Selfish Conscious Mathematical Model based on Reliable

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1 Proc. of Int. Conf. on Advances in Information Technology and Mobile Communication Selfish Conscious Mathematical Model based on Reliable Conditional Survivability Co-efficient in MANET Routing J.Sengathir1 and R.Manoharan2 1 Research Scholar, Department of Computer Science and Engineering, 1 Pondicherry Engineering College, Pondicherry, India. 2 Associate Professor, Department of Computer Science and Engineering, 2 Pondicherry Engineering College, Pondicherry, India. 1 [email protected],2 [email protected] Abstract The reliable dissemination of data between the nodes in a Mobile Ad hoc Network (MANET) highly depends on the degree of collaboration established among them. Reputation of the nodes present in an ad hoc network is considered as a crucial aspect, expected for maintaining co-operation among mobile nodes. Moreover, determining the reputation level for each and every mobile node in MANETs is a challenging task due to the dynamic movement of nodes and computation overhead. Hence, a need arises for devising a new mathematical model that posses the capability of detecting the selfish nodes present in an ad hoc environment. The proposed mathematical model mainly depends on a factor called Reliable conditional Survivability Co-efficient (RCSC). The performance of the proposed model is analyzed through ns-2 simulations by varying threshold levels for selfish detection. The proposed Mathematical model detects and mitigates the existence of selfish nodes to a maximum extent. Index Terms Selfish Node, Threshold range, Exponential distribution, Conditional Survivability Co-efficient I. INTRODUCTION In mobile ad hoc network, establishing co-operation among the mobile nodes is a critical issue that has not been explored from the recent past [1].The mobile nodes in MANET are highly dynamic in nature and also due to the lack of centralized infrastructure, maintaining the co-operation between nodes is crucial [2].The selfish nodes are the nodes which deny to co-operate between other nodes by not forwarding other nodes packets [3] while relaying its own packet only. This kind of misbehavior in mobile ad hoc networks could occur for various reasons. The selfish nodes misbehave to save its resources or to enhance their access in service related to others [4]. Selfish intensions of nodes may result in denial of service attacks which could decrease the performance and the fairness of the networks [5]. In the extreme case of selfish behavior, the network may become non functional [6]. Many context aware probability based approaches were proposed in [7] [8] [9] that could detect and mitigate selfish behavior of nodes in MANET. Elsevier, 2013

2 In this paper, an effective conditional survivability coefficient based mathematical model which could identify and mitigate selfish nodes to a maximum extent has been proposed. This is achieved through the computation of RCSC for each and every node based on the second hand information obtained from neighbors. The protocol used for our study is a reactive and tree based protocol called AODV. The Organization of the paper is as follows, the paper commences with the brief discussion of existing mathematical models in the literature for detecting and mitigating selfish node along with their limitations in section 2. The Section 3 presents the proposed Mathematical model Known as Reliable Conditional Survivability based Mathematical Model (RCSBMM). The Simulation setup parameters and Evaluation metrics are discussed in Section 4. The Section 5 illustrates the exhaustive experimental analysis and results discussion. The summary of results and future enhancement is given in Section 6. II. LITERATURE SURVEY From the last decade, a number of probabilistic based mathematical models have been proposed for detecting the existence of selfish nodes in an ad hoc environment. Most of the approaches for detecting selfish nodes were mainly based on Bayes theorem, Dempster Shafer theory, Pathrater and Watchdogs. Some of them are discussed below: Thomas M.Chen and Varadharajan Venkataraman [10] proposed an optimal mechanism useful for selfish detection based on a posterior probability. The authors used two threshold limits called belief and plausibility for predicting the compromised nodes. The Dempster Shafer theory of evidence contributed by them is best suited for computing the value of nodes uncertainty towards co-operation. They also used a numerical procedure for combining multiple evidences obtained from the neighbor nodes. C.Zouridzki et al[11] proposed a framework based on trust for determining whether the packets forwarded by the mobile nodes are reliable in an ad hoc scenario. They considered that each node creates a reputation about the other node with the aid of both first and second hand data obtained for neighbors. This opinion metric was taken as a factor to detect malicious node. They also used trust and confidence limits for capturing the statistical decision about the reliable delivery of packets. Hernandez Orallo et al [12] proposed a mathematical model that computes the total time as well as total cost for identifying selfish nodes with the help of watchdogs. In this model, the communication established between any two mobile nodes follows Poisson distribution. They used two states for detecting selfish behavior of nodes. The two states are POSITIVE and NONINFO. The modeling of the network has been done with the help of continuous parameter Markov chain, represented with the aid of transition matrix in canonical form. Rizvi and Elleithy [13] proposed a mathematical model based on time division technique to diminish the malicious behavior of mobile nodes. This is achieved by evading the needless eradication of terrible nodes. The fallacy between the selfish and malicious nodes is well studied in this paper. This paper also contributes a reliable trust and collaboration environment for mobile nodes. Md.Amir Khusru Akthar and G.Sahoo [14] proposed a model for detection of selfish node in MANET based on the parameter called P(S|Pos) computed using Bayes Theorem. According to the author, for the node behaving selfish should have the parameter value less than 0.5. The proposed model of this paper also classifies the nodes of the network as normal node and selfish node. The authors also contributed a method based on prior probability and continuous Bayes theorem for examining the transmission of a normal node towards selfish node. This gives the affiliation between the number of nodes and their conditional probability towards selfishness. S.Buchegger and J.L.Boudec [15] proposed a approach for determining the reputation of each and every participating node of ad hoc network based on Bayesian theorem. The reputation rating is calculated using Beta distribution which is the conjugate of Bernoulli distributions. Initially the prior condition is taken as BETA (1, 1) and the uniform distribution on BETA (0, 1) is determined. The reputations are computed based on first hand observation and the reputation information published by neighboring nodes in the network. The classification of normal nodes and misbehaving nodes were done based on threshold value. They also addressed the various issues that could arise due to reputation fading. A. Extract of the Literature The probabilistic strategies for detecting and mitigating selfish nodes available in the literature lack in the following issues. They are: I. A conditional probability based detection mechanism for selfish nodes has not been explored. 263

3 II. A detection mechanism which has ability to identify selfish behavior of nodes based on conditional Laplace stleltjes transform has not been proposed. III. The conditional probability based approach which takes in to account of the various scenarios under which a node exhibits its selfish behavior has not been explored. III. RELIABLE CONDITIONAL SURVIVABILITY BASED MATHEMATICAL MODEL (RCSBMM) Let x be the overall lifetime of the network. Consider and as the constant rate of survival and constant rate of failure respectively, provided0 . Let us consider C 1 as the probability of a node to be normal node. Likewise C2 be the probability of a node to be in selfish node. We define y as the Random Variable such that, Y=0, if the nodes are normal Y=1, if the nodes behavior is selfish during Route discovery. Y=2, if the nodes behavior is selfish during Route Reply. Y=3, if the nodes behavior is selfish during data relay. Let w be the residual lifetime of a node existing in selfish node. Here x1 and x2 are the time to failure of normal and selfish nodes. We consider, ~ exp() , ~ () and because of memory less property of the exponential distribution, ~ (). First , We define the Probability mass function of the Random Variable y as follows ( )

4 (0) = , (1)

5 (1) = , (2) ( )

6 (2) = and (3)

7 (3) = (4) Here the life time of node is given by ( , ) + Since are exponentially distributed with parameter + The Conditional survivability rate of a node in normal mode is given by (5) (! = 0) = = (! = 3) (5) " This is obtained based on conditional Laplace stieltjes transform of X [16] [17] . Likewise in the case of conditional survival rate of a selfish node either in route discovery on route reply node is given by (6) (! = 1) = = (! = 3) (6) " " According to the theorem of the total transform, ( )( ) () = $ + % (7) " " The above eq. (7) gives the conditional survival rate of a network. Here, () = " () = " + (1 &) (8) Here the total probability at which the node could be either in normal node or selfish is given by & = when c' = c + c (9) Therefore, The conditional survivability of a node is given by eq. (10) () * (-) = (1 &)( + ) (). + / . (). 4 (10) Hence Reliable Conditional survivability of a node is given by eq. (11) 56 (-) = (1 &) (). + 7( + ) . (). 8 (11) Where - 0. The reliability of a node given by eq. (11) is considered as a parameter called RCSC. This formulated approach is distributed in each and every node of a network, which could aid in maintaining the performance of the network. 264

8 A. Algorithm for Reliable Conditional Survivability based Mathematical Model Algorithm: The Reliable conditional Survivability based mathematical model for detecting selfish nodes in an Ad hoc environments Notation: SRCN: Source Node DRTN: Destination Node RCSC: Reliable Conditional Survivability Co-efficient 1. SRCN broadcasts RREQs packets through all the feasible paths directed towards DRTN. 2. DRTN sends back RREPs to the SRCN with the help of reverse route established during Route discovery 3. SRCN relays the data packets to the DRTNs through established optimal transmission path 4. Each Node computes CRSC monitoring their neighbors. 5. If(0

9 V. EXPERIMENTAL ANALYSIS OF RELIABLE C ONDITIONAL SURVIVABILITY BASED MATHEMATICAL MODEL (RCSBMM) From the fig.1 it is obvious that when the maximum threshold of 0.10 is assigned, the Packet Delivery Ratio increases. This is due to the isolation and mitigation of large number of selfish nodes. But, when a minimum threshold of 0.30 is assigned, the Packet Delivery Ratio considerably decreases to the extent of 22%. Fig.1 Performance Analysis for RCSBMM based on number of selfish nodes and Packet delivery ratio From the fig.2 it is obvious that when the maximum threshold of 0.10 is assigned, the Control Overhead decreases. This is due to the isolation and mitigation of large number of selfish nodes. But, when a minimum threshold of 0.30 is assigned, the Control Overhead considerably increases to the extent of 42%. Fig.2 Performance Analysis for RCSBMM based on number of selfish nodes and Control Overhead From the fig.3 it is obvious that when the maximum threshold of 0.10 is assigned, the Total Overhead decreases. This is due to the isolation and mitigation of large number of selfish nodes. But, when a minimum threshold of 0.30 is assigned, the Total Overhead considerably increases to the extent of 32%. From the fig. 4 it is obvious that when the maximum threshold of 0.10 is assigned, the Throughput increases. This is due to the isolation and mitigation of large number of selfish nodes. But, when a minimum threshold of 0.30 is assigned, the Throughput considerably decreases to the extent of 26%. 266

10 Fig.3 Performance Analysis for RCSBMM based on number of selfish nodes and Total Overhead Fig.4 Performance Analysis for RCSBMM based on number of selfish nodes and Throughput Fig.5: The chart representing the range set for detecting selfish nodes From the fig.5, it is apparent that the maximum and minimum value for selfish node detection to a larger extent was found to lie between 0.10 and 0.30. It also illustrates that the value of 0.15 can be set as the saddle point for maximum detection of selfish nodes. 267

11 VI. CONCLUSION The detection of selfish nodes based on conditional probabilistic Mathematical model is well examined in this paper. An exhaustive analysis was performed to determine the impact of reliable conditional survivability, which aids in the detection and mitigation of selfish nodes. The results of simulation clearly prove that our proposed mathematical model, when implemented could perform better in terms of Packet Delivery Ratio, Control Overhead, Total Overhead and Throughput. This solution facilitates to standardize the minimum and maximum threshold value for detecting maximum number of selfish nodes. This approach also investigates the conditional reliability of both the nodes and the network as a whole. REFERENCE [1] Abusalah.L, Khokar.A, and Guizani.M. : A survey of secure mobile ad hoc routing protocols. IEEE Communications surveys tuts. Vol.10 no.4, pp.78-93, (2008). [2] Cho.J.H, Swami.A and Chen.I.R. A Survey of trust Management in mobile ad hoc networks. IEEE Communications surveys tuts.(2008). [3] Sarvanko.H, Hyhty.M, Katz.M and Fitzek.F.: Distributed resources in wireless networks. Discovery and cooperative uses. Forth ERCIM eMobility Workshop in conjunction with WWIC (2010) [4] Zhang and W.Lee, Intrusion Detection in wireless Ad-hoc networks, in Proceedings of MOBICOM, pp.275- 283,(2000). [5] Y. Huang, W. Fan, W.Lee and P.Yu, Cross-Feature analysis for detecting Ad-hoc routing anomalies, in proceedings of the 23rd Internation Conference on Distribution Computing System (ICDCS 2003), Providence , RI, pp .478-487. May (2003). [6] S.Marti, T.Gilui, K.Lai, and M.Baker , Mitigating routing Misbehavior in mobile Ad hoc networks, in proceeding of MOBICOM 2000. pp 255-265,( 2000). [7] P.Michiradi and R.Molva, CORE, A Collaborative Reputation Mechanism to enforce node cooperation in mobile Ad hoc networks, Sixth IFIP conference on security communications, and multimedia (CMS 2002), Portoroz Slovenia 2002. [8] T. Moreton and A.Twigg , Enforcing collobaration in [email protected] routing services,2003 [9] S.Bansal and M.Baker, Observation based Cooperation Enhancement in Ad hoc networks, Techinical Report, 2003. [10] Chen T.M, Varatharajan.V: Dempster-Shafer Theory for Intrusion Detection in Ad Hoc Networks. IEEE Internet Computing (2005) [11] Zouridaki.C, Mark.B.L, Hejmo.M and Thomas.R.K. A quantitative trust establishment framework for reliable data packet delivery in MANETs. Proceedings of the 3rd ACM Workshop on security of ad hoc and sensor networks, vol 1, pp.1-10, (2005). [12] Hernandez-Orallo, Manuel.D, Serraty, Juan-Carlos Cano, Calafate.T and Manzonis.: Improving Selfish Node Detection in MANETs Using a collaborative Watchdog. IEEE Communication Letters, Vol 16, No.5, (2012) [13] Syed S.Rizvi and Khaled M.Elleithy: A new scheme for minimizing malicious behavior of mobile nodes in Mobile Ad Hoc Networks, IJCSIS Internation Journal of computer Science and Information Security. Vol.3, No.1, (2009). [14] Md.Amir Khusru Akhtar and Sahoo.G. Mathematical Model for the detection of selfish Nodes in MANETs. International Journal of Computer science and Informatics, 2231-5292, Vol 1(3), pp 25-28 (2011) [15] Buchegger.S and Boudec.J.L. A robust reputation system for [email protected] and mobile ad hoc networks. In Proc. 2nd Workshop on economics of Peer- to Peer system, (2004) [16] J. Virtamo: CONTINUOUS DISTRIBUTIONS, 38.3143 Queuing Theory / Continuous Distributions pp.1-19 (2000). [17] F.W.Steutel, K.van Harn, Infinite divisibility of probability distributions on the real line, Marcer Dekker, pp.21- 28,(2004). 268

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