1. Introduction ISSN: Issue 2, Volume 7, February 2008

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1 J. Levendovszky, A. Boárszky, B. Karlóca, A. Oláh Enery balancn by combnatoral mzaton for wreless sensor networks J. LEVENDOVSKY, A. BOJÁRSKY, B. KARLÓCAI, A. OLÁH Faculty of Informaton Technoloy Pazmany Peter Catholc Unversty Prater utca 50/a, H-083, Budapest HUNGARY http//: Abstract: - In ths paper novel protocols are developed for wreless sensor networks (WSNs) n order to ensure relable packet transmsson and maxmze lfespan at the same tme. The mal transmsson eneres are derved whch uarantee that the packets are receved by the Base Staton (BS) wth a ven relablty subect to achevn the lonest possble lfespan. These protocols can be appled n bomedcal applcatons where enery consumpton and lonevty s of crucal mportance. The mzaton has been carred out for the chan protocol (when nodes are forwardn the packets toward the BS va the nehbourn nodes) and for the shortcut type of protocols (when a packet may et to the BS by ben frst transferred n the chan up to a certan node whch then sends t drectly to the BS). The new results have been tested by extensve smulatons whch also demonstrated that the lfespan of WSN can snfcantly be ncreased by the new protocols. Keywords: Communcaton systems, Communcaton system routn, Network relablty, Protocols.. Introducton Due to the recent advances n electroncs and wreless communcaton, the development of lowcost, low-power, multfunctonal sensors have receved ncreasn attenton []. These sensors are compact n sze and besdes sensn they also have some lmted snal processn and communcaton capabltes. However, these lmtatons n sze and n enery make WSNs dfferent from other wreless and ad-hoc networks [2]. As a result, new protocols must be developed wth specal focus on enery balancn n order to ncrease the lfetme of the network whch s crucal n case applcatons, where recharn of the nodes s out of reach (e.. medcal applcatons, mltary feld observatons, lvn habtat montorn etc., for more detals see [3]). The paper addresses relable packet transmsson n WSN when packets are to be receved by the Base Staton (BS) wth a ven relablty, n terms of keepn the error probablty under a ven threshold [4]. Snce the success of every ndvdual packet transmsson depends on the dstance and the transmsson enery [5,6], the probablty of correct recepton wll dmnsh exponentally wth respect to the number hops, n the case of multhop packet transfers [7]. As a result to ncrease relablty two dfferent protocols wll be nvestated: Chan protocol when packet transfer takes place over a D chan of nodes (created some routn alorthm runnn pror to the packet transfer), and the nodes send each packet to ther nehbours on the nearsde of the BS. Shortcut protocol when the packet travels n the chan up to a certan node whch then sends t drectly the BS (shortcut). Our concern s to derve the mal transmsson eneres for each scenaro needed to acheve a ven relablty (.e. a packet s receved correctly by the BS wth a ven probablty reardless of ts source node) and yeldn the lonest possble lfespan of the network. As demonstrated n the paper ths leads to a constraned mzaton problem whch s solved by combnatoral mzaton tools. The soluton yelds the mal enery matrx G, the G element of whch ndcates what s transmsson enery node should appled to transmt the receved packet when t s ornated from node (the destnaton of the transmsson depends on the specfc protocol, e,. n the case of chan protocol node must retransmt the packet to ts nehbour, whle n the shortcut protocol node may choose to send the packet drectly to the BS). ISSN:

2 J. Levendovszky, A. Boárszky, B. Karlóca, A. Oláh 2. The model After the routn protocol (e.. PEDAP [8]) has found the path to the base staton the subsequent nodes partcpatn n the packet transfer can be rearded as a one dmensonal chan labeled by =,..., N and depcted by the F.. F. One dmensonal chan model for WSN The system s characterzed as follows: the topoloy s unquely defned by a dstance vector d = ( d,..., dn ), where d, =,..., N denotes the dstance between node and -, respectvely; the enery needed to transmt packet over α 2 d Θσ dstance d s ven as = + 0 dctated ln p by the Rayleh model, where d s the dstance, α depends on the propaaton type, p s the relablty of correct recepton, Θ s the 2 threshold, σ s the nose enery, whle 0 represents the consumpton of the electroncs durn transmttn and recevn; the functon connectn the relablty parameter p of the transmsson wth the transmsson enery s denoted by p =Ψ ( ) for short, furthermore f a packet s transmtted from node to the nehbourn node - then the correspondn transmsson power s denoted by p and the relablty of ths snle transmsson p =Ψ ; s ( ) we assume that only one node enerates a packet at a tme; the nodes operate n a tme synchronous manner where the dscrete tme (clock snal) s denoted by k = 0,,2,... ; the ntal battery power on each node s the same and denoted by C and the enery state of the nodes at the k th tme nstant s expressed by c ( k) = c ( k),..., c ( k) ; vector ( ) As a result, a WSN s fully characterzed by vectors, p, and c respectvely. N 3. Relable packet transfer wth a ven probablty In ths secton we nvestate relable packet forwardn as a constraned mzaton problem. Ths problem arses from the fact that n the case of multhop communcaton, the probablty of correct = packet recepton at the BS s P C p, and the = α 2 d Θσ assocated eneres are = + 0, ln p =,...,. As a result, a ven P C can be acheved by several choces of p -s (.e. several factorzatons) yeldn dfferent enery consumptons. Our concern s to pck the mal factorzaton whch wll yeld mnmal enery consumpton n terms of maxmzn the remann enery on the bottleneck node (the node whch has the smallest enery). We wll treat ths constraned mzaton problem n two dfferent scenaros: chan protocol (packets are transferred downward n the chan towards the BS n a nodeby-node fashon); shortcut protocol (frst the packet s traveln n the chan from node to node, then from a certan node t s drectly transmtted to the BS). In the frst case, we are concerned wth dentfyn the mal enery scenaro to yeld maxmum lonevty. In the second case, not only the mal enery vector but also the mal node ndex must be found where the shortcut to the BS wll take place. 3.. Relable packet transfer by chan protocol In ths case, we assume that every node retransmts the receved packet to ts nehbour towards the BS. For a packet enerated at node and traveln to the BS the relablty constrant s ven as = ( ) PC = Ψ = ε () In order to ensure maxmum lonevty, our obectve s to enforce a packet transfer whch maxmzes the mnmum remann enery expressed as follows: ISSN:

3 J. Levendovszky, A. Boárszky, B. Karlóca, A. Oláh :maxmn c ( k + ), (2) where c ( k ) c ( k) + = and = (,...,,0...0). Here k denotes the number of packets sent to the BS. The mzaton method to solve (2) s descrbed n Secton 5. Once the mal soluton () = (,...,,,0...0), =,..., N has been found the soluton can be downloaded to each node (n our example to node l) n the Table. Table. Routn table of chan protocol Source node ndex N N- Transmsson enery whch maxmzes the lfespan : : l+ l ( N ) l, ( N ) l, ( l ) + l, () l l, When a packet arrves at node l from source node then t can be retransmtted to from node l to node l- () wth the correspondn enery read out form l, (), the table. In ths way, G, = and the tables downloaded to the node are obtaned from the correspondn column of G Relable packet transfer by shortcut protocol In ths case, the packet emtted by node traverses down n the chan to node n a node-by-node fashon and from node t ets drectly transmtted to the BS. The enery needed to transmt the packet from node l to node l- n the chan s denoted by l, + l, whereas the enery needed to et the packet from node drectly to the BS s denoted by G. ( G) ( l) Ψ Ψ = ε, (3) l= + In order to ensure maxmum lonevty, our obectve aan s to enforce a packet transfer whch maxmzes the mnmum remann enery of partcpatn nodes, ven as: :maxmn cl ( k + ), l (4) where ( ) ( ) c k + = c k and l l l ( 0,..,0, G, +...,,0...0 ) =, where k denotes the number of packets sent to the BS. Once the mal soluton () = 0,..,0, G,...,,0...0 has been ( + ),, found the soluton can be downloaded to each node (n our example to node l). When a packet arrves at node l from a ven source node then t can be retransmtted from node l to node l- or t can be shortcut to the BS wth the correspondn eneres read out form the table. 4. Protocol mzaton In ths secton the mzaton process s descrbed to obtan the enery vectors whch maxmze the lfespan n the case of the dfferent protocols. As was seen n the prevous chapter, protocol mzaton amounts to solvn the mzaton problems n (2) and (4). The requred transmsson probablty can be calculated by the follown: p = PC, (5) therefore the follown ntalzed p r can be calculated: M : C p = P. (6) Snce (2) s defned over a dscrete set the mum s souht by stochastc search akn to the Mathas alorthm. The transmsson probablty mzaton (TPO) alorthm s descrbed n F. 2. Then the relablty constrant can be expressed as ISSN:

4 J. Levendovszky, A. Boárszky, B. Karlóca, A. Oláh F. 2 The flow daram of the TPO alorthm The steps of the TPO alorthm are ven as follows: STEP 0. STEP. STEP 2. STEP 3. we set the ntal p vector n unform manner; by matrx P mod, we modfy vector p subect to the condton that the product of the components remans the same: P = P Pmod, k and Pk = Pk Pmod, k, k, ; we calculate the transmsson enery vector m ; ( ) we evaluate the obectve functon (2) and check whether the newly obtaned soluton ( m) s better the prevously stored ; STEP 4. f yes then ( m) ets stored and we set m = 0 ; STEP 5. f not then ( m) s dscarded and STEP 6. remans unchaned whle m= m+ ; f m equals the smulaton parameter N smparam then the alorthm ends. One must note that nstead of the alorthm descrbed above, any other methods of combnatoral mzaton can be used, such as Genetc Alorthms or Smulated Annealn. However, based on the emprcal studes and smulatons we ran, we found that n the present case our alorthm convered faster to the mal soluton than other methods. 5. Numercal results In ths secton the performance of the protocols descrbed above are nvestated by extensve smulatons. 5.. Network descrpton and the propaaton model The smulatons were carred out n three dfferent scenaros all of them ncludn 0 sensors and placn them: equdstantly; random I (ther dstances were selected subect to truncated Gaussan dstrbuton); random II (ther dstances were selected subect to Posson dstrbuton); We set the follown parameters: The propaaton model s determned by the α 2 d Θσ Rayleh fadn, yeldn = + 0 ; ln p Condtonn enery needed by the electroncs 0 = 50μW ; Threshold: Θ= 0 6 ; Averae nose enery: σ = 0.; Propaaton parameter: α = 2 ; Intal enery: (0) = 00mW ; =,..., N. The lfespan was defned as the number of steps untl whch each node has the enery to transmt packets complyn wth the ven relablty parameter. As soon as, a node (the bottleneck node) oes flat (ben not able to partcpate n the relable packet transfer, because of falln short of the requred enery), then network s consdered dead Performance analyss Based on the dscusson above, one must note that the mzaton should be carred out after each packet transmsson as the remann enery c ( k) chanes wth respect to k. Snce the underlyn mzaton s tme consumn, we let the system run L steps after each mzaton cycles wthout chanes wth respect to the transmsson eneres. As a result, enery mzaton takes only every L steps, where we 2 r ISSN:

5 J. Levendovszky, A. Boárszky, B. Karlóca, A. Oláh nvestated the case of L=,3,5,7,5,20,50,00. In ths way, the computatonal overhead s reduced on the expense of achevn submal enery consumpton (the lfespan of the system s slhtly reduced). Fure 4. shows the effect of ncreased mzaton cycle on the lfespan (mzaton takes place only after each L steps). One can nfer that the larer L becomes the smaller an can be obtaned, whch s explaned by the fact that between two consecutve mzatons, the network must operates n nonmzed tme wndows. The next fure depcts the lfespan acheved by the shortcut protocol compared wth the mzed chan and non-mzed short-cut. The nvestated WSN contaned 0 nodes the locatons of whch were subect to Gaussan and the requred relablty was set 0.9 ( ε = 0.09 ). The fure exhbts the chane of enery on the bottleneck node wth respect to the number of sent packets. F. 4 The effect of ncreased mzaton cycle on the lfespan In the F. 5 the rato of mzed lfespan versus the non-mzed lfespan s depcted, as a functon of the relablty parameter and the number of nodes. We run the smulatons for dfferent relablty parameters: ε = 0.;0.09;0.08;0.05;0.0. One can see that the best an n lfespan s obtaned when ε=0. (P req = 0.9). On the other hand, the smaller the relablty parameter, the more complex the mzaton becomes. Furthermore, the an s further ncreased, when the number of nodes rows. F. 6 Mnmum node enery as functon of packets (P req =0.9, N=0) From the fure, one can see that the shortcut protocol s able to carry much more packet n ts lfetme than the chan protocol. In the follown bar chart the enery dynamcs of the bottleneck node of the chan and shortcut protocols are compared when the nodes are dstrbuted subect to equdstant, Gaussan and Possonan manner. F. 5 Lfespan on the bottleneck node (P req = P C ) F. 7 (Gan n span n the case of development protocols n the equdstant, Gaussan and Possonan located nodes (P req =0.9, N=0) It can be seen that the shortcut protocol tends to be the most superor, especally n the case of nodes dstrbuted n a Possonan fashon. ISSN:

6 J. Levendovszky, A. Boárszky, B. Karlóca, A. Oláh 6. Conclusons In ths paper, novel enery balancn packet forwardn methods have been developed to maxmze the lfespan of WSNs and to ensure relable packet transfer at the same tme. We have mzed the transmsson eneres of the nodes n order to mnmze the enery consumpton of the bottleneck node (the node wth the lowest avalable enery) subect to satsfyn a ven the relablty constrant. Two scenaro has been studed extensvely: () the tradtonal chan protocol (nodes are passn the ncomn packet to ther nehbours closer to the BS); () the random shortcut protocol (nodes make random choces subect to an mzed probablty mass functon) whether to forward the packet to the nehbourn node or sendn t drectly to the BS). The underlyn protocol mzaton was reduced to a constraned mzaton problem whch has been solved by a stochastc search alorthm. The performance of the protocols have been analyzed and compared to each other n the case of a 0-node WSN where the nodes were dstrbuted n equdstant or random fashon subect to Gaussan and Posson dstrbuton. The relablty constrant was set 0.9. Form the performance analyss one can nfer, that the shortcut protocol provdes loner lfespan (the obtaned an s approxmately.2). The results can drectly be used n any applcaton where enery consumpton and lfespan are of concern. One prmary taret feld s related to bomedcal applcatons, where the enery consumpton of sensoral mplants must be mnmzed (n order to avod the hazard of alvanc recharn va the human body). In ths case, relable but low-enery packet transfers of measurements from the body to the montorn BS s ndeed of crucal [9]. Our future plan s to extend the mzaton to protocols where transmsson from a node s allowed to any other nodes (not only to the nehbourn node or to the BS). Snce ths type of protocols has a hue combnatoral state space further work on the mzaton alorthm s needed as well to make the alorthm faster. References: [] C.Y. Chon and S.P. Kumar.. Sensor networks: Evoluton, opportuntes, and challenes. IEEE Proceedns, Auust, 2003 pp [2] A. Goldsmth and S. Wcker. Desn challenes for enery-constraned ad hoc wreless networks. IEEE Wreless Communcatons Maazne Vol. 9 Auust, 2002., pp [3] A. Manwarn, J. Polastre, R. Szewczyk, D. Culler, and J. Anderson.. Wreless sensor networks for habtat montorn. Frst ACM Workshop on Wreless Sensor Networks and Applcatons, Geora: Atlanta, September, [4] D. Puccnell and M. Haen. Wreless Sensor Networks-Applcatons and Challenes of Ubqutous Sensn. IEEE Crcuts and Systems Maazne Vol. 5,Auust, : [5] Wend Henzelman, Anantha Chandrakasan, and Har Balakrshnan. Enery-Effcent Communcaton Protocols for Wreless Mcrosensor Networks. Proc. Hawaaan Int'l Conf. on Systems Scence January, [6] N. Pantazs, D. Kandrs: Power Control Schemes n Wreless Sensor Networks, WSEAS Transactons on Communcatons, Issue X, Vol. 4, October 2005, pp [7] J. Levendovszky, B. Hey: Optmal Statstcal Enery Balancn Protocols for Wreless Sensor Networks. WSEAS Transactons on Communcatons, Issue V, Vol. 6, May 2007, pp [8] W. Henzelman, A. Snha, A. Wan, A. Chandrakasan. Enery-scalable alorthms and protocols for wreless mcrosensor networks. Proc. Internatonal Conference on Acoustcs, Speech, and Snal Processn (ICASSP '00), June, [9] F. Rahman, N. Shabana: Wreless Sensor Network based Personal Health Montorn System, WSEAS Transactons on Communcatons, Issue V, Vol. 5, May 2006, pp Acknowledment The research reported here was supported by the Natonal Offce for Research and Technoloy n Hunary. ISSN: