Applied Mathematics. Elixir Appl. Math. 84 (2015)

Transcription

1 3341 V.Vnoba and S.M.Chthra/ Elxr Appl. Math. 84 (015) Avalable onlne at (Elxr Internatonal Journal) Appled Mathematcs Elxr Appl. Math. 84 (015) Bayesan Inference Approach for Energy Effcent Wreless Sensor Networks Usng Game Theory V.Vnoba 1 and S.M.Chthra 1 Department of Mathematcs, K.N. Govt. Arts college, Thanjavur, Inda. Department of Mathematcs, R.M.K College of Engneerng and Technology, Chenna, Inda. ARTICLE INFO Artcle hstory: Receved: 0 May 015; Receved n revsed form: 19 June 015; Accepted: 9 June 015; Keywords Wreless sensor networks, Game Theory, Bayesan Game Theory, LEACH and ELEACH protocols. ABSTRACT In ths paper, we propose a dfferent approach for effcently conservng energy n wreless sensor networks. Our approach towards energy consumng n sensor networks s fully dstrbuted to consume very low energy for fndng the path along wth data transmsson. We use two protocols LEACH and ELEACH-M to fnd the route for data transmsson and make ts performance by comparng the route dscovery of those two protocols. Bayesan nference s used to nference the mssng data from the nodes that were not actve durng each sensng. Game theory offers mode for dstrbuted allocaton of energy resources and thus provdes a way of expectng the characterstcs of wreless sensor networks. We make game approach to obtan the optmal probabltes of sleep and wake up states that were used for energy conservaton. 015 Elxr All rghts reserved. Introducton Recently, ncreasng research attenton has been drected toward wreless sensor networks: collectons of small low-power nodes physcally stuated n the envronment that can ntellgently delver hgh-level sensng results to the user node. The most complex desgn efforts are long-lved systems, largescale that truly requre self-organzaton and adaptvely to the envronment. The small low-power hardware platforms that ntegrate sensng, processng, computaton, and wreless communcaton have led to wdespread nterest n the desgn of wreless sensor networks. Such networks are envsoned to be large-scale dense deployments n envronments where tradtonal centrally wred sensors are mpractcal. The wreless ad hoc network s to allow a group of communcaton nodes to set up and mantan a network lfetme among themselves and wthout the support of a base staton or a central controller. The wreless ad hoc networks are useful for stuatons that requre quck or nfrastructure less local network deployment, such as crss response, mltary applcatons, possbly home and offce networks. Ad hoc networks could, empower medcal personnel and cvl servants to better coordnate ther efforts durng large-scale emergences that brng nfrastructure networks down. An mportant subclass of ad hoc networks s wreless sensor networks. The most central premse of sensor networks s the dstrbuted collecton of data from a physcal space, provdng an nterface between the dgtal and physcal domans. Sensor networks consst of a potentally large number of sensor modules that ntegrate sensng capabltes, memory, communcaton and processng. Ths sensor modules form ad hoc networks n order to share the collected physcal data and to provde ths data to the network user or operator. Wreless Sensor networks have a wde range of applcatons, n mltary, medcal, envronmental, ndustral, and commercal. Based on the applcatons of ad hoc and sensor networks, new challenges emerge. The lack of nfrastructure n ad hoc and sensor networks requres the nodes to perform the network setup, management and control among themselves and each node must act as a router and data forwarder n addton to playng the role of a data termnal. Dstrbutng network management across the nodes places a burden on the resources of ndvdual nodes. The addtonal load of each node complcates the protocol desgn and performance optmzaton of ad hoc and sensor networks. Game theory s a useful and powerful mathematcal tool for analyzng and predctng the behavor of ratonal and selfsh enttes. In the present work we propose to use the model-based approach, Bayesan Exploraton [8], to take account of all dynamc features and acheve good routng scheme through tral-and error nteractons wth the envronment. Related Work There are many energy-effcent routng algorthms have been proposed based on the herarchcal topology. LEACH [3] s called as a classcal clusterng algorthm. It randomly selects the cluster heads n a perodcal way and evenly dstrbutes energy consumpton of the entre networks to each sensor node, whch ams to reduce energy consumpton and mprove the whole network lfetme. It s smple; however, t has some defcences: () t does not guarantee about even dstrbuton of cluster heads over the network. Some of the very bg clusters and very small clusters may exst n the network at the same tme. () Cluster head (CH) selecton s unreasonable n heterogeneous networks where nodes have dfferent energy level. () Due to ths protocol each cluster head transmts data to base staton (BS) over a sngle hop, whch may consume more energy. LEACH and PEGASIS [4] s a chan-based protocol and each node communcates only n a close neghbor node and takes turns to transmt data to the snk. In HEED [5], cluster heads are decded based on the average mnmum reach ablty power and closer to the clusters or to be the snk, t saves the energy to the nter-cluster. Most of the clusters around the snk wll produce a large number of summary packets that leads to heavy traffc load. Selected and approprate cluster-head electon s an essental consderaton Tele: E-mal addresses: srlakshmvj@gmal.com 015 Elxr All rghts reserved

2 334 V.Vnoba and S.M.Chthra/ Elxr Appl. Math. 84 (015) and nodes locaton and connectvty have been ntally focused. NECHS [7] uses fuzzy logc technque consderng two factors: neghbor nodes and remanng energy. Cluster heads elected n [8] are determned to have mnmum composte dstance of sensors to cluster head and cluster head to base staton. The cluster-head selecton depends on remanng energy level of sensor nodes for transmsson n [9]. The frst trajectory based clusterng technque for selectng the cluster heads and meanwhle extenuates the energy whole problem n H. Munaga, et al. [10]. DBCP [11] mproves LEACH on the bass of a metrc of nodes relatve densty. In general, Game theory and mechansm desgn have been used wth great success n analyzng routng algorthms n the planner network topology. FDG [14] s a game theoretc approach wth the probablty of strategy selecton based on the mxed strategy Nash equlbrum of the game. Comparng to AODV [15], t lmts the number of redundant broadcasts n dense networks whle stll allowng connectvty. VGTR [16] judges the energy consumpton of the paths and takes notce of nodes wth low remanng energy or hgh nformaton value. The dstance between nodes, remaned energy and load traffc together contrbute to the cost of transmsson n [17]. The am of algorthm s to mantan a postve proft of all nodes. Most of the routng algorthms adopt game theory on the herarchcal topology. DEER [18] adopts a game-theoretc model wth both remaned energy and average energy loss on among neghborng nodes under consderaton whle evaluatng the utlty functon for determnng cluster heads. Intra-cluster and nter-cluster routng schemes ncludes n DTTR [19] wth the utlzaton of multstage fntely repeated games and the lnk qualty ndcaton (LQI) based metrc method, the energy consumpton s balanced. F. Kazemeyn, et al. [] combnes a modfed verson of the AODV protocol wth coaltonal game theory to fnd the cheapest route n a group wth respect to power consumpton. How to choose correspondng leaders s not mentoned though.. In [], the Nash barganng soluton (NBS) s used for analyzng clusterng based sensor network. Harsany transformaton s ntroduced to form a statc game of complete but mperfect nformaton. G. Z. Zheng, et al. [3] analyzes routng n WSNs based on a Bayesan game. Routng Protocols Routng s complex n WSN due to dynamc nature of WSN. It has a lmted battery lfe, computatonal overhead, no conventonal addressng scheme, self-organzaton and lmted transmsson range of sensor nodes [4], [5] and [6]. As sensor has lmted battery and ths battery cannot be replaced due to area of deployment. Therefore the network lfetme depends upon sensors battery capacty. Most needed management of resources s to ncrease the lfetme of the wreless sensor network and Qualty of routng protocols. It depends upon the amount of data (actual data sgnal) successfully receved by Base staton from sensors nodes deployed n the network regon. of routng protocol has been proposed for wreless sensor network. Manly there are three types of routng protocols we have (1) Flat routng protocols () Herarchcal routng protocols (3) Locaton based routng protocols. The category of Herarchcal routng protocol s provdng maxmum energy effcent routng protocols [1], [], [3], [4] and [7]. of herarchcal routng protocol has been proposed s consderng as a Basc energy effcent herarchcal routng protocol s LEACH (Low Energy Adaptve Clusterng Herarchy). Many protocols have been derved from LEACH wth some modfcatons and applyng advance routng technques. Ths paper dscus and compare a herarchcal routng protocols. They are all energy effcent routng protocols and provde qualty enhancement to LEACH-M. Leach protocol (low energy adaptve clusterng herarchy) LEACH s one of the frst herarchcal routng Protocols. It s used n wreless sensor networks for ncreasng the lfe tme of network and performs self-organzng and re-clusterng functons for every round [1]. In the LEACH routng protocol each and every sensor nodes act as a clusters. In every cluster one of the sensor node acts as cluster-head and remanng sensor nodes as member nodes of that cluster. Cluster-head only can drectly communcate all the nformaton s to snk and member nodes use cluster-head as ntermedate router n case of communcaton to snk. It collects the data from all the nodes, aggregate the data and route all the meanngful nformaton to Snk. Due to these addtonal responsbltes Cluster-head dsspates more energy and f t remans cluster-head permanently t wll de quckly as happened n case of statc clusterng so n ths way LEACH can solve the problem by randomzed rotaton of cluster-head to save the battery of ndvdual node [4], [5]. In ths ways LEACH maxmze lfe tme of network nodes and also reduce the energy dsspaton by compressng the date before transmttng to cluster-head. LEACH routng protocol operatons based on rounds. Each round normally conssts of two phases. () Setup phase and () steady state phase. In the setup phase cluster-head and cluster are created and the whole network nodes are dvded nto multple clusters. Some nodes elect themselves as a cluster-head ndependently from other nodes and these nodes are elect themselves on behalf suggested percentage P and ts prevous record as cluster-head. Nodes whch were not cluster-head n prevous 1/p rounds generate a number between 0 to 1 and f t s less then threshold T(n) then nodes become cluster-head. Threshold value s set through ths formula. P 1 T n 1 P r mod f n ϵ G ( ) p 0, otherwse Where G s set of nodes that have not been cluster-head n prevous 1/p rounds, P s the cluster-head probablty, r s current round. If the node becomes cluster-head n current round and t wll be a cluster-head after next 1/p rounds [4], [5], [6] then t ndcates that every node wll serve as a cluster-head equally and energy dsspaton wll be unform throughout the network. Noncluster-head node wll select ts multple of cluster-head from where node receved advertsements. Cluster-head fnally wll create TDMA (Tme Dvson Multple Access) schedule for ts assocated members n the cluster. In Steady state phase starts when clusters have been created. In ths phase nodes communcate to cluster-head durng allocated tme slots otherwse nodes completely keep sleepng. Due to ths man attrbute LEACH mnmze energy dsspaton and extend battery lfe of all ndvdual nodes. An amount of energy can be used n fgure (a) s amp K 3d d 1 Whereas the amount of energy used n fgure (b) s amp K 3d d 1 These are all the amount of energy depleton by data transfer formula.

3 3343 V.Vnoba and S.M.Chthra/ Elxr Appl. Math. 84 (015) Energy beng dsspated to run the transmtter s E elec 50nj / bt. Fgure 1. Drect transmsson and Mnmum transmsson energy Energy dsspaton of the transmsson amplfer s 100 pj / bt / m amp E K, d E K Kd Transmsson cost s Tx elec amp and fnally the Recevng cost s E K E K Rx Where K s the length of the message n bts d s the dstance between nodes n s a random number between 0 and 1 and represents the path-loss exponent ( ). elec In [3], new cluster head selecton algorthm s establshed, n whch cluster head s decded by Snk node accordng to ts energy n the lst. The man energy consumpton of these handlngs comes to snk node whose energy s free, therefore, ELEACH-M an balance energy consumpton and prolong entre network perod comparng wth LEACH. However, n ELEACH-M, cluster nodes frequently need to send control frame to cluster head, makng waste energy of the network. Besdes, the mprovement of ELEACH-M a data delvery mechansm s only consdered on the aspect of energyeffcency, not data-effcency. In [4] Zhou desgns based on the Dfferentated Servces, whch dvdes data nto common and exgent. When dealng wth common data, the request of data relablty s not very hgh, therefore, source node can choose a path to snk node dependng on probablty for data delvery, whch can save energy. Emergency takes place only to ensure the exgent data delvered to snk s accurate, the source node wll synchronously start all non-nter secant paths to Snk, satsfyng users requre for unexpected emergent events. In other words, ths paper uses redundancy manner to mprove ts relablty. The followng fgure 4. Shows that dfferent processes of nodes n LEACH protocol. Fgure. LEACH bad and good Scenaro Both of these dagrams s the optmum scenaro, comparatvely second s better because the cluster-heads are spaced out and the network s more properly sectoned n fgure. Eleach-M (Enhancement Of Mult-Hop - Protocol) It s an mproved verson of LEACH called enhancement of mult-hop leach (ELEACH-M). There was no matter wth the dstance from the CH to BS. The CH always communcates wth the BS so t wll consume a lot of energy. The focus only on the heterogeneous sensor networks, n whch two types of sensors are dsplayed: Frst s Hgh capacty sensor and second s a smple sensor. The sensors whch have a large capacty

4 3344 V.Vnoba and S.M.Chthra/ Elxr Appl. Math. 84 (015) processng capabltes and communcates very ntensvely and acts as cluster head s a hgh capacty sensor whle others are n smple sensors and they have lmted power, afflated to the closest CH n ther neghborhood and communcates wth t drectly Moble Enhanced. The followng fgure 5. Shows that Routng of Mult-hop LEACH Protocol. We assume the followng notons λ 1 : Arrval rate of TCP λ : Arrval rate of UDP μ 1 : servce rate of TCP μ : Servce rate of UDP L: Length of queue A t : of TCP arrved at queue A u : of UDP packets arrved at queue P t : of TCP stored at queue P u : of UDP packets stored at queue D t : of TCP to be dropped n model-1 D t: of TCP to be dropped n model- D u : of UDP to be dropped P dt : probablty that droppng TCP packets n model-1 P dt: probablty that droppng TCP packets n Model-. D t s computed as follows n model-1 Fgure 5. Routng of Enhancement of Mult-hop LEACH Protocol Authors n [7] ntroduced a new verson of LEACH wth a moblty factor. ELEACH-M uses the same threshold formula based on the orgnal LEACH. It s used to calculate the threshold, but ELEACH-M takes nto consderaton the moblty of nodes durng data transfer phase, whch LEACH does not. The moblty tself s a challenge because moble node can leave cluster whle t s transmttng data to a CH. ELEACH-M solves ths problem by confrmng whether a moble node stll able to communcate wth CH or not to TDMA schedule. In the begnnng of each TDMA slot, the CHs transmt the message to REQ-DATA-TRANSMITION. If the moble node s unable to receve the message then the CH wats for the request n the next TDMA slot and f the node msses two successve TDMA frames, t consders tself out of range, and the CH wll remove unreachable nodes from ts member lst. Analytcal Model We consder two models Model-1 & Model -, model -1 for sngle queue and model- for Double queue are shown n fgures 6 & 7. Fg 6. Model -1 Sngle queue Fgure 7. Model-.Double queue D t = [A t -[L-(P u +P t ) ] f [L-(P u +P t )] A t 0 f [L-(P u +P t )] >A t P dt s computed as follows Dt Pdt A t D / t s computed n model - as follows [A t -(L / - P t )] f (L / - P t) A t D t = 0 f [L / - P t ] >A t P / dt s computed as follows P ' dt D A ' t t P dt P dt f ( P u > L / ) Here we proved that Probablty that droppng TCP packets n Model- s less than Probablty that droppng TCP packets n Model-1. Game Theory In early 1950's John Nash recognzed that n non cooperatve games there exst sets of optmal strateges (socalled Nash equlbrum) used by the players n a game such that no player can beneft by unlaterally changng hs or her strategy f the strateges of the other players reman unchanged. Recently game theory has been used extensvely to model networkng problems, where dfferent players may have dfferent strateges for network usage. Game theory s a formal way to analyze nteracton among a group of ratonal players who behave strategcally. A game s the nteractve stuaton, specfed by the set of players (.e., sensor nodes), the possble actons of each node, and the set of all possble payoffs. Games n whch the actons of the players are drected to maxmze ther own proft wthout subsequent subdvson of the proft among the players are called Cooperatve Games. Game theory provdes a good framework wth concepts of a coalton and coaltonal value and dfferent notons of stablty. Cooperatve game-theoretc models can be used to do ths for self-motvated agents (sensor nodes), each of whch has tasks t must fulfll and resources t needs to complete these tasks. Although the agents (sensor nodes) can act and reach goals by themselves, t may be benefcal to jon together. Behavor of sensor nodes can be coordnated based on Nash Equlbrum proposed n Game theory to acheve some desred objectves. The proposed game s expressed as: N,, where N s S P the set of sensor nodes, S the set of strateges of sensor nodes, and P the payoff functon for node.

5 3345 V.Vnoba and S.M.Chthra/ Elxr Appl. Math. 84 (015) () Payoff functon The payoff functon between sensor nodes s composed of two mportant factors: cooperaton, reputaton. The Stronger cooperaton between two nodes means the more relable data communcaton between them. Also, the more a node cooperates, the better ts reputaton s. The payoff between two sensor nodes should be dependent on ther dstance and each node's transmtter sgnal strength. () Game Strategy Each sensor node utlze ts strategy accordng to the nformaton t attaned n precedng tme slots n the lght of the followng factor: (1) reputaton sensor nodes have not made enough reputaton to trust each other and cooperate wth each other, () dstance d s the closer to two nodes, the more they j trust each other. All the sensor nodes wll cooperate wth each other successfully accordng to reputaton level, and closeness of sensor nodes. Bayesan Theory of Games Bayesan ratonal pror equlbrum requres agent to make ratonal decsons and statstcal predctons. Startng wth frst order non nformatve pror and keeps updatng wth statstcal decson theoretc and game theoretc reasonng untl a convergence of conjectures s acheved. So far we have been assumng that everythng n the game was common knowledge for everybody playng, n fact the players may have prvate nformaton about ther own payoffs, about ther type or preferences etc. In ths stuaton the way of modelng of asymmetrc or ncomplete nformaton s by recurrng to an dea generated by Harsany (1967). The key s to ntroduce a move by the Nature, whch transforms the uncertanty by convertng an ncomplete nformaton problem nto an mperfect nformaton problem. In a Bayesan game, a state refers to a possble scenaro that may be realzed n the game. Bayesan games are n multple states and types that are used to summarze the degree to whch each player can dfferentate between the states. Due to nstance, n a Bayesan game wth two states, a player wth two types can dstngush between the states whle a player wth one type cannot. For a player wth multple types n Bayesan, each type has a separate set of preferences that correspond wth a partcular state of the game. The dea s the Nature moves determnng players types, a concept that embodes all the relevant prvate nformaton about them such as payoffs, preferences, belefs about other players, etc. Defnton A Bayesan Game s a game wth ncomplete nformaton n a normal form that conssts of 1,,.....I. () Players () a fnte acton set for each player () A fnte type set for each player (v) A probablty dstrbuton over type belefs about the players types). (v)utltes u j a A : A1 XA X... AI X 1X ϴ p / (Common pror X... Now t s mportant to dscuss a lttle bt each part of the defnton. Players types contan all relevant nformaton about certan player s prvate characterstcs. The type s only observed by player, who uses ths nformaton both to make decsons and to update hs belefs about the lkelhood of opponents type. (Usng the condtonal probablty p / I. Combnng actons and types for each player t s possble to construct the strateges. Strateges wll be gven by a mappng from the type space to the acton space, s : A wth elements s. In words a strategy may assgn dfferent actons to dfferent types. Fnally, utltes are calculated by each player by takng expectatons over types usng hs or her own condtonal belefs about opponents types. Hence, f player uses the pure strategys, other players use the strateges s and player s type s, the expected utlty can be wrtten as s / s, Eu u s s,, p /, Bayesan Nash Equlbrum (BNE) A Bayesan Nash Equlbrum s bascally the same concept than Nash equlbrum wth the addton that players need to take expectatons over opponents types. Defnton A Bayesan Nash Equlbrum (BNE) s a Nash Equlbrum of a Bayesan Game, (.e) ' ' E s / s, E s / s, s S and for u u for all all types occurrng wth postve probablty. Theorem: Every fnte Bayesan Game has a Bayesan Nash Equlbrum. Bayesan Network The prmary hypothess varable for the Bayesan network was the degree of nterest. We could not test the accuracy of predcton drectly related to the hypothess varable. Bayesan network survey ncludes two ndcators of degree of nterest, nterpersonal counterproductve behavor and organzatonal counterproductve behavor. We used these varables as crtera to examne the extent to whch the changes n the Bayesan network affected ts ablty to predct counterproductve behavor. The followng strategy was used to test the predctons of the Bayesan network. The network processed a number of cases n whch the values of varables ncluded n the paper. These values were entered nto the network as fndngs (or evdence), and the network then predcted the probablty of counterproductve behavor based on ths evdence. The predcted values were then compared to the actual values to assess the correctness of the predctons. For the orgnal and then the revsed Bayesan network, we conducted ths analyss for a set of cases smulated usng the Bayesan network to get an upper bound on the possble accuracy of model predcton and repeated the analyss usng actual cases from the survey data set. The two sources are () smulated cases that were generated by the Bayesan network tself, and () emprcal cases based on responses to the survey. The emprcal cases were drawn drectly from the survey measures, but were normalzed to have means and standard devatons that corresponded to the comparable varables n the Bayesan network. The smulated cases provded a baselne aganst whch the qualty of the predctons of emprcal cases was assessed. Smulaton and Results In ths secton, t descrbes the smulaton and varous parameters chosen for smulaton. The varous performance metrcs used to compare the performance of LEACH aganst ELEACH-M. The followng table 3 shows the varous parameters and ther values.. I

6 3346 V.Vnoba and S.M.Chthra/ Elxr Appl. Math. 84 (015) The ELEACH-M has been mplemented by usng Network Smulaton-(NS-), t s a standard smulator. The channel bandwdth s Mbps. A free space rado propagaton model s used n whch the sgnal power attenuates s 1/r, where r s the dstance between the nodes. All the nodes have the same transmsson range of 50 meters. The dstrbuted coordnaton functon of IEEE80.11 s used MAC layer. All nodes can overhear packets destned for others. The nodes are deployed at random locatons n a 1000mx 1000m regon. Smulator NS-.34 Verson Network Model Network sze 1000m x 1000m of Nodes 50 Node placement Unform Physcal Layer Sgnal Propagaton Two-ray ground Model reflecton model Transmsson Range 50m MAC Layer IEEE Routng Layer Moblty Model Traffc Model Lnk Bandwdth Interface Queue Mbps FIFO-BASED, Sze 50 ELEACH-M, LEACH Requested bandwdth 0.1Mbps to 0.6 Mbps Smulaton Tme 300 Sec Random-way pont model Maxmum Speed 5,10,15,0 m/s Pause Tme 5 sec Constant Bt Rate (CBR) of Source- 3 to 10 Destnaton pars Data Packet Sze 51 bytes Energy Intal energy of each 6 Joules Consumpton node Model Transmttng Power 0.360mW Recevng Power 0.335mW Idle Power 0.13mW For the moble scenaros, the random waypont model s used for node moblty. In ths model, a node chooses a random pont n the network. It moves towards ts destnaton pont at a constant speed. The speeds are unformly chosen between the mnmum and maxmum speeds and are set 0 m/s and 0 m/s, respectvely. If the node reaches ts destnaton pont, t stays there for a certan pause tme, after whch t chooses another random destnaton pont and repeats ths process and the smulaton ends after 300sec. The data traffc s generated by Constant Bt Rate (CBR) sessons ntated between the source and destnaton. All the nodes are assumed to have the same amount of battery capacty wth full energy at the begnnng of the smulaton and ntal energy of each node s 6 Joules. Whle transmttng power and recevng power of each node s 0.360mW and 0.335mW respectvely. In ths smulaton, a group of data rates rangng from 3 kbps to 104 kbps s appled, the moblty scenaro s wth a pause tme of 3 seconds and the maxmum node speed s 5 m/s. The followng quanttatve metrcs are used to measure the performance of protocols. Packet Delvery Rato Packet Delvery Fracton (PDF): The rato of the number of packets generated by the sources to the number of packets receved by the destnatons. PDF= ( of Data packets receved/ of Data packets sent) * 100. From fgure 8, t can be seen clearly that the LEACH-M and ELEACH-M have approxmately equal PDR at low data rate (data rate below 51 kbps). When the data rate of traffc flow ncreases to kbps to 56 kbps. Fgure 8. Data rate Vs Sent Data packets Fgure 9. Data rate Vs Receved Data Fgure 10. Data packet delvery rato versus speed The PDR of LEACH suddenly drops from 98% to 60%. At hgher data rates ELEACH-M performs better than to LEACH, because In the ELEACH-M, the route s selected based on bandwdth and energy. Packet delvery rato s drectly proportonal to the bandwdth and energy. Fg.9 shows that number receved data packets n ELEACH-M are greater than number receved data packets n LEACH. The comparson of packet delvery rate Vs speed s shown n fgure 10. The packet delvery rate of ELEACH-M s hgher than LEACH due to less lnk breaks. In LEACH, three events may occur; soluton s mmedately alternatve path s chosen wthout delay. The probablty of lnk falure n the ELEACH-M s less than the probablty of lnk falure n the LEACH, as the speed of the nodes ncreases, the probablty of lnk falure ncreases and hence the number of packet drops also ncreases. The ELEACH-M has hgher packet delvery rato than LEACH. End -To-End Delay Average end-to-end delay s the delay of data propagaton, transfer and the delays caused by queung, bufferng and retransmttng data packets. The delay of each packet= the tme

7 3347 V.Vnoba and S.M.Chthra/ Elxr Appl. Math. 84 (015) of receved data packets - the tme of sent ths data packet. The average end to end delay s then computed as: Average delay =Total delay of each data packets / total data packets receved. Generally, there are three factors affectng end-to-end delay of a packet: () Route dscovery tme, whch causes packets to wat n the queue before a route path s found. () Bufferng watng tme, whch causes packets to wat n the queue before they can be transmtted. () The length of routng path. The more number of hops a data packet has to go through, the more tme t takes to reach ts destnaton node. Whle n the real tme communcatons, each packet whch arrves late could be useless although they reach the destnaton successfully. Real tme traffc s delay senstve. Routng Overhead It s equal to the number of routng packets transmtted per data packet delvered at destnaton. Each hop-wse transmsson of a routng packet s counted as one transmsson. It s also known as Normalzed Routng Load (NRL). It s also defned as NRL = of control packets generated /number of receved data packets. The routng overhead s an mportant metrc to compare the performance of dfferent protocols snce t gves a measure of the effcency of protocols, especally n a low bandwdth wth congested wreless envronments. Protocols that transmt a large number of packets can also ncrease the probablty of packet collsons and watng tme of data packets n transmsson buffer queues. Fgure 11. Data rate Vs Average Delay Fgure 13. Overhead Vs Data rate Fgure 1. Average delay Vs Speed From fgure 11, t can be seen clearly that the ELEACH-M and LEACH have low and approxmately equal average delay at low data rate (data rate below 56 kbps). When the data rate of traffc flow ncreases to kbps to 51 kbps. It shows that networks wth the ELEACH-M routng protocol can provde lower end to end delay for traffc flows than the LEACH because the ELEACH-M always choose to fnd a route wth satsfyng data rate and energy. In addton to that, durng the transmsson, the QoS of the traffc s montored. Fgure 1 depcts the varaton of the average end-to-end delay as a functon of moblty of nodes. It can be seen that the general trend of all curves s an ncrease n delay wth the ncrease of velocty of nodes. Manly the reason s that hgh moblty of nodes results n an ncreased probablty of lnk falure that causes an ncrease n the number of routng redscovery processes. Ths makes data packets have to wat for more tme n ts queue untl a new routng path s found. The delay of ELEACH-M remans approxmately equal at all Statc snks. In LEACH, the delay ncreases quckly as node moblty ncreases. In the avalablty of alternate node-dsjont routng paths n ELEACH-M elmnates route dscovery latency that contrbutes. In addton, when a congeston state occurs n a routng path, the source node s dstrbuted ncomng data packets to the other node-dsjont routng paths to avod the congeston. Ths reduces the watng tme of data packets n queue. Fgure 14. of control packets Vs Data rate Fgure 15. of control packets Vs Speed Fgure 13 shows the Overhead Vs data rate. At low moblty; sngle path routng generates less overhead than multpath. At hgh moblty, frequently lnks falure, so the route dscovery s repeatedly performed by the sources to fnd new routes due to overhead ncreases. It has shown that the normalzed routng load n ELEACH-M performs better than the LEACH when speed ncreases. The normalzed routng load n LEACH ncreases more quckly than that n ELEACH-M wth the ncrease of moblty. ELEACH-M generates less overhead due the followng reason, whle durng route dscovery tself. It elmnate the some paths f they don t support QoS, ths result n an ncreased packet delvery rato, decreasng end-to-end delays

8 3348 V.Vnoba and S.M.Chthra/ Elxr Appl. Math. 84 (015) S. No. for data packets, lower control overhead, and fewer collsons of packets. Fgure 14 and fg.15 show the number of control packets Vs date and the number of control packets and speed respectvely Energy consumpton The nodes n a WSN are typcally powered by batteres whch have lmted energy reservor. It becomes very dffcult to recharge or replace the battery of nodes. In such stuatons energy conservatons are essental. The lfetme of the nodes show strong dependence on the lfetme of the batteres. In the WSN nodes depend on each other to relay packets and the lst of some nodes may cause sgnfcant topologcal changes, undermne the network operaton, and affect the lfetme of the network. The comparson of energy consumpton s shown Fg.16 and fg 17. Fgure 16. Energy consumpton aganst Data rate Fgure 17. Energy consumpton aganst Lfe Tme Result (I) Eleach-M of Data sent (X) of Data Receved (Y ) PDF= Y/X*100 of Control generated (Z) Total energy Consumpton Total delay of data packets (II) Leach S. No. of Data sent X of Data Receved Y PDF= Y/X*100 of Control generated Z Total energy Consumpton Total delay of data packets Concluson In ths paper, we proposed an energy effcent protocol for WSNs. Our approach can be useful for applcatons that requre scalablty, prolonged network lfetme and node are dspersed n a large spacous feld. It depends on overhead and load, the path falure manly depends on due to lack energy of any one node on selected path. That t was elmnated n ELEACH-M. The ELEACH-M consumes less energy than to LEACH and to maxmze the lfetme of network. Each node mantans mnmum energy level drng the transmsson of data, each node checks whether ts energy reaches to threshold or not. If ts energy reaches to threshold value, then node sends a EERP packet to the source node n reverse path. The source node mmedately selects the alternate route. References [1] Akyldz and W. Su, Y. Sankarasubramanam and E. Cayrc, A Survey on Sensor Networks, IEEE Commun. Mag., vol. 8, (00), pp. 10. []. WANG Xuan-zheng, LI La-yuan, ZHANG We-hua, and ZHANG Lu- mn, Research on routng protocol for wreless sensor networks, APPLICATION RESEARCH OF COMPUTERS, 009, pp. 6(4) [3] Zhou Xn-Lan, Wang Run-Yun, Relable Data Delvery Algorthm based on Dfferentated Servce n WSNs, Electronc Computer Technology, 009 Internatonal Conference on 0- Feb. 009 pp [4] W. Henzelman, A. Chandrakasan, and H. Balakrshnan, Energy-effcent routng protocols for wreless mcrosensor networks, n Proc. 33rdHawa Int. Conf. SystemScences(HICSS), Mau, HI,Jan [5] Henzelman W. B., Chandrakasan A. P., Balakrshnan H., An applcaton- specfc protocol archtecture for wreless mcrosensor networks, IEEE Trans on Wreless Communcatons, Vol. 1, No. 4, 00, pp , do: /TWC [6] X. H. Wu, S. Wang, Performance comparson of LEACH and LEACH- C protocols by NS, Proceedngs of 9th Internatonal Symposum on Dstrbuted Computng and Applcatons to Busness, Engneerng and Scence. Hong Kong, Chna, pp , 010 [7] P.T.V.Bhuvaneswar and V.Vadeh Enhancement technques ncorpo- rated n LEACH- a survey Department of Electroncs Engneerng, Madras Insttute Technology, Anna Unversty Chenna, Inda, 009. [8] D. S. Km and Y. J. Chung, "Self-organzaton routng protocol supportng moble nodes for wreless sensor network," n Proc. Frst Internatonal Mult-Symposums on Computer and Computatonal Scences, Hangzhou, Chna, 006. [9] C. Xu and L. Cao, G. A. Zhang and J. Y. Gu, Edtors, Applcaton Research of Computers, vol. 3, (010), pp [10] W. Henzelman, A. Chandrakasan and H. Balakrshnan, Energy-effcent Routng Protocols for Wreless Mcrosensor Networks, Proceedngs of the 33rd Annual Hawa

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