OTIMIZE THE OWER CONTROL AND NETWORK LIFETIME USING ZERO - SUM GAME THEORY FOR WIRELESS SENSOR NETWORKS Vinoba.V 1, Chithra.S.M 1 Departent of Matheatics, K.N. Governent Arts college, Tail Nadu,( India.) Departent of Matheatics, R.M.K College of Engineering and Technology, Research Scholar, Bharathidasan University, Tail Nadu, (India.) ABSTRACT A wireless sensor networ is one of the ost attractive research fields in the counication networs. This will creates a great popularity regarding their potential use in a wide variety of applications lie onitoring environental attributes, intrusion detection, and various ilitary and civilian applications. The ain perforance of these sensor networs is aintaining networ life tie while satisfying coverage and connectivity in the deployent region. In this paper, we loo at the proble of aintaining energy level of the sensor node, reliable routing and ulti-hop in WSN within a finite two-person zero-su gae theoretic approach. The gae theoretic schee is based on odels that express the interaction aong players, in this case, nodes, by odeling the as eleents of a social networs in such a way that they act as to aintaining the axiu utility. Siulation results are shows the effectiveness of the proposed gae with various path loss exponents and also the proposed gaes is able to aintain the energy level of the networ life tie. Keywords: Wireless Sensor Networs, Two-person zero-su Gae Theory, Routing, Life tie. I. INTRODUCTION Wireless Sensor networs is one of the ost proising and interesting areas in the past years. This networ consists of a large nuber of sense nodes. These nodes are able to gather the inforation and process it and send it to the relevant destinations. Also, these nodes for a networ by counicating with each other either directly or through other nodes. One or ore nodes aong the will serve as sin(s) that are capable of counicating with the user either directly or through the existing wired networs. The priary coponent of the networ is the sensor, essential for onitoring real world physical conditions such as sound, teperature, huidity, intensity, vibration, pressure, otion, pollutants etc. at different locations. The nodes are deployed in hostile environent it is not feasible to replace the batteries. Therefore energy conservation is very crucial for WSN s both for each sensor node and the entire networ level operations to prolong the networ lifetie. Energy constrained networs, such as Wireless sensor networs are coposed of nodes typically powered by batteries, for which replaceent or recharging is very difficult, if not ipossible. With finite energy, we can only transit a finite aount of inforation. Therefore, iniizing the energy consuption for data transission becoes one of the ost iportant design considerations for such networs [1]. One of the desired features of wireless sensors networs is their capability to function unattended in unind environents and 577 a g e
inaccessible terrains in which up to data onitoring schees are unsafe, heavy-handed, and soeties infeasible. Now days, soe research efforts have focused on establishing efficient routing paths for transitting pacets fro a sensor node to a sin in WSN s. Routing eans finding the best possible way for data transission fro source node to the destination node in the networ by considering networs paraeters. The other iportant factor that ust be considered in the networ is Load Traffic Distribution. Usually the traffic load in wireless sensor networs is unbalance. For exaple, sensors which are nearer to the source have ore data load. Therefore, optiization of load distribution, called Load Balancing, is one of the iportant factors for iproving the efficiency of the networs. Optiization of load traffic distribution in WSN could increase the lifetie of the networ. Since, there is ore power consuption in nodes with ore traffic load then the data transaction in the networ could be optiized. Gae Theory is based on odels that express the interaction aong players, in this case nodes, by odeling the as an eleent of a social networs in such a way that they act to axiize their own utility. This allows the analysis of existing algoriths and protocols for WSN s as well as the design of equilibriu-inducing echaniss that provide incentives for individual nodes to behave in socially constructive ways. In this paper, by using Zero-Su Gae Theory approach for WSN, optial route in WSN is found. In this approach, routing and sensor nodes are assued to be the gae and players respectively. All players want to increase their benefit. So we use a ixed strategy odel as well as profit and loss calculation for each player. II. RELATED WORKS The ain goal of routing in WSNs is to guarantee successful pacet delivery fro source to sin node under constraint requireents lie energy consuption, end to end delay, pacet delivery ratio and QoS etc. In addition to energy consuption, ore challenges and design issues are pointed out [1]. Lifetie is the one of ain design issue in WSN and the lifetie of the sensor node is ainly depends on the battery energy level. Since WSN is coposed of very sall nodes, their energy resources are very liited this iposes tight constraints on the operation of sensor nodes. The transceiver is the eleent which drains ost power fro the node (Fedora and Collier 007), thus the routing protocols will significantly influence the lifetie of the overall networ. Energy-aware Routing protocol (Shah and Rabaey 00) is siilar to directed diffusion with the difference is, it aintains a set of paths instead of or enforcing one optial path. These paths are aintained and chosen by eans of a certain probability, which will depend the energy consuption of each path. By selecting different routes at different ties, the energy of any single route will not deplete so quicly, the networ lifetie increases. Data centric, hierarchical and location based routing protocols gives the iportance on energy efficiency and increased networ lifetie, with little concern on quality easures. This group of routing protocols in addition to the energy efficiency focuses on QoS etrics such as latency, bandwidth and efficiency. QoS based protocols ephasize on acnowledging the data at the right tie, differentiating data based on priorities and propose 578 a g e
reliable routing algoriths. These protocols are concerned on the networ fault tolerance and resilience of the networ on node failures or node alfunctioning. III. MATHEMATICAL MODEL Gae Theory is a theory of decision aing under conditions of uncertainly and interdependence. In the distributed sensor networ the gae equation has to be found, with application of a gae strategy. It is assued that all the nodes in the sensor networs are the sae and that all nodes are in the interference range. The activity of all the nodes is at the sae level and it increases with the increase of power level transission. A gae has three coponents: (i) a set of players (ii) a set of possible of actions for each player and (iii) a set of strategies. A player s strategy is a coplete plan of actions to be taen when the gae is actually played. layers can act selfishly to axiize their gains and hence a distributed strategy for players can provide an optiized solution to the gae. In any gae, utility represents the otivation of players. A utility function, describing player s preferences for a given player assigns a nuber for every possible outcoe of the gae with the property that a higher nuber iplies that the outcoe is ore preferred. A Zero-su gae is a atheatical representation of situation in which a participant s gain or loss of utility is exactly balanced by the losses or gain of the utility of the other participants. The present survey covers research on infinite zero-su two-person gaes in noral for [3].( i.e., zero-su two-person gaes with infinite sets of player strategies in which the player strategies are eleents of certain abstract sets. In this article we do not consider dynaic and differential gaes. Definition: 3.1. The zero-su two-person gae in noral for is forally defined as a triple X, Y, in which X and Y are arbitrary infinite sets representing the sets of strategies of layers I and II respectively and is a real function defined on the set function or ernel of the gae. (If X Y of all situations and is called the payoff : X Y R is the payoff function of layer I. layer II s payoff in the situation x, y is x, y, where x X, y Y the gae being zero-su) Definition: 3. The existence of optial ( gae is equivalent to satisfaction of the following equations: ax x X sup x X inf x y yy y Y, = inf x y, = in yy inf yy x X optial) strategies for the opponents in a zero-su two-person sup x, y = υ ------------ (3.1) sup x, y = υ ------------ (3.) x X The quantity υ is called the value of the gae. Even in the siplest cases, however, equations (1) and () fall short of being satisfied. Their proof requires the iposition of rather stringent algebraic constraints on the strategy sets X, Y and the function (such as concavity in x and convexity in y ) as well as topological constraints ( the sets X and Y are topological spaces, and the function has properties of the continuity type). 579 a g e
It is reasonable, therefore, to extend the strategy sets of the players in such a way that the payoff function, now defined on a new extended set of situations, will satisfy the required constraints.the extended strategy sets ust be convex and include the usual strategies. Let algebra of subsets of X containing all one-eleent subsets, let be a algebra of subsets of Y, and let the function be bounded and easurable under the algebra x. A probabilistic easure defined on is called a ixed strategy of layer I (II). If is a ixed strategy of layer I and is a ixed strategy of layer II, then the payoff function, under the conditions of the ixed situation, is defined by the integral, = x, y d x d y. X Y If the set of pure strategies of a player is infinite (and especially if it is denuerable ), then in the choice of his set of ixed strategies there is a certain arbitrariness, which rests on the particular choice of algebra of subsets of the pure strategy set on which the probabilistic easure is defined[].various randoizations of pure strategy sets have been investigated by Wald and Bieriein.Clearly, the sets of ixed strategies are convex and, if the ordinary, or so-called pure, strategies are regarded as corresponding degenerate easures, include all the pure strategies of the players. Under the conditions of ixed strategies the payoff function turns out be linear in each of the variables. Theores establishing the validity of equations (1) and () for an infinite gae or its ixed extension are called existence theores (or iniax theores). The proof of existence theore, (i.e.) the identification of classes of gaes for which a value of the gae exists (or does not exist), is one the fundaental probles of the theory of infinite zero-su two-person gaes [4]. A pair of optial strategies of each player in a zero-su two-person gae ( or the set of optial strategies for each player) in conjunction with the process of finding those strategies is nown as a solution of the gae. In the infinite gae, as in any zero-su two-person gae X, Y, the principle of player s optial behavior is the saddle point (equilibriu) principle. Definition: 3.3. Saddle point The point x, y for which the inequality x, y x, y x y, ----------- (3.3) holds for all x X, y Y is called saddle point. This principle ay be realized in the gae if and only if = = = x y, where = = ax x X in yy inf x, y y Y sup x, y x X ------------------------ (3.4) 580 a g e
(i.e) the external extree of axiin and iniax are achieved and the lower value of the gae is equal to upper value of the gae is the value of the gae.. The gae for which the (4) holds is called strictly deterined and the nuber Definition: 3.4. Saddle points, optial strategies The point x, in the zero-su two-person gae X, Y, is called the y equilibriu point if the following inequality holds for any strategies x X and y Y of the layers I and II, respectively: x, y x, y x y ------------ (3.5)., The point x, y for which equation (5) holds, is called the Saddle point and the strategies x & y are called optial strategies for the players I and II, respectively. NOTE: Copare the definitions of the saddle point equation (3) and the Saddle point equation (5), A deviation fro the optial strategy reduce the player s payoff where as a deviation fro the optial strategies ay increase the payoff by no ore than. In conclusion we will point out a special class of zero-su two-person gae in which X = Y = [0, 1]. In these gaes, situations are the pairs of nubers x, y, where x, y 0,1 such gaes are called the gaes on the unit square. The class of the gaes on the unit square is basic in exaination of infinite gaes. Exaple 1: Suppose each of the players I and II chooses a nuber fro the open interval (0,1). Then layer I receives a payoff equal to the su of the chosen nubers. In the anner we obtain the gae on the open unit square with the payoff function x, y for layer I. x, y x y =, x 0,1, y 0,1 --------(3.6). Here the situation (1,0) would be equilibriu if 1 and 0 were aong the players strategies, with the gae value being 1 Actually the external extree in (4) are not achieved but in the sae tie the upper value is equal to the lower value of the gae. Therefore =1 and layer I can always receive the payoff sufficiently close to the gae value by choosing a nuber 1-, >0 as a sufficiently sall nuber (close to 0), layer II can guarantee that his loss will be arbitrarily close to the value of the gae. The following theore yields the ain property of optial strategies. Theore1: For the finite value of the zero-su two-person gae X, Y, to exist, it is necessary and sufficient that, for any >0, there be optial strategies x, y for the players I and II, respectively, in which case li 0 x, y = --------------- (3.7). 581 a g e
roof Case (i) first to prove the Necessary condition: Suppose the gae has the finite value. For any >0 we choose strategy x fro the condition Sup x, y x X ----------- (3.8) And strategy x fro the condition Inf x, y yy -------------------- (3.9) We now that = ax x X inf x, y yy, = Fro equation (8) & (9) we obtain the inequality in yy sup x, y x X x, y x, y x, y ---------------- (3.10) for all strategies. Consequently, The relations x, y ----------------- (3.11) x, y x, y x y,, li 0 x, y = follows fro Sup x, y and Inf x, y x X yy. Sup x, y Inf x, y x X yy Case (ii) Next to prove the sufficient condition: If the inequalities x, y x, y x y, hold for any nuber 0, then _ Inf (3.1) yy Sup x X x, y Sup x, y x, y Inf x, y Sup Inf x, y x X yy x X y y _ ----------- _ Hence it follows that, the inverse inequality holds true. Thus, it reains to prove that the value of the gae is finite. Let us tae such sequence n that li 0 Let n _ n n. n, where any fixed natural nuber is. We have x, y x, y x, y, x, y x, y x, y. x, y x, y Thus. 58 a g e
Since li 0 for any fixed value of relationship equation (10) we obtain the inequality x y ; Hence = li x, y, This copletes the proof of the theore. 0., then there exists a finite liit li x, y 0. Fro the IV. LIFETIME EXTENSION ALGORITHM In this section, we propose a infinite zero-su gae theory life tie extension algorith. In order to ipleent the algorith, the node i receives the su of interference power fro sin node to the destination node [6]. The lifetie sensor node aintained according to the equation and li x, y = 0 The latency at the source node L S is given by, ax x X inf x y y Y, = in yy sup x, y = υ x X L S T sleep T T 1 T data -------------------- (4.1) The latency at the interediate node is sae as that of source node, which is given in equation (13). The end-to-end latency for ulti-hop N L transission is given by, i 1 L L i -------------------- (4.). V. SIMULATION RESULTS AND DISCUSSION The proposed algorith has been siulated and validated through siulation. The sensor nodes are deployed randoly in a 100x100 eters square and sin node deploy at the point of (50, 50), the axiu transitting radius of each node is 80 ; other siulation paraeters are displayed in Table1. In this section, we first discuss utility factor and pricing factor s influences on transitting power, and then evaluate the algorith with other existing algorith. Figure1. Shows that the average delivery delay with increasing transission rate. Table 1. Siulation araeters araeters Value Nuber of Nodes 50-100 Networ Area 100 X 100 Sensing Range Initial Energy of sensor node 16 KJ 583 a g e
Lin Reliability International Journal of Advanced Technology in Engineering and Science www.ijates.co Sending and Receiving Slot Transission Range acet Size 50sec 50eter 64 Bytes Energy threshold E 0.001joules th Channel Frequency Receiving power ower consuption in sleep ode.4ghz 36W 0.36J Type of ode Mica Radio Bandwidth 76bps 0.4 0.35 0.3 DD Flooding Energy Aware Routing LRR Lin Reliability 0.5 0. 0.15 0.1 0.05 0 0 30 40 50 60 70 80 90 100 Nuber of Nodes Figure 1: Average Delivery Rate with various Transission Rate The average delay eans the average delay between the instant the source sends a pacet and oent the destination receives this pacet. When the transission rate is 1 pacet per second, we can see that the average delivery delay of DD, Flooding, and Energy Aware is lower than the proposed LRR protocol. 584 a g e
In the proposed protocol, when the pacets reach at destination, the relay or interediate nodes have a lower ultiple strategies. In the forwarding node selection gae, the probability that a great aount of pacets are forwarded by the sae node is relatively low. Thus, the average delivery delay of our protocol does not significantly increase with an increase in transission rate. The following table shows the networ life tie of nodes in the respective routing protocols. Routing rotocols Nodes Alive 100 700 Rounds Rounds Nuber of Nodes 0 Nodes 100 Nodes LRR (roposed) 100 45 0.15 0.4 Flooding 59 18 0.05 0.07 DD 4 5 0.035 0.15 Energy Aware 68 0 0.1 0.34 VI. CONCLUSION In this paper, we introduce a zero-su gae theory for aintaining a sensor networ lifetie. In this networ connectivity of nodes forward to any pacets to its neighbor nodes. Zero-su gae theory iproves the networ lifetie. Direct diffusion (DD) protocol, after 400 rounds, about 5% of nodes alive. In proposed lin reliability routing (LRR) protocol, after 550 rounds Networ lifetie is increasing about 70%. ath reliability for direct diffusion (DD) protocol is rando. ath reliability for proposed lin reliability routing (LRR) protocol, increases Nuber of nodes increases to above 70 nodes, the path reliability is ore than 0.3. This shows that our proposed odel and algorith increases the networ lifetie. Also, we will be optiizing the algorith to find the axiu usefulness function of all nodes that cooperate in path. REFERENCES [1] F.Ayldiz, W.Su, Y. Subraanian, Sanaras and E. Cayirci, Wireless sensor networs: a survey Coputer Networs, [] Vol.38, p. 393-4, 00. [3] Theory of Gaes and Econoic Behavior -Von Neuann and Morgenstern-1953. [4] Gae theory in Wireless sensor networs edro O.S.Vazdeelo, Cesar Fernandes, Raquel A.F, Mini Antonio 585 a g e
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