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Abstract- This paper provides a critical analysis of the recent

research wok and its impact on the overall performance of a

mobile Ad hoc network. In this paper, we clarify some of the

misconceptions in the understating of selfishness and miss-

behavior of nodes. Moreover, we propose a mathematical model

that based on the time division technique to minimize the node

misbehavior by avoiding unnecessary elimination of bad nodes.

Our proposed approach not only improves the resource sharing

but also creates a consistent trust and cooperation (CTC)

environment among the mobile nodes. We believe, that the

proposed mathematical model not only points out the weaknesses

of the recent research work but also approximates the optimal

values of the critical parameters such as throughput, transmission

over head, channel capacity etc. The simulation results

demonstrate the success of the proposed approach that

significantly minimizes the malicious nodes and consequently

maximizes the overall throughput of the Ad Hoc network than the

other well known schemes.

I. INTRODUCTION

Misbehavior in mobile ad-hoc networks occurs for several

reasons. Selfish nodes misbehave to save power or to improve

their access to service relative to others [1]. Malicious

intentions result in misbehavior as exemplified by denial of

service attacks. Faulty nodes simply misbehave accidentally.

Regardless of the motivation for misbehavior its impact on the

mobile ad-hoc network proves to be detrimental, decreasing

the performance and the fairness of the network, and in the

extreme case, resulting in a non-functional network [2]. This

paper addresses the question of how to make network

functional for normal nodes when other nodes do not route and

forward packets correctly. Specifically, in mobile ad-hoc

networks, nodes do not rely on any routing infrastructure but

relay on packets for each other. Thus communication in

mobile ad-hoc networks functions properly only if the

participating nodes cooperate in routing and forwarding.

However, it may be advantageous for in nodes not to

cooperate, such as a selfish node wants to preserve own

resource to save power, memory, network-bandwidth, and

local CPU time. Therefore nodes assume themselves that other

nodes would forward the packet. This selfish or malicious

intention of nodes can significantly degrade the performance

of mobile ad-hoc-networks by denial of service.

In this paper, we focus on the design of a new time division

based scheme that can avoid unnecessary elimination of

malicious nodes while at the same time maximize the

throughput of the system by increasing the recourse sharing

among the mobile nodes. The existing methods/algorithms not

only creating a performance bottleneck (i.e., by increasing the

network congestion, transmission overhead etc.) but also

diminishing the self-growing characteristic of a peer to peer

network. These methods such as CONFIDANT [3] and CORE

[4] force the participating nodes to adopt the same behavior as

the other selfish nodes that have already been removed from

the network due to the lack of resources. We believe that we

should not propose any algorithm/method that becomes the

reason for reducing the network resources and consequently

force the existing participating nodes to behave exactly in the

same way as other removed nodes. Instead, we strongly

believe that we should come up with something that not only

improves the resources and resource sharing but also creates a

consistent trust and cooperation (CTC) environment among

the mobile nodes.

The rest of this paper is organized as follows: Section II

describes the research that has already been done in this area.

The proposed analytical and mathematical models for CTC are

presented in Section III. The simulation results are provided in

section IV. Finally, section V concludes the paper.

II. RELATED WORK

The terms reputation and trust are being used for various

concepts in the literature, also synonymously [5, 6]. We define

the term reputation here to mean the performance of a

principal in participating in the base protocol as seen by

others. The key thing in reputation system is watchdog and

pathrater which have been proposed by Marti, Giuli, Lai and

Baker [7]. They observed increased throughput in mobile ad-

hoc networks by complementing DSR with a watchdog for

detection of denied packet forwarding and a path rater for

A Novel Approach for Creating Consistent

Trust and Cooperation (CTC) among Mobile

Nodes of Ad Hoc Network

Khurram S.Rajput, Khaled M. Elleithy, Syed S. Rizvi

Computer Science and Engineering Department

University of Bridgeport

Bridgeport, CT 06605

{krajput, srizvi, elleithy}@bridgeport.edu

trust management and routing policy rating every path used,

which enable nodes to avoid malicious nodes in their routes as

a reaction. Their approach does not punish malicious nodes

that do not cooperate, but rather relieves them of the burden of

forwarding for others, whereas their messages are forwarded

without complaint. This way, the malicious nodes are

rewarded and reinforced in their behavior. They used a

watchdog that identifies misbehaving nodes and a pathrater

that helps routing protocols avoid these nodes. When used

together in a network with moderate mobility, the two

techniques increase throughput by 17% in the presence of 40%

misbehaving nodes, while increasing the percentage of

overhead transmissions from the standard routing protocol's

9% to 17%. During extreme mobility, watchdog and pathrater

can increase network throughput by 27%, while increasing the

overhead transmissions from the standard routing protocol's

12% to 24%.

CORE, a collaborative reputation mechanism proposed by

Michiardi and Molva [4], also has a watchdog component;

however it is complemented by a reputation mechanism that

differentiates between subjective reputation (observations),

indirect reputation (positive reports by others), and functional

reputation (task-specific behavior), which are weighted for a

combined reputation value that is used to make decisions

about cooperation or gradual isolation of a node.

III. THE PROPOSED ANALYTICAL AND MATHEMATICAL MODEL FOR

CREATING CONSISTENT TRUST AND COOPERATION (CTC)

The creation of mathematical model can be viewed as a

formalization of the proposed hypothesis. Based on the

proposed mathematical model, we perform the numerical and

simulation analysis for variety of scenarios in two parts. First,

we use the mathematical model to run different scenarios in

order to determine the performance of Ad-hoc networks by

analyzing different critical network parameters such as

throughput, transmission overhead and the utilization.

Secondly, we use the same set of parameters as a performance

measure.

A. The Proposed Analytical Model

We model the Ad-hoc network in much the same way as

other researcher does except this paper introduces the new

concept of time division. The idea of time division can simply

be envisioned by considering a particular node of a network

that has a potential to misbehave in the absence of the

sufficient resources require to forward the packets of the

neighboring nodes. This implies that if one can ensure that the

network has enough resources that can be shared equally

among the network nodes, then it can be assumed that the

possibility of node misbehavior degrades significantly. Thus

this reduction in the node misbehavior can be achieved

through the time division technique that divides the time

asymmetrically into the following two times: transmission-time

required for node-packets and transmission-time required for

neighbor-packets. The asymmetric division enables a node to

effectively adjust the time required to transmit its own packets

and/or the neighbor’s packets. The reason for using the

asymmetric division of the available time is to allow a node to

effectively utilize the time by dividing it with respect to its

current status (i.e., the available recourses) and consequently

utilizing the bandwidth in an efficient manner. The efficient

utilization of the bandwidth satisfies the requirement of the

fairness which is one of the key factors that forces a node to

unfair with its neighbor. This indirectly points that we reduce

the chances of misbehave since the node now has a total

authority on the available resources. It should also be noted

that we adopt an asymmetric approach to work with the time

division method for this research which opposed to the

conventional division of time (i.e., the symmetric or equal

division employed by many different techniques). In other

words, the proposed method optimizes the performance by

effectively reducing the chances of node misbehave at the

expense of comparatively complex logic.

B. The Proposed Mathematical Model

Before going to develop the actual mathematical model

based on the above analytical model, it is worth mentioning

some of our key assumptions. These assumptions help

understanding the complex relationship between a large

numbers of parameters. For the proposed mathematical model,

we assume that a system has Knodes where each individual

node knot only works as a normal mobile station but also

works as a packet forwarding device for the other nodes. In

addition, we assume that any kind of topology can be

implemented among the mobile nodes to construct the Ad-hoc

network. For the ease of simplicity, we perform the numerical

analysis for a single node k. This can be further extended for

the whole network by computing the collective behavior of the

Ad-hoc network.

The primary principal of Ad-hoc network is that it allows

each node of the network to fully participate in the

construction of the network. The word fully participation leads

us to the fact that a node not only transmits its own packets to

the other neighboring nodes but also provides its services to

other nodes as a forwarding device. For the proposed method,

we assume that a node can decide to transmit its own packets

with a certain probability while at the same time it can also

deny the transmission of the other neighboring packets with a

difference of a certain probabilities. In simple words, we can

develop a relationship between these two probabilities as

follows: a node can transmit the self generated packet(s) with

a probability of p where as it can transmit its neighbor

packet(s) with the probability of q.

Suppose, pis the probability for which a node forwards

personal packets where as p (I – p) is the probability for which

a node transmit packets received from one ore more neighbors.

In addition, we assume that

k

is total number of packets that

can be transmitted by a certain node of the Ad-hoc network.

The total numbers of packets include both the self generated

packets and the packets receive from one or more nodes.

Taking this into account, we can say that if the probability of

transmission of a single packet is (1-p)xwhere xrepresents a

single packet, then the probability to transmission kpackets

would be (1-p)kwhere k represents the total number of packets

that a node can transmit. This leads us to the following

mathematical fact:

1

k

p

(1)

Equation (1) can simply be formalized for knumber of

packets as follows:

1

k

p p

(2)

As mentioned earlier, the proposed method is exclusively

dependent on the time division methodology where a node can

divide the time asymmetrically to represent the time it needs to

transmit self generated packets as well as the time it takes to

transit the packets arriving from one or more nodes. To make

our proposed approach more realistic, we assume that if the

packet that resides in a certain node is not delivered to its

intended destination within the specified time, then that packet

must be discarded by the node. The lost of the packet at the

node level forces us to retransmit the packet. For the ease of

understating, we assume that the time a node takes to transmit

self generated packet can be represented as

t

pp

where as the

time it takes to forward the packets received from one or more

neighbors is represented as

t

np

. It should be noted that the

total available time per node is just the sum of the time a node

takes to transmit self generated packet and time it takes to

forward the packets received from one or more neighbors.

This relationship can be mathematically expressed in the

following equation:

i pp np

t t t

(3)

where irepresents the index of node that can be expended

from 1 to K(i.e., Krepresents the total nodes present in a Ad-

hoc network)

The maximum throughput is defined as the asymptotic

throughput when the load is very large. In packet switched

network where the load and the throughput are equal, the

maximum throughput may be defined as the load in bits per

seconds. Thus this in turns lead us to a fact that the maximum

throughput can not be defined in the presence of packet drops

at the node level. As mentioned earlier, to make our model

more realistic we consider the possibility of packet drops and

consequently the packet retransmission at the node level. The

throughput from the proposed algorithm for a certain node of

the Ad hoc network can be computed as follows:

put

T Total Packets Forwarded Total Time

(4)

The denominator of (4) is derived from (3) where as the

numerator of equation is determined by using (1) and (2). One

can see that as we increase the left hand side of (2), it causes a

decrease in the left hand side of (4). It should also be noted

that as we increase the sum of (1) and (2), it significantly

increases the left hand side of (4). To make these relationships

simple, we can say that the increase in the sum of (1) and (2)

causes an increase in the throughput where as an increase in

the total time that is determined by (3) causes a decrease in the

throughput per node. This is because the more we increase the

time, the more bandwidth we need to reserve to satisfy the

transmission requirements.

A significant increase in the bandwidth utilization (which is

beyond the scope of the available bandwidth per node)

represents degradation in the throughput that indicates an

increase in the possibility of node misbehavior. Thus, this

implies that the proposed algorithm is not only improving the

performance but also providing a chance to choose the optimal

values of critical parameters. Equation (4) can be further

simplified in the following form:

' '

Node s Packets Neighbour s Packets

Tput Total Time

(5)

To formalize the above discussion, we can combine

probabilities of transmission from (1) and (2) with the total

available time per node from (3) in (5). Thus this expresses the

node throughput not only by means of total available time but

also by means of the total number of packets a node can

transmit. The final result can be expressed in the following

equation:

1 1

k k

i

put

T p p t

(6)

It should be noted that (6) gives node throughput by

considering the time

t

i

spends on a single packet (that is the

time spend on one packet is the sum of the time spend on self

generated packets and the neighbor packets). Solving (5) for

k

number of packets in terms of the total time required by a

node can be expressed in the following equation:

1 1

k k

pp k np k

i

t t t

1k

(7)

where kin (7) represents the number of packets that are

bounded between 1 and the infinity. The first and the second

quantity of the right hand side of (7) are indicating the time

required transmitting the self generated packets and the time

required to transmit the neighbor packets. The generic time

equation can simply be stated as:

t no of packet data rate

(8)

Using (8), one can now compute the two major components

of the proposed time division algorithm. It is essential in order

to understand the concept of asymmetric division. One of the

two asymmetric time division quantities can be quantified as

follows:

(1 )k

tP P

np

D

R

(9)

where

D

R

in (9) represents the data rate.

Recall one of our fundamental assumptions that a node

transmits

k

number of packets in total time

t

i

. This

assumption allows us to set up a lower and upper bound on the

number of packets that a node can transmit. Therefore, the

limit for

k

should exist somewhere zero to infinity. One of the

main reasons for recalling this assumption is make a more

generalized form of (9). Taking these two factors into account,

one can generalize (9) as follows:

1

1

k

k

np kR

P P

tD

where 1K

(10)

The numerator of (10) is just a summation of total packets

forwarded by a node with respect to the probabilities set up at

static time. If

t

pp

is the total time taken by a node to forward

its own

k

number ofpackets, then equation for

t

pp

can be

rewritten as.

1

(1 )

R

k

kP

tpp D

where 1K

(11)

Equation (11) is the summation of probabilities of one

packet to k number of packets per node in the presence of a

certain data rate. By substituting the value of total time

t

i

from (3) into (6), we get

(1 ) (1 )

k k

put

pp np

Tp p p

t t

(12)

In order to generalize (12), we need to substitute the values

of

t

pp

and

t

np

from (10) and (11), respectively, into (12), we

get:

1

(1 ) (1 )

(1 ) (1 )

k k

kR

put k k

p p p

D

Tp p p

(13)

The first two quantities in denominator of (13) represent the

summation of the time a node takes to transmit the personal

packet and the neighbor’s packets. It should be noted that (13)

is generalized in a sense that it accommodates k number of

packets that a node can deal at a certain point of time. To

make it simple, we can rewrite equation as follows:

1

(1 ) (1 )

(1 ) (1 )

k k

k

R R

k k

p p p

D D

Tput of node p p p

(14)

Equation (14) is the total throughput of a node for

k

number

of packets that a node can transmit. Let us assume that

Np

is

the power of node and Kis the number of packet that a node

can transmit. Taking these assumptions into account, one can

derive a generic expression for utilization as follows:

pout pin

U N N

(15)

We call (15) as a generic mathematical expression of

utilization, since both the numerator and the denominator are

unknown and need to be determined to find out a more

specific expression. Therefore, this new concept of power

division leads us to the following mathematical expression for

node-utilization with respect to the node’s personal packets.

1

K

Pout pp

ppout

N K t

(16)

It should be noted that (16) is a more specific form of (15)

since it only account for the personal packets. Thus the

opposite hypothesis leads us to the following mathematical

expression for the node utilization with respect to the personal

packets:

1

nout np

K

pnout

K

N K t

(17)

Contrary to (17), there should be an equivalent possibility of

node inputs that can easily be computed as follows:

1

K

nin np

pnin

N K t

(18)

It should be noted that (18) can be useful to compute the

output of the nodes in terms of the inputs of the node. In other

words p

out

Nis the sum of work on outgoing personal and

neighbor packets that lead us to derive the simple

mathematical relationship:

( )

N N N

pout pp out pnout

(19)

In order to show that (19) is a valid true mathematical

relationship between the input and output lines of a node, one

needs to give another relationship as follows:

N N

pin pnin

(20)

This should now be clear that one of the reasons for

deriving the above two relationship is to derive a more general

expression from (16) and (17). Therefore, by substituting (16)

and (17) into (19), we get the following equation:

1

kppout nout

ppout kpp np

KK

Nt t

(21)

Similarly, we can derive another expression using (20) which

opposed to (21) as follows:

1

K

nin

Pin np

K

Nt

(22)

The last two equations (i.e., (21) and (22)) can now be used

to derive the final expression for utilization as follows:

1

KK

pout nout

t t

kpp np

UK

nin

tnp

(23)

All lines that are used for transferring the data or packets

are also used for receiving the data or packets from neighbor

nodes. This implies that the utilization per channel or line can

be computed using (23). If we denote this line-utilization as

(24), we can extend it to generalized (23).

1

k

pout nout np

Rknin

K K t

UK

(24)

If we assume that nnumbers of routes are attached through

the targeted node, then the utilization of the targeted node on

all routes can simply be computed by summing the utilization

of each node per channel. This can lead us to the following

equation:

1

n

n

t R

n

U U

1where n

(25)

This can also be interpreted as follows:

1 2 3 ........

t R R R Rn

U U U U U

(26)

Therefore, the total utilization of system can be derived

from (23) and (25) as follows:

1 1

n k

pout pp nout np

tn k nin np

K t K t

UK t

(27)

We perform some simplification in (27) that results the

following equation:

1 1

1

n k

t pout np pp nout

n k nin

U K t t K

K

(28)

The above equation can be used to compute the total

utilization of a certain node for all packets that it can forward

and/or receive from one of its neighbor though all possible

channels.

IV. THE EXPERIMENTAL VERIFICATION AND THE

PERFORMANCE ANALYSIS OFTHE CTC

We have shown that the system throughput can be measured

in term of packets that neighboring node is generated as well

as the self generated packets. To make the proposed

methodology up to the standard, we derive the formula for

computing the packet drop per node using (5). As mentioned

earlier, we determine the behavior of the malicious node in

terms of the number of packets that should have transmitted to

the intended destination. For taking this into account, one can

say that the effective throughput of a node is entirely

dependence on how efficiently the node is forwarding the

neighbor packets and thus creating a consistent trust

environment among the nodes.

A. Case I

For case-1, we assume that the self generated packets per

node are constant. We assume that one of the neighboring

nodes of the target node sends packets at a certain rate that

will increase linearly over the total simulation time. This

assumption helps understanding the true performance of the

proposed CTC algorithm. Fig. 1 shows the simulation results

of packet-drops per node with respect to the number of packets

generated by one of the neighboring nodes. It should be noted

that as we increase the self generated packets, the number of

packet-drops per node is increased. In addition, it can be seen

in Fig. 1 that for a small value of neighbor packet generation

(typically 500), both CTC and DSR are overlapping each

other. However a slight increase in the neighbor packet

generation causes a performance difference between these two

approaches.

B. Case II

CASE-II is different from CASE-I in such a way that both

inputs of a node-forwarding system become a linear function

of the node-time. The simulation result of this case satisfies the

proposed mathematical model discussed in Section III in a

way that the overall packet drop performance of both

Figure 2: Neighbor packet generation vs. packet drop

Figure 1: Neighbor packet generation vs. packet drop

investigated algorithms decreases. It can be seen that the

packet drop is more rapid in Fig. 2 with respect to the

neighbor-generated packets. In harmony with our expectations,

as the number of neighbor-generated packets increased, the

packet-drop performance of the proposed algorithm degraded.

However, the performance degradation of the proposed

algorithm was small compared to the performance degradation

of the DSR algorithms.

C. Case III

The parameters-assumption for CASE-III is different from

the previous cases in such a way that now one input (that is the

neighbor-generated packets) of a node-forwarding system

becomes a linear increasing function of the node total time

where as the input (that is the neighbor-generated packets)

becomes a linear decreasing function of the node total time.

The expected output of this simulation was exactly the same as

we were expecting based on our proposed mathematical

model. That is the values of packet-drop for both CTC and

DSR decreases as compared to the other two cases we

discussed above.

D. Case IV

For this case, we assume that the neighbor-generated packet

is a constant function of time. On the other hand, we consider

self-generated packets as a linear increasing function of the

total node time. It should be noted that the term linear increase

or decrease implies a constant uniform change in the system

parameter with respect to time. This case can also be

considered as a reciprocal of CASE-I from its fundamental

assumptions point of view. Thus we should also expect a

reciprocal output for this simulation.

V. CONCLUSION

This paper proposed both analytical and mathematical

model that can be used to effectively reduce the number of

malicious nodes and packet drops. Our simulation results

demonstrated that the proposed mathematical model not only

points out the weaknesses of the recent research work but also

approximates the optimal values of the critical parameters.

Simulation results presented in this paper show that how the

performance of mobile Ad hoc networks degrades significantly

when the nodes eliminations are frequent. The simulation

results of this paper are completely based on the proposed

mathematical model for both lightly and heavily loaded

networks. These results addressed many critical system

parameters such as packet drop and packet loss versus

malicious nodes, neighbor packet generation and drop ratio,

and throughput per node per system.

REFERENCES

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detecting Ad-hoc routing Anomalies,” in Proceedings of the 23rd

International Conference on Distributed Computing Systems (ICDCS

2003), Providence, RI, pp. 478–487, May 2003.

[3] S. Marti, T. Giuli, K. Lai, and M. Baker, “Mitigating routing

Misbehavior in mobile Ad hoc networks,” in Proceedings of

MOBICOM 2000, pp. 255–265, 2000.

[4] P. Michiardi and R. Molva, “CORE: A Collaborative Reputation

Mechanism to enforce node Cooperation in mobile Ad hoc networks,”

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(CMS 2002), Portoroz, Slovenia, 2002.

[5] T. Moreton and A. Twigg, “Enforcing collaboration in P2P routing

services,” 2003.

[6] S. Bansal and M. Baker, “Observation-based Cooperation Enforcement

in Ad hoc networks,” Technical Report, 2003.

[7] S. Marti, T. Giuli, K. Lai, and M. Baker, “Mitigating routing

Misbehavior in mobile Ad hoc networks,” in Proceedings of

MOBICOM 2000, pp. 255–265, 2000.

Figure 4: Neighbor packet generation vs. packet drop

Figure 3: Neighbor packet generation vs. packet drop