripts. Finally, the
results presented in this paper will be evaluated in relation to both.
A. Simulator
The simulator was central for providing reliable results in this investigation. ns-2 was known
to be strongly valid with a large test suite and wide history of use in academia. The creation
of simulations and understanding of the architecture had a small learning curve due to the
thorough documentation and established user base; this allowed the basic capability of the
simulator to be found quickly. Further into developing the experiments, it was found that ns-2
did not a have a very reliable development cycle, due to parts of the simulator being broken
between releases as other parts were changed. Three of the ad hoc routing protocols built into
ns-2 did not work with the new wireless framework that was introduced in more recent
versions of ns-2; two of these had solutions from the community of users, but the last one did
not and thus could not be used. This was because even though ns-2 had a comprehensive test
suite for checking the validity of the simulator, it did not report errors if one of the tests failed
to run. It was also found that the internal documentation of the code and API was not well
maintained, so it was hard to extend and add new ad hoc routing protocols. These two facts
together limited the specific types of routing protocols in ns-2 that could be used in this
investigation - had more been available, a wider range of protocols could have been tested
and more of their aspects could have been compared.
A more suitable simulator would have been chosen if a simple experiment was
implemented for each in a short list of candidates. This would have allowed the issues found
along with other potential issues to have surfaced before work began on the experiments to
prevent future limitations. Candidates should have been chosen according to a better
internally documented API and higher code quality, along with the conditions for the
investigation as already mentioned.
Once the simulations were created, there was no inbuilt method to validate them with ns-2
to make sure they conformed to the experiments. Extra scripts had to be created with more
ways of measuring and analysing the simulation traces to validate that the simulation was as
intended for this experiment. Internal methods or a validation suite would have allowed them
to be tested in a more standard and efficient way whilst the simulations were developed and
extended.

15
B. Framework
The design of the framework allowed the simulations and traces to be run and processed far
more easily and reliably than if they were done manually. This meant that many more
simulations could be run once it was created to test the simulations themselves. As the
framework had no automated tests, it was only tested by investigating the output of simple
simulations. This made it hard to find and remove errors that came about in unforeseen
conditions. As the raw traces from the simulations were archived, they could be reparsed if
any errors were found in the framework; yet it would have been better to construct test cases
for the framework that would test all its functions before the simulations were run to prevent
the need for reparsing.
When the initial simulations were run within the framework, it was found that they took
up considerable processor time for the simulation and parsing code. This was due to running
more complex simulations multiple times, compared with the preliminary simulations and
was solved by having a dedicated computer for this task. It would have been desirable to
create a framework that is able to run and parse the simulations and traces asynchronously.
This would mean they could have been distributed across different computer systems
allowing more flexibility in the allocation of hardware resources.
Along with the raw traces, it would have been more efficient to archive the statistics
created during processing to save time when regenerating all of the reports and graphs if they
needed to be changed. This would have been simple to implement, but was only found to be
needed once many simulations had taken place.
Python was a good language to use, as it allowed quick prototyping and testing of the
design and rapid development to complete the needed features. The documentatio n for lesser-
used libraries was not as complete or maintained; but due to the nature of the language, these
did not slow it down as much as they could have. The already available libraries to parse the
ns-2 packet traces saved a lot of time of programming and testing, as they had already been
used by other research projects.
Overall, it would have been good to finish the framework earlier in the investigation so
that it could have been tested and redesigned based upon preliminary simulations before the
simulations in the experiment were run. After this point, it was very limiting to what extent
the framework could be changed.
C. Algorithms
The mobility model implemented was chosen as it appeared to be a sensible choice to use,
and there was not initially much of a believed affect from mobility models on the results. This
turned out to be incorrect as it was found with certain topologies that the results exhibited a
certain pattern, so the mobility model used did have an impact on the results in the mobile
simulations. The random waypoint model was found to have density waves where the nodes
tended to appear more likely at the centre of the topology [17].
The random direction model would have been a better choice, as it has a more even
distribution over the topology. This model picks a random angle and then finds a point on the
perimeter at this angle which it travels to at a random velocity. The mobility model used
should also be analysed before it is implemented in the simulation to make sure it has the
correct distribution to realistically represent the motion of the desired application.
Packet flows added to the network were allocated in a way that saturated the network as
was needed to find the maximum network performance. No analysis took place to see if the
distribution of the flows could have affected the simulations and results. The randomisation
of these could be one of the main factors in the random variations in the results. A

16
preliminary investigation into the distribution of network flows would make the results more
reliable and allow more thorough analysis of the data.
D. Results
The relationships described between the density of nodes and the network properties
measured were characterised by trends found in the data. Regression was used to describe the
trends between each variable and the density which had a statistical relevance given by the
coefficient of determination that defined how much of the data was explained; this was above
0.68 in all cases. This meant there was still 30% of the data which was unexplained by the
regression used, and therefore remained unexplained in the results. Deviations from the
regression used could have been due to either anomolous values in the results that came from
the random variables used in the simulations, or because the incorrect regression type was
used. To improve the strength and reliability of the results, this issue would have to be
improved to explain more of the data. The values measured from the simulations also had a
very large standard deviation compared to the average values used. There was no particular
trend or reason behind this other than, again, the large number of random variables used in
the simulations that would cause such a spread of the measured values.
These problems could be improved if a larger number of iterations were run for each
parameter value so that more values could be analysed to improve the accuracy of the
statistics over the random variables. Another way would be to reduce the number of random
variables in the simulations to limit the number of possible variables the measurements could
depend upon. The simulations could then be built up once relationships have been found with
simpler experiments, in order to gain more proper results for this paper.
The average number of neighbours for each node was between 3 to 4 for static nodes and
4 to 6 for mobile nodes which are both lower than was found by Royer, Melliar-Smith, and
Moser in [14] and Kleinrock and Silvester in [11]. This could be because, when the degree of
each node and the number of components were measured from a graph of the network in the
simulations, the position and range of each node was used to form the graph as opposed to the
data from the neighbours in the routing algorithms. This meant that the values obtained were
only an approximation and were not the representation of the view from the routing
algorithms. The resulting data was similar for each routing protocol and did not take the
differences between them into account. The limitation was due to the inability to access the
variables of the routing protocols inside ns-2. To improve the results of this, a simulator
should be used where data from all the components can be accessed in a way that can be
measured by the side of the traces.
The results and trends found were more reliable for simulations with static nodes than
with mobile nodes. This was partly due to the flaw in the mobility model, but also because
only three routing protocols were being used, so any comparison between them was rather
weak. Running simulations on a wider range of routing protocols of different types, along
with a fair mobility model, would give more reliable results for mobile nodes.
VI.CONCLUSION
This investigation set out to find out how the density of nodes affects the overall performance
of ad hoc networks. It was found that the relations were spread over many layers of the
networking stack, with many being dependent on each other. Some of these were discovered
in analysis but many relations requiring further research were found which are detailed
below.
For static nodes it was found that there was an optimum node density where the
performance was maximal; different routing protocols varied the magnitude of this point but

17
not the relative location. This also verifies the assumption by Royer, Melliar-Smith, and
Moser in [14] that a single routing protocol can be used to generalise the results for any
routing protocol, for static nodes. Two maxima were found for throughput: one relating to the
optimum point and the other to a phenomenon when all the nodes were in range at the
expense of increased latency. To find trends in the performance between the characteristics of
routing protocols, a wider range would have to be investigated.
The performance for mobile nodes was found to be dependent on the routing protoco l
used in the network. AODV showed the same trend as static nodes, DSR showed a similar
trend but with a lower maximum, and DSDV did not show a similar trend at all. This was
mainly due to the protocols efficiency at creating routes for dynamic topologies; if routes
could not be created quickly enough, the dependence on the density of nodes from some
properties of the physical layer were lost. This showed that the performance of the network
with mobile nodes does vary with density, but also that additional research focusing on a
wider range of mobility models and routing protocols would be needed to find more specific
trends.
It was found that networks in the simulations were not always connected at lower
densities due to the range of the radio, even though this was known to happen, since, as the
density was varied, it did affect the magnitude and application of the results. To be able to
analyse the relationships between routing protocols and the performance as the density varies
more thoroughly, the connectivity of the network at different densities with different mobility
models should be investigated. This would allow a more detailed understanding of the range
of topologies on which to base further investigations in this area.
In summary, this investigation concludes that the density of nodes does affect the
performance of an ad hoc network, but to quantify the findings in a way to be of use to
applications, further research in this field is required.
REFERENCES
[1]. A Review of Current Routing Protocols for Ad Hoc Mobile Wireless Networks. Royer, E M and Toh, C K.
1999, IEEE Personal Communications, Vol. 6, pp. 46-55.
[2]. The DARPA Packet Radio Network Protocols. Jubin, J and Torrnow, J D. 1987. Proceedings of the IEEE.
pp. 21-32.
[3]. Inter-vehicle communications and their applications to intelligent vehicles: an overview. Tsugawa, s. 2002,
Intelligent Vehicle Symposium, 2002. IEEE, Vol. 2, pp. 564-569.
[4]. Getty, J. One Laptop Per Child. [Online] http://www.laptop.org/en/laptop/hardware/.
[5]. Sensor networks: an overview. Tubaushat, M and Madria, S. 2003, Potentials, IEEE, Vol. 22, pp. 20-23.
[6]. Tanenbaum, A S. Computer Networks. s.l. : Pearson Education Inc., 2003. 0-13-038488-7.
[7]. The capacity of wireless networks. Gupta, P and Kumar, P R. 2000, Informat ion Theory, IEEE
Transactions on, Vol. 46, pp. 388-404.
[8]. A review of routing protocols for mobile ad hoc networks. Abolhasan, M, Wysocki, T A and Dutkiewicz,
E. 2004, Ad Hoc Networks 2, Vol. 2, pp. 1-22.
[9]. Highly Dynamic Destination Distance-Vector Routing (DSDV) for Mobile Computers. Perkins, C and
Bhagwat, P. 1994, ACM SIGCOMM Computer Communication Review, Vol. 24, pp. 234-244.
[10]. Dynamic Source Routing in Ad Hoc Wireless Networks. Johnson, D B and Maltz, D A. 1996, Mobile
Computing, Vol. 353, pp. 153-181.
[11]. Optimum transmission Radii for packet radio networks. Kleinrock, L and Silvester, J. 1978. National
Telecommunications Conference, Birmingham, Ala. Vol. 1, pp. 431-435.
[12]. On the Minimum Node Degree and Connectivity of a Wireless Multihop Network. Bettstetter, C. 2002,
International Symposium on Mobile Ad Hoc Networking & Computing, pp. 80 -91.
[13]. Determination Of Critical Transmission Range In Ad-Hoc Networks. Sanchez, M, Manzoni, P and Haas,
Z J. 1999, Mult iaccess, Mobility and Teletraffic for Wireless Comm. (MMT).
[14]. An Analysis of the Optimum Node Density for Ad hoc Mobile Networks. Royer, E M, Melliar-Smith, P M
and Moser, L E. 2001, Communicat ions, 2001. ICC 2001. IEEE International Conference on, Vol. 3, pp. 857-
861.
[15]. The Ad hoc On-Demand Distance Vector Protocol. Royer, E M and Perkins, C E. 2001, Ad Hoc
Networking, pp. 173-219.

18
[16]. Performance Analysis of Traffic Load and Node Density in Ad hoc Networks. Nilsson, A. 2005. Proc.
European Wireless (EW 2004). pp. 24-29.
[17]. A Survey of Mobility Models for Ad Hoc Network Research. Camp, T, Boleng, J and Davies, V. 2002,
Wireless Communication & Mobile Computing (W CMC): Special issue on Mobile Ad Hoc Networking:
Research, Trends and Applications, Vol. 2, pp. 483-502.