International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) is an online Journal in English published bimonthly for scientists, Engineers and Research Scholars involved in computer science, Information Technology and its applications to publish high quality and refereed papers. Papers reporting original research and innovative applications from all parts of the world are welcome. Papers for publication in the IJETTCS are selected through rigid peer review to ensure originality, timeliness, relevance and readability. The aim of IJETTCS is to publish peer reviewed research and review articles in rapidly developing field of computer science engineering and technology. This journal is an online journal having full access to the research and review paper. The journal also seeks clearly written survey and review articles from experts in the field, to promote intuitive understanding of the state-of-the-art and application trends. The journal aims to cover the latest outstanding developments in the field of Computer Science and engineering Technology.
International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: firstname.lastname@example.org, email@example.com Volume 1, Issue 2, July – August 2012 ISSN 2278-6856 Maximizing Network Lifetime using Reliable Energy Efficient Routing Protocol Based on Non Cooperative Game Theory for Wireless Sensor Networks Chitra.S.M1, Vinoba.V2 and Padmavathy.T.V3 1 Research Scholar, Bharathidasan University, TamilNadu, India, 2 K.N.Government Arts College,, TamilNadu, India 3 R.M.K. college of Engineering and Technology, TamilNadu,, Chennai as military, agricultural, industrial, and biomedical Abstract: Wireless sensor networks create numerous applications . Furthermore, they could easily be used in fundamental coordination problems. For example, in a different environments such as unreachable or dangerous number of application domains including homeland security, regions. Since there is no need to use a large amount of environmental monitoring and surveillance for military wire and complicated configuration and installation for operations, a network’s ability to efficiently manage power these sensors in the network, we could use them with consumption is extremely critical as direct user intervention lower cost in comparison with traditional networks. after initial deployment is severely limited. In these settings, Recently, some research efforts have focused on limited battery life gives rise to the basic coordination problem of maintaining coverage while maximizing the establishing efficient routing paths for transmitting network’s lifetime. In this paper we proposed game theory. packets from a sensor node to a destination in wireless Game theory (GT) is a mathematical method that describes sensor networks . Routing means finding the best the phenomenon of conflict and cooperation between possible way for data transmission from source node to intelligent rational decision-makers. In particular, the theory the destination node in the network by considering has been proven very useful in the design of wireless sensor networks parameters (e.g. stability, consumed and networks (WSNs).In this paper; we propose the game theory remained power, data transmission speed, and etc). in the analysis of resource management in wireless sensor networks. The game theoretic scheme is proposed to study Network Lifetime is one of the important factors. power control in a multi-source transmitting to multiple Shortening the route length can help reduce the clusters in wireless sensor network. A game where each transmission overhead and delay time, as well as increase sensor chooses its transmitting power independently to the packet delivery ratio. Therefore, these networks must achieve a target signal it is shown that the game has Nash be designed and used in a way to optimize the power equilibrium and it is unique under certain constraints. consumption and life time of the network. In this paper, Numerical results are provided to show the effectiveness of by using Game Theory approach for WSN, optimal route the proposed game considering distance-dependent attenuation with various path loss exponents. in WSN is found. In this approach, routing and sensor Keywords: Wireless Sensor Networks, Game Theory, nodes are assumed to be the game and players Routing, Lifetime. respectively. All players want to increase their benefit. So we use a mixed strategy model as well as profit and 1. INTRODUCTION loss calculation for each player. In this model, the destination node pays a recognition to the source node for Wireless Sensor Networks is a new technology which is used in a huge majority of applications. This network is a each data packet successfully reception. Moreover, the graph which consists of a large number of sense nodes. source node pays a portion of this credit to each These nodes are able to gather the information and intermediate node or relay node that participates in data process it and send it to the relevant destinations. The packet transaction. Furthermore, each node sustains a sensors have some individual characteristics such as cost for each data packet transaction to other node. This small dimension and low power consumption. Because of cost is called Transmission Cost and related to different these characteristics, they could be used in different fields parameters. Also each node transmits the received data such packet to the next hope with the probability, calculated by the reliability of the node. This parameter is depending on Volume 1, Issue 2 July-August 2012 Page 210 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: firstname.lastname@example.org, email@example.com Volume 1, Issue 2, July – August 2012 ISSN 2278-6856 several items, e.g. failure probability, sleep cycling, etc. Meanwhile, each node also receives all the location information from all its one hop neighbors. When nodes 2. RELATED WORKS acquire their neighbor location information, they compute There are some secure routing protocols for ad hoc the distance between themselves and the sink, and the networks , , but because of the assumption of small distance between every one hop neighbor and the sink. scale networks, large memory and high power they are not suitable for WSNs. Some security protocols for 4. MATHEMATICAL MODEL wireless sensor networks were also proposed. The authors In the distributed sensor network the game equation has to be found, with application of a game strategy. It is in , addressed secure communication in resource assumed that all the nodes in the sensor network are the constrained sensor networks by introducing two low-level same and that all nodes are in the interference range. The secure building blocks. The Security Protocols for Sensor activity of all the nodes is at the same level and it Networks (SPINS) consists of SNEP and µTESLA. SNEP increases with the increase of power level transmission. provides confidentiality, authentication, and freshness In the non-cooperative game theory, it is assumed that between nodes and the destination, and µTESLA provides nodes are transmitting high power, because of a high authenticated broadcast. But disadvantage of SPINS interference. Thus, the equilibrium game strategy has protocol is: route discovery depends on the detection of been applied for control of non-cooperative behavior. authenticated beacons and node to node authentication by Powers levels of the nodes are the minimum transmit the destination. power and the maximum transmit power. Secure Auction-based routing (SAR) was proposed in Theorem 1: Every game with complete information , based on the concept of sealed auctioning. In this and a finite tree has atleast one equilibrium point. case nodes of the sensor network are the players of the Although not all finite n-person non-cooperative games game which compete with each other, to be a member in have pure strategy equilibria we can ask about the the route and the amount of the bid that each bidder situation if mixed strategies are permitted. His result, suggests is the amount of utility it had achieved during which generalizes the Von Neumann mini-max theorem, is the main objective of this section and certainly provides past plays. This idea is implemented on DSR protocol one of the strongest arguments in favour of equilibrium although this protocol is not well suited for WSNs, and points as a solution concept for n person non-cooperative the other drawback is that when a packet on a path does games. not get to the destination, all the nodes on that path get The mini-max principles say, minimizes the maximum negative reputation, regardless of being malicious or losses ie minimizes the number of node failure due lake of normal. Utility-based dynamic source routing (UDSR) energy threshold level. The maximum losses with respect was proposed in . It was based on a two player, non- to different alternatives of player B(node2), irrespective of cooperative and non zero-sum game between attacker and player A’s (node1) alternatives, are obtained first. The IDS residing at base station. It has the same two minimum of these maximum losses is known as the mini- weaknesses of SAR protocol, although the IDS can only max value and the corresponding alternative is called as defend one cluster and the attacker can also attack only Mini-Max strategy. one cluster at a time. Let index set I be the set of nodes. For an n person The authors in , ,  proposed Game theory game I ,2,3,.....n. Let xi be an arbitrary mixed 1 which has been used in sensor networks, with th incentives for forwarding nodes and punishing strategy for the i player, and the probability of misbehaving nodes . In the autonomous sensor distribution of set S i of that player’s pure strategies. The network using non cooperative game technique, Nash probability assigned by xi to some i S i is denoted Equilibrium is used to get optimal solutions of energy conservation. Optimal probability of the two states is the by xi ( i ) . Since the game is non-cooperative, the sleep and wakeup use in repeated games. mixed strategies of all players (1,2,3,.....n) , viewed as probability distributions are jointly independent. The 3. PROPOSED RELIABLE ENERGY probability x ( ) of arriving at the pure strategy n - tuple EFFICIENT ROUTING PROTOCOL is 1 , 2 , ....., n , i S i is assumed to Due to the resource constraints, a sensor node in our protocol does not need to have global information about be x( ) x1 1 x 2 2 .......x n n . In terms of pure the network. The following sections explain the strategies the payoff to player i is given by Pi , mathematical model to prolong the network lifetime. In the proposed work, since the nodes are static, all nodes where Pi : S S1 x.....xS n R , that is Pi is a function know their own locations before network initialization. In which maps each ( 1 ,...... n ) S to a real the initialization stage of the network, each node sends its own location information to its one hop neighbors. Volume 1, Issue 2 July-August 2012 Page 211 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: firstname.lastname@example.org, email@example.com Volume 1, Issue 2, July – August 2012 ISSN 2278-6856 number. If mixed strategies xi , i I are used the payoff tries to maximize their utility. In the game theory no player is getting benefit by changing their strategy until will be the statistical expectation of Pi with respect to the other player changes their strategy. The set of strategy distribution x , namely, and the corresponding utilities is a foundation of Nash equilibrium. Every player should show their best response Pi x1 , x 2 ,....x n Pi x of their strategy, which results in Nash Equilibrium. S Let us consider non-cooperative n person game in which n Pi x1 ,...., x n ...... Pi 1 ,......, n x j j each player or each node i I has exactly two pure 11 n S n j 1 strategies, either i 1 (node1) or i 2 . The payoff (1) is, It is convenient to introduce the following notation: Pi ( 1 ,..... n ) i 1 i , j , i I (5) For the strategy n tuple x ( x1 ,.....x n ) then this can be ji ' ' written as, x xi ( x1 ,....xi 1 , xi , xi 1 ........x n ) . This Where is the kronecker given by 1, if i j means that the player i has in x replaced the strategy i , j (6) xi by xi' . Now equation (1) can be written as, 0 otherwise n If node i uses a mixed strategy in which pure strategy 1 is P x i ..... ...... .......P i 1S1 i 1Si 1 i i1Si1 Snn x j 1 j 1 j j chosen with probability pi (i I ) , then pi 1 , 1 (2) 1 2 n 1 Definitions: i I and for n 2,3 this is the only equilibrium Anon-cooperative game I, X i iI , Pi iI , in point. which the sets of players is I , the set of strategies for Proof: For node1, if 1 1, then P1 = 0 unless player i is X i and the payoff to player i is given by 2 ...... n 2, in which case P1 1. If 1 2, Pi : X i R , Here the sets X i could be taken to be then P = 0 unless 2 ...... n 1, in which case 1 iI sets of pure or mixed strategies. If the X i to consist of P1 2 similarly for other players also. Consider now the mixed strategies then is called the mixed extension of mixed strategy n -tuple x x1 ,.....x n , where the original pure strategies. A mixed strategy n - tuple xi ( pi , 1 pi ) for 1 i n and pi is the probability x x1 ,.....x n , xi X i , is an equilibrium point of an of choosing i 1 . n person non-cooperative game if for each From the above observation we obtain, i,1 i n, and x X i , Pi x x Pi x . ' i ' i Pi ( x) p i (1 p i ) 2 (1 p j ) p j (7) j 1 j 1 Theorem 2: A mixed strategy n -tuple x x1 ,.....x n is Also an equilibrium point of a finite game if and only if for Pi x i (1 p i ) if i 1 (8) each player index i, Pi x i Pi x (3) j 1 for every pure strategy. Pi x i 2 p j if i 2 (9) j 1 Theorem3: For any mixed strategy n -tuple x x1 ,.....x n each player i,1 i n, possesses a According to theorem 2, “A mixed strategy n tuple x x1 ,.....x n is an equilibrium point of a finite game pure strategy ik such that xi ik 0 and if and only if for each player index i , Pi x k i P x . i (4) Pi x i Pi x for every pure strategy i S i ”. x is an equilibrium point iff 5. LIFETIME EXTENSION FOR NASH EQUILIBRIUM (1 p j ) pi (1 p j ) 2(1 pi ) p j and ji j i j i In game theory, players are picking their own strategies simultaneously. Any finite n person non-cooperative 2 p j pi (1 p j ) 2(1 pi ) p j for every j i j i j i game has at least one mixed strategy equilibrium point. By using Nash equilibrium condition every player iI . Volume 1, Issue 2 July-August 2012 Page 212 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: firstname.lastname@example.org, email@example.com Volume 1, Issue 2, July – August 2012 ISSN 2278-6856 6. LIFETIME EXTENSION ALGORITHM Rearranging equation (1), then In this section, we propose a non-cooperative game lifetime extension algorithm. In order to implement the (1 pi ) (1 p j ) 2(1 pi ) p j this can be algorithm, on the one hand, the node i receives the sum j i j i n simplified as, of interference power x and n S n j 1 j 1 j j on the (1 p ji j ) 2 p j j i (10) other hand, the lifetime of sensor node increased by twice according to the equation (9).When a node want to send Similarly rearranging the (2) gives data message, it will search its information table and (2 2 2 p i ) p j pi (1 p j ) compute its transmitting power according equation (2), j i j i then send the power value to sink node, iterate this 2 p j (1 p j ) (11) process until reach Nash Equilibrium. j i j i From equation (3) and (4) it follows that x is an 7. SIMULATION RESULTS AND equilibrium point if and only if, DISCUSSION The proposed algorithm has been simulated and validated (1 p ji j ) 2 p j for every i I j i (12) through simulation. The sensor nodes are deployed randomly in a 100x100 meters square and sink node deploy at the point of (50, 50), the maximum transmitting For n 2 or 3 the system of equation (5) has no solution radius of each node is 80m, other simulation parameters with any pi 0 or 1 , but for n 4 these are several such are displayed in Table 1. In this section, we first discuss utility factor and pricing factor’s influences on solutions, for example p1 p 4 1, p 2 p3 0. If transmitting power, then evaluate the algorithm of NGLE n 5 , we can find the solutions with algorithm and compare it with other existing algorithm. p1 p 4 1, p 2 p3 0 , and the remaining Table1: Simulation Parameters n 4 pi arbitrary. To complete the analysis suppose Parameters Value 0 p i 1 for every i I . Transmission Range 250 m Considering the equation (12) for i k , i l , where Network Area 100 x 100 Number of Sensors 50-100 k l , then Packet rate 5 pkt/sec (1 p j ) 2 p j and (1 p j ) 2 p j ji j i j l j l Packet size 50bytes Radio Bandwidth 76kbps Let A (1 p j ) and B p j ,since Transmitting Power 75mW ( 270J) Receiving Power 36mW (129.6J) 0 p i 1 for all i Power Consumption in Sleep 100µ W (0.36 J) Then the expression can be written as mode A 2B A 2B Sending and Receiving Slot 50msec , 1 pk p k 1 pl pl Type of mote Mica2 Since A 0 and B 0 , then p k p l , but k and Inital energy of sensor node 2KJ Energy Threshold E thd 0.001mJ l where arbitrary, so that every player or every node use Network Lifetime the same mixed strategy in x . Equation (12) can be 100 LEACH 90 LEACH-M rewritten as , HEED 80 REER (1 p ) n1 2 p n 1 , by solving p can be calculated as, 70 N b of N es Alive 1 60 od n 1 (1 p ) 2 p 50 um er 40 1 30 n 1 1 p (1 2 ) 20 1 10 p 1 (13) 0 0 50 100 150 200 250 300 350 400 450 500 n 1 Number of Rounds 1 2 Figure 1: Network Lifetime of Sensor Networks Volume 1, Issue 2 July-August 2012 Page 213 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: firstname.lastname@example.org, email@example.com Volume 1, Issue 2, July – August 2012 ISSN 2278-6856 The network lifetime for each simulation is showed in source and destination, it has the high probability to be Figure 1. These curves are showing that lifetime of the forwarding node. Thus, the proposed REER protocol network for various routing protocols after 500 rounds, consumes less node energy for transmitting data between about 27% of nodes in the network are alive in the the nodes. proposed REER routing protocol, but 1%,5% and 7% of nodes are alive in existing protocols LEACH, LEACH-M Energy Consumption REER and HEED respectively. So the network lifetime is 4500 HEED Energy Consumption (mJ) increasing about 73% with using of our model and 4000 LEACH-M 3500 algorithm. 3000 LEACH Average Delivery Delay 2500 160 2000 LEACH 1500 LEACH-M 140 1000 HEED 500 REER 0 A vearge Deliv ery Delay(m sec) 120 20 40 60 80 100 Transmission Rate (packets/Second) 100 80 Figure 3: Energy Consumption with various Transmission Rate 60 Packet Delivery ratio REER 40 HEED 100 LEACH-M 20 90 Packet Delivery ratio(%) 0 10 20 30 40 50 60 70 80 90 100 80 LEACH Transmission Rate (Packets/Second) 70 60 Figure 2: Average Delivery Rate with various 50 Transmission Rate 40 30 20 Figure 2 shows the average delivery delay with increasing 10 0 transmission rate. The average delivery delay means the 20 40 60 80 100 average time delay between the instant the source sends a Transmission Rate (packets/Second) packet and moment the destination receives this packet. When the transmission rate is 1 packet per second, we Figure 4: Packet Delivery Ratio with various can see that the average delivery delay of LEACH, Transmission Rate LEACH-M is lower than the proposed REER protocol and HEED. This is because LEACH is always tries to Figure 4 shows the packet delivery ratio of proposed discover a high speed path for forwarding packets. Since protocol is compared with existing protocols. The plot the transmission rate increases, the average delivery delay infers that the proposed REER protocol has better of LEACH increases significantly. This is because performance than LEACH, LEACH-M and HEED. With congestions occur at the intermediate nodes in LEACH. the increase of transmission rate, LEACH, LEACH-M In the proposed protocol, when the packets reaches at and HEED always forward packets along the relay nodes destination, the relay or intermediate nodes have a lower by perimeter approach. This leads to a high probability of forwarding probability than normal nodes by using packet congestion around the relay node. In REER multiple strategy. In the forwarding node selection game, protocol, since the process of forwarding node selection is the probability that a great amount of packets are a game process, the source has lower probability to make forwarded by the same node is relatively low. Thus, the the same candidate gain too much benefit from the game average delivery delay of our protocol does not process. This is the reason the packet delivery ratio of our significantly increase with an increase in transmission protocol does not significantly decrease with the increase rate. of transmission rate. Figure 3 shows the energy consumption of the four protocols. For LEACH, LEACH-M and HEED protocols, 8. CONCLUSION the source always selects the node closest to the In this paper, we introduce a game theory for extending destination in the neighbor set. However, normally the sensor network lifetime. In the process of network closest node is the local superior decision, not the global initialization, we use the connectivity property of nodes to optimal decision. This has been proven by lemma 2. For determine the connectivity of nodes that can be forward our protocol, in the forwarding node selection game, if any packets to its neighbour nodes. This approach some node has a lesser angle with the line formed by improves the transmission success rate and decreases the Volume 1, Issue 2 July-August 2012 Page 214 International Journal of Emerging Trends & Technology in Computer Science (IJETTCS) Web Site: www.ijettcs.org Email: firstname.lastname@example.org, email@example.com Volume 1, Issue 2, July – August 2012 ISSN 2278-6856 transmission delays of packets. In the aspect of setting up  L. Buttyan and J.P. Hubaux, “Nuglets: A the routing path, we consider the residual energy. We Virtual Currency to Stimulate Cooperation in conclude the forwarding probability and payoff function Self organized Mobile Ad-Hoc of forwarding participants. Finally, the Nash Equilibrium Networks,”Technical Report DSC/2001/001, exists when it is assume for minimum and maximum Swiss Fed. Inst. Of Technology, Jan. 2001. threshold for channel condition and power level. By  W. Wang, M. Chatterjee, and K. Kwiat, using Non cooperative game theory the network lifetime “Enforcing Cooperation in Ad Hoc Networks is extended, that is after 500 rounds 27% of node are alive with Unreliable Channel,” Proc. Fifth IEEE Int’ where as 1%,5% and 7% of nodes are alive in existing Conf. Mobile Ad-Hoc and Sensor Systems protocols LEACH, LEACH-M and HEED respectively. (MASS), pp. 456-462, 2008. So the network lifetime is increasing about 73% with  V. Srinivasan, P. Nuggehalli, C. Chiasserini, and using of our model and algorithm. R. Rao,“Cooperation in Wireless Ad Hoc In our future, we plan to implement our algorithm in s Networks,” Proc. IEEEINFOCOM, vol. 2, pp. 808- real application scenario to verify the effectiveness in the 817, Apr. 2003. real world. Also, in this paper, we assume that all nodes are stationary. There are some application scenarios where we need the nodes to be able to move. In such a case, we will need to consider the nodes’ mobility in our future work. REFERENCES  I. F. Akyldiz, W. Su, Y. subramaniam , Sankaras and E. Cayirci, “Wireless sensor works: a survey”, Computer Networks, vol. 38, , 2002, pp. 393-422.  Chang, C.Y.; Shih, K.P.; Lee, S.C.; Chang, S.W. RGP: Active route guiding protocol for wireless sensor networks with obstacles. In Proceedings of IEEE MASS, Vancouver, Canada, October 2006; pp. 367-376.  K. Sanzgiri, B. Dahill, B.N. L E.M. Royer, “A Secure Rohoc Networks”, In Proc. of on Network Protocols (IC2002, pp. 78-87. Levine, C. 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