A Decentralzed Lfetme Maxmzaton Algorthm for Dstrbuted Applcatons n Wreless Sensor Networks Vrgna Pllon, Mauro Franceschell, Lug Atzor, Alessandro Gua Dept. of Electrcal and Electronc Engneerng, Unversty of Caglar 09123, Caglar, Italy {vrgna.pllon,mauro.franceschell,l.atzor,gua}@dee.unca.t Abstract We consder the scenaro of a Wreless Sensor Networks (WSN) where the nodes are equpped wth a programmable mddleware that allows for quckly deployng dfferent applcatons runnng on top of t so as to follow the changng ambent needs. We then address the problem of fndng the optmal deployment of the target applcatons n terms of network lfetme. We approach the problem consderng every possble decomposton of an applcaton s sensng and computng operatons nto tasks to be assgned to each nfrastructure component. The contrbuton of energy consumpton due to the energy cost of each task s then consdered nto local cost functons n each node, allowng us to evaluate the vablty of the deployment soluton. The proposed algorthm s based on an teratve and asynchronous local optmzaton of the task allocatons between neghborng nodes that ncreases the network lfetme. Smulaton results show that our framework leads to consderable energy savng wth respect to both snk-orented and cluster-orented deployment approaches, partcularly for networks wth hgh node denstes and non-unform energy consumpton or ntal battery charge. Draft verson, publshed as: V. Pllon, M. Franceschell, L. Atzor, A. Gua, A decentralzed lfetme maxmzaton algorthm for dstrbuted applcatons n Wreless Sensor Networks, ICC12: IEEE Int. Conf. on Communcatons (Ottawa, ON, Canada), pp. 1372-1377, 2012. Ths work has been partally supported by the European Communty s Seventh Framework Programme under project HYCON2 (Grant Agreement n. FP7-ICT-2009-5/N.257462.)
I. INTRODUCTION Thanks to the ncreasng processng and transmsson power of current nodes n Wreless Sensor Networks (WSN), these have become complex systems that are capable of makng decsons and actng upon the nformaton gathered about the montored envronment. Indeed, reducton n the cost of the devces has ncreased nodes capacty, thus they can perform some processng before sendng the data to a snk. Stll, one of the man open research challenges s the maxmzaton of the network lfetme. Devces n a WSN are typcally battery powered, battery that sometmes could be dffcult to replace, such as n the case of subterranean or underwater nodes. These consderatons contrbute to the vson of an horzontal ambent ntellgent nfrastructure wheren the sensng, computng and communcatng nfrastructure s set wth a programmable mddleware that allows for quckly deployng dfferent applcatons runnng on top of t so as to follow the changng ambent needs. Based on ths scenaro, we focus on the need for a logc that decdes on the optmal deployment soluton of a target dstrbuted applcaton. Heren, optmalty s expressed n terms of network lfetme and a deployng soluton s such that defnes whch part (sngle task) of the applcaton has to be executed by each network component. In [1], we have proposed a centralzed soluton that s based on the assumpton that a central node s aware of the status of each node, selects the optmal applcaton deployment and send the correspondng settng to all the nvolved network components. Wth the ntenton to reduce the problem complexty, to reduce the overhead related to the communcaton of the central node wth the rest of the network (for node settngs), and to mprove the capablty of the network to adapt to topology and energy changes, n ths paper we propose a dstrbuted soluton. The proposed algorthm s based on an teratve and asynchronous local optmzaton of the task allocatons between neghborng nodes. The resultng scheme s based on gossp, whch conssts n a communcaton paradgm n whch at each nstant of tme each node n the network has some postve probablty to nteract wth one of ts neghbors. Smulaton results show that our framework results n consderable energy savng wth respect to both snk-orented and cluster-orented deployment approaches, partcularly for networks wth hgh node denstes and non-unform energy consumpton or ntal battery charge Ths paper s organzed as follows. The second secton provdes the prelmnares; the thrd secton ntroduces the problem and adopted approach; the fourth secton descrbes the decentralzed soluton amed at maxmzng the network lfetme; the followng secton presents some smulaton results; and conclusons are drawn n the last secton. A. Past Studes II. PRELIMIARIES Reducton of energy consumpton has always been a key challenge for Wreless Sensor Networks. There are a great number of works whch have focused on the maxmzaton of the network lfetme, each one takng nto account a dfferent approach to acheve t: some are focused on effcent routng technques [2], [3]; others are amed at mnmzng transmsson energy consumpton by sendng data over may short hops rather than fewer long hops [4]; others propose the use of relay nodes so as to balance network energy consumpton among nodes [5], [6]. However, none of the studes mentoned above consders the possblty of processng data n the nodes of the path to the destnaton. Because most of the energy spent n a Wreless Sensor Network depends on the amount of data that s transmtted over the network, reducng the amount of data may result n a reducton of the transmsson energy consumpton. Ths prncple has been only partally adopted by LEACH [7], where sensors serve as Cluster Heads aggregatng the data and, ndeed, decreasng the number of bytes sent over the network. Energy consumpton balancng s guaranteed by a random rotaton of the role of Cluster Head. Gven the computatonal capacty of modern sensors, a step forward could be taken not just by aggregatng data, but by processng them before they arrve at ther destnaton whenever possble and on the bass of the network topology and power resource detecton. In [1] an overlayng framework that determnes the dstrbuton of tasks among the nodes n a WSN by means of a centralzed optmzaton algorthm amed at maxmzng the network lfetme was presented. However, one major drawback of ths algorthm s ts nablty to react quckly to network changes. In ths paper we propose a framework of decentralzed lfetme optmzaton for WSNs, adoptng a soluton n whch the communcaton scheme s based on gossp [8], [9], [10]. Gossp algorthms are decentralzed and asynchronous, they consst n a communcaton scheme n whch at each nstant of tme each node n the network has some postve probablty to nteract wth one of ts neghbors. By the teratve nteracton between nodes, several examples of emergng behavors have been developed such as load balancng [11], dstrbuted averagng [9], dstrbuted convex optmzaton over networks [12], falure detecton [13] and many more. Thus, communcaton schemes based on gossp that mmc the act of gosspng n a crowd of people, are easy to mplement, do not requre network routng or mult-hop communcatons, are nherently asynchronous and decentralzed n nature. B. Energy Consumpton As mentoned n [1], energy consumpton n WSNs s determned by three man components: sensng, processng and transmsson.
The sensng energy consumpton e sens s determned by the specfc characterstcs of the sensor. The processng energy consumpton e proc s proportonal to the complexty of the task that s, the number of nstructons needed to complete t and to the ngress data data n the hgher the number of samples nvolved n the processng, the hgher the energy consumpton. Callng M task the number of nstructons for the task, smp n the number of samples to be processed and e nstr the average energy consumpton per executed nstructon (determned on the bass of the devce datasheeet), then e proc (task, data n ) = M task smp n e nstr (1) Fnally, the energy consumpton e tx requred to transmt a packet of k bts from a node A to a node B wth a constant rate R s: e tx (k, P T 0A, η A, P R0B, φ AB, δ AB ) = k R ( P R0B + P T 0A + φ AB δ α AB η A ) (2) where: P T 0 and P R0 are the components of power consumpton of the transmttng and recevng crcutry; η s the dran effcency of the Power Amplfer; φ s a coeffcent proportonal to the recepton power and the characterstc parameters of the antennas; δ s the dstance between transmtter and recever; α denotes the path loss exponent. III. PROBLEM FORMULATION The model we consder s smlar to the one descrbed n major detals n [1]. The set of nodes n the WSN s defned n the set X = {1,...,,..., N}, where can be a sensng node, a router or an actuator (or node wth a combnaton of these roles). The node N refers to the snk (we assume to have only one snk n the network). In our problem settng, let the network be descrbed by a drected acyclc graph G = {X, E}, where E {X X} s the set of edges, each representng a pont-to-pont communcaton channel between the nodes; edge (, j) has ts tal n node and ts head n node j, wth ts orentaton representng the drecton of the nformaton flow. Let N = {j X : (, j)or(j, ) E} be the neghborhood of node, namely the nodes that share a communcaton channel wth node. Let N out, = {j X : (, j) E} be the set of nodes that receve nformaton from node and N n, = {j X : (j, ) E} the nodes that send nformaton to node. We complete the network descrpton wth the dstance matrx = (δ j ), whch contans the parwse dstances (n meters) between adjacent nodes. If nodes and j are not adjacent, then δ j = ; the matrx Φ = (φ j ), wth the parameters φ j ntroduced n Secton II-B, calculated for each couple of adjacent nodes and j. If nodes and j are not adjacent, then φ j = ; the set of characterstc parameters V = {P R0, P T 0, η }, whch are useful to compute the transmsson energy consumpton as defned n (2) n Secton II-B. We assume that a gven operaton O, whch can be decomposed nto a sequence of tasks, has to be deployed n the network. Ths could represent dverse operatons, ncludng: computng the average temperature n certan geographcal areas, measurng the lght ntensty n a room, vdeosurvellance of a specfc geographcal area, or a combnaton of these. We then defne the sequence C s = {c s 1,..., c s W } of the sensng tasks whch must be executed by the network to perform the operaton O, where W s the total number of sensng tasks requred. We also defne the sequence C p = {c p 1,..., cp L } of the processng tasks whch must be executed by the network to perform the operaton O, where L s the total number of processng tasks requred. If, for nstance, O s a measurement of temperature from a geographcal areas that has to be spatally averaged, the set C s would be made of a number of elements correspondng to the number of geographcal areas where the temperature has to be measured. C p would certanly be measurement of temperature and spatal averagng. Tasks are lsted n C p n prorty order: f a node has to execute both c p 1 and cp 2, the former must be executed before the latter. As to the sensng we assgn a bnary state M {0, 1} W to each node, whch codes the sensng operatons executed by node. The status m w of the node s equal to 1 f the node performs the relatng sensng task. As to the processng tasks, we assgn a bnary state vector s {0, 1} L to each node that represents the processng tasks currently assgned to the node. To each confguraton of the node settng corresponds dfferent energy consumpton, as t wll better explaned n the followng sectons. We assume that dfferent nodes consume dfferent amounts of energy for the same processng to nclude heterogenety of devces n the modelng. To each node s assocated a bnary vector d {0, 1} L whch represents the knds of processng that node s allowed to execute. In partcular, the followng holds X, and l {1,..., L}, d l s l. To smplfy the notaton we denote the matrx that collects all the statuses of each node as S = [s 1, s 2,..., s N ] T and the matrx that represents all the constrants on the executon of processng as D = [d 1, d 2,..., d N ] T. We consder a scenaro where the sensng operatons are already assgned to the network members (.e., bnary vectors M are gven, for = 1,..., N). Dfferently, the processng tasks n O can be executed accordng to dfferent solutons: gathered data can be mmedately sent to a snk, or t can be processed before beng transmtted. In the case of the latter, the number of bts to be sent would be smaller, reducng the transmsson energy consumpton; however, processng energy consumpton
could be hgher n ths second case. Quantfyng the energy consumpton n both cases, t could be possble to establsh whch one determnes a reducton of battery consumpton n the sensors, ncrementng the network lfetme. The addressed problem s then defned as the processng status matrx S that mnmzes the mpact of the operaton O on the network, maxmzng the network lfetme. In the followng, we elaborate the consdered scenaro by defnng further constrants and provdng a dstrbuted soluton. IV. DEPLOYMENT OF DISTRIBUTED APPLICATIONS In the followng, we present the proposed soluton towards a dstrbuted applcaton deployment n WSN. The followng Subsectons present: the constrants on the traffc generated by the dstrbuted applcatons; the cost functons bult on the bass of the energy consumpton formulas; the network lfetme maxmzaton algorthm. A. Constrants on the Traffc Flows In our scenaro we assume that the sources of traffc n the network (the sensors) generate samples of k bts at a certan frequency f. The processng n the network s performed on ths type of traffc flow comng from dfferent nodes. The generc node receves the traffc T n over whch t performs the task correspondng to ts assgned status s. The effect of ths task s the generaton of the output traffc T out, whch s computed by functon p as follows T out = p(t n, s ) (3) The output traffc s then sent to the next node. The data generated by p n node s modeled by the H-dmensonal vector T out = (t out 1,..., tout,..., tout H ), where each element tout = {kout, f out } corresponds to a traffc flow where each sample of k out out bts s transmtted at the frequency f. The number of bts kout for each output flow tout resultng from p(x, y) s ether constant or lnear wth the number of nput flows, but t cannot be non lnear. Further detals are avalable n [1]. Data T out are sent to the followng node j accordng to the drected acyclc graph G. Node j receves data from all adjacent nodes that reach the snk through j Tj n = { T out 0 s no actons z, wth z = (4) 1 otherwse N n, As defned by (3), data Tj n receved by node j are processed, accordng to the status of j. There are many processng tasks that can be performed n a WSN. For each one of these, an operator p(x, y) s defned. Note that for our objectve, ths operator s needed to fgure out the traffc flows that wll be traversng the network for each deployment scenaro. We dentfed three common knds of processng, whch are spatal, temporal and sngle sample processng. We refer to [1] for further detals about ths dstncton. B. Cost Functons The objectve of the proposed algorthm s to evaluate the vablty of each deployment soluton on the bass of cost functons that are connected to energy consumpton. We consder three cost functons: one for the sensng, one for the processng and one for the transmsson. The sensng cost functon for the node s expressed as E sens = W w=1 f out e sens w m w (5) wth e sens w representng the sensng energy consumpton for node performng sensng task w f ts status m w s equal to 1, as defned n Secton II-B. Recall that f out s the node output traffc frequency, whch also represents the sensng frequency. We defne processng cost functon as follows E proc = L H l=1 h=1 f out e proc (c s l, T n ) s l (6) where e proc s the processng energy consumpton defned n (1) whch depends on the task c sl that has to be executed, whch n turn depends on the status s l of the node, and the receved data T n descrbed n (4). Because the processng cost depends on the number of processng per second performed by the same node, t s proportonal to the frequency f out of each of the H egress traffc flows, where H s the sze of T out as descrbed n Secton IV-A. The number of samples to calculate e proc s defned dfferently for each knd of processng p(x, y) detected n Secton IV-A. Both sensng and processng are followed by a transmsson. The related cost functon s E tx = f e tx (T out, V, V j, j N n, j N n, φ j, j N n, δ j ) (7)
wth f transmsson frequency and e tx transmsson energy consumpton defned by (7) dependng on: the data to be transmtted T out ; the characterstc parameters V of the node ; the characterstc parameters V j of all the j nodes that wll receve the data from whch, for a connected graph, s just one; the parameter φ j concernng nodes and j; the dstance δ j between and j. Gven (5), (6) and (7), the overall cost functon for any node s E = ( E sens + E proc + E tx ) (8) C. Algorthm descrpton We consder a network descrbed by a drected acyclc graph G = {X, E} (see III) n whch the nformaton flow has reached a statonary state. The processng state of the network s descrbed by the processng matrx S, where s l = 1 f node processes task l, else s l = 0. Our objectve s that of modfyng the processng state so as to maxmze the lfetme of the network τ(s), ntended as the tme n whch at least one node has exhausted ts energy reserve from the battery: n fact when ths condton s reached the network topology s dsrupted. If we denote the energy reserve of node at tme t as (t) then we can defne τ(s) = nf{t ( X) (t) = 0}. Assumng a statonary state, we observe that the optmal processng state s: S opt = arg max S τ(s) = arg max mn S X E (S) where the last equaton follows from the fact that n a statonary state the tme requred for a node to dran ts battery s /E where E s the energy consumed (per unt of tme). Snce the tasks a node can process are lmted, we get a constraned optmzaton problem of the form: max S mn X s.t. X d s S {0, 1} N L E (S), (9) where d, as prevously defned, s the characterstcs vector of the tasks that can be processed by node and s s the processng state of node. We wsh to solve problem (9) n a decentralzed way by teratvely and asynchronously solvng an equvalent local optmzaton problem that nvolves at each teraton only one node and ts n-neghbors N n,. We now propose the man result of ths paper, namely the Decentralzed Lfe Maxmzaton for WSNs Algorthm (DLMA). Algorthm 1 (Decentralzed Lfe Maxmzaton for WSNs): 1) Each node X s ntalzed wth the resdual energy of the battery and state s = {0} L (no processng assgned). 2) Let k = 0 and t 0 = 0. 3) At tme t k+1 > t k, a node not nvolved n a gossp, and thus, as defned n II-A, not communcatng wth any of ts neghbours, s selected at random to nteract wth nodes n ts n-neghborhood N n,. 4) If any node n N n, s already nvolved n a gossp, then k = k + 1 and go to 3. 5) Node, wth a current processng state s (whch s the state of node at current tme t k+1 ), obtans the state s j for all j N n,. 6) Solve the followng local mxed nteger lnear programmng problem n the unknown varables α and s j for j
N n, {}: 12 mn α s.t. E j (s k : k N n, {}) γ j < α j N n, {} d j s j T out (s Nn, {} ) T out ( s Nn, {} ) α R + s j {0, 1} L j N n, {} j N n, {} and let ts optmal soluton be (α opt, s Nn, {},opt ). 7) If s Nn, {},opt exsts then set the new processng status to s j = s j,opt, for all j N n, {}. 8) Let k = k + 1 and go to 3. We wll formally prove n the followng (see Theorem 4.1) that at each teraton k of the prevous algorthm, the objectve functon of (9) ether mproves or does not change, although we cannot guarantee that the optmal soluton of (9) s eventually found as k ncreases. However, Algorthm 1 offers several advantages wth respect to centralzed algorthms to compute a soluton for problem (9). Both problems (9) and (10) are hard to solve. However, the computatonal complexty of the local optmzaton s functon only of the number of nodes nvolved n the optmzaton, thus despte beng a mxed nteger lnear programmng problem, ts complexty does not grow by ncreasng the number of nodes n the network and s small n absolute terms f the number of processng that may be allocated locally between the nodes s small. Snce the allocaton of processng s dynamc, the algorthm reacts to unexpected drops n battery charge by changng the status of the nodes nvolved. We now characterze the behavor of the network whle algorthm DLMA s beng executed. Theorem 4.1: Consder a WSN that executes Algorthm 1. Let the ntal processng state S be feasble for problem (10) n E (S) each neghborhood N of G. Let V (t) = max X be the nverse of mnmum lfetme n the network set by the nodes wth the smallest rato between energy reserve and power consumpton. Then, f the network executes Algorthm 1 t R + : V (t + ) V (t). Proof: Durng the algorthm executon, at each teraton k two stuatons may occur: Case 1: The processng state matrx S of the network does not change, then V (t + ) = V (t) by defnton. Case 2: The processng state matrx S changes accordng to the soluton of the local optmzaton problem (10). The soluton of problem (10) mnmzes locally the energy consumpton for the node wth the shortest lfetme between nodes and j N. Thus, f a feasble soluton s found, and we update the processng state of the nodes nvolved n the optmzaton from s Nn, {},opt to s Nn, {},opt then mn j Nn, {} mn j Nn, {} (10) E (s Nn, {},opt ) E ( s Nn, {} ). (11) Now we need to show that the nodes not nvolved n the local optmzaton do not decrease ther lfe-tme as a result. In the proposed local optmzaton a processng state update s performed only f each sngle nformaton flow passng from node to the nodes n N out, s not ncreased due to the constrant T out (s ) T out ( s ). Now the transmsson cost for any node n N out, can only decrease as T out (s ) s decreased, as shown n eq. (7), and so does ts processng cost, as shown n eq. (6). Furthermore also the nodes n the downstream path toward the snk receve a smaller nformaton flow thus consumng less power. Fnally, the nodes n the upstrem path have ther nformaton flow left unchanged and such s ther power consumpton. Thus t follows that mn j X E (S opt ) mn j X E (S), and V (t + ) V (t) thus provng the statement. 1 Wth a slght abuse of notaton we denote by s Nn, {} the set of vectors s that represent the avalable processng tasks n the nodes n the set N n, {}. 2 Wth a slght abuse of notaton we denote by E j (s Nn, {} ) the energy consumed by node j as functon of the local processng assgnment, t s ntended that the contrbuton of other nodes to ths term can be computed smply by consderng the term Tj n set of vectors s that represent the avalable processng tasks n the nodes n the set N n, {}.
TABLE I PERCENTAGE VALUES OF ENERGY CONSERVATION USING DLMA, FOR COMPARISONS DLMA-C, DLMA-CH AND DLMA-CO Node densty [nodes/m 2 ] UC-UE [%] DLMA-C DLMA-CH DLMA-CO 0.2 65.9 33.7 22.0 0.3 69.9 32.1 19.4 0.4 72.2 36.5 20.0 NUC-NUE [%] DLMA-C DLMA-CH DLMA-CO 0.2 72.2 49.1 11.2 0.3 76.8 49.7 10.3 0.4 78.9 55.5 10.6 A. Test Cases and Smulatons Setup V. PERFORMANCE ANALYSIS To evaluate the effectveness of the algorthm on a realstc WSN, two test cases have been taken nto account, accordng to some of the most sgnfcant realstc scenaros consdered n past works, such as n [14]: unform energy consumpton and unform ntal energy at each node (UC-UE); non unform energy consumpton and non unform ntal energy (NUC-NUE) at each node (the energy consumpton of the nodes has been assgned randomly from 60% to 140% of the energy consumpton n case UC-UE; the ntal energy has been assgned randomly from 20% to 100% of the total battery charge). The analyss has been conducted n a MatLab envronment, consderng an outdoor agrcultural scenaro. It has been supposed to montor a rectangular-shaped envronment, where the nodes have been deployed wth denstes of 0.2, 0.3 and 0.4 nodes/m 2. It has been assumed that the nodes deployment follows a unform dstrbuton. Each node s equpped wth sensors gatherng nformaton of temperature, humdty, PH and lght exposure. The data are then sent to the Coordnator. We have focused our analyss on one operaton: calculaton of the mean values of gathered nformaton over an hour, startng from the values gathered every 10 mnutes. We have assumed that each sensed value s represented as a double numercal value, whch s 64 bts long. The nodes communcate usng IEEE 802.15.4 rado nterfaces on the 2.4 GHz frequency band. The packets maxmum sze s 137 bytes, wth a payload of 0 to 125 bytes. To keep thngs smple, any possble overhead has not been taken nto account. The local optmzaton problem has been solved usng the nteger lnear programmng solver GLPK (GNU Lnear Programmng Kt). B. Analyss of Case Studes The optmzaton algorthm has been appled to each of the cases mentoned n V-A. The results have been compared wth three other mechansms: ) data processed only by the Coordnator (mechansm C); ) data processed by every Cluster Head found n the path to the Coordnator (mechansm CH); ) centralzed optmzaton algorthm descrbed n [1] (mechansm CO). In the followng we present a comparson between the results obtaned usng the DLMA algorthm and those obtaned usng wth mechansms C, CH and CO. Specfcally, we focus on the percentage of the energy conservaton ganed when usng the proposed algorthm wth respect to the alternatve methods. We refer to these results wth: DLMA-C, DLMA-CH, and DLMA-CO. Tab.I shows the results for the operaton defned n Secton V-A. The results show an average mprovement of 57.7% of the proposed strategy for comparsons DLMA-C and DLMA-CH, whle, as t should be expected, we observed an average decrement of 15.6% for comparson DLMA-CO. As a matter of fact, ths s the drawback of the DLMA wth respect to the centralzed optmzaton algorthm whch fnds an optmal soluton. As for the smulaton results of the centralzed optmzaton algorthm, the best results are obtaned for heterogeneous networks, whch are the most common n real scenaros. Ths s because, unlke other mechansms where the processng s performed on fxed nodes regardless the energy consumed by the sngle nodes, the nodes chosen by the algorthm to perform the processng are those weghtng less on the network. The tendency of an mprovng energy conservaton when node densty ncreases s due to two factors: n case NUC-NUE, when the number of nodes n an area ncreases, t s more lkely that among neghborng nodes there are nodes where the processng cost s lower due to ther hgher battery level or energy consumpton; the hgher the number of nodes n the same
area, the larger the clusters formed, the bgger the amount of data that can be processed before they arrve to the Coordnator, reducng the energy cost. Fg. 1. Network lfe percentage decrement wth respect to tme expressed n days, for mechansms C, CH, CO and DLMA, for a node densty of 0.3 nodes/m 2 n case NUC-NUE Fg.1 shows the percentage decrease of the network lfe expressed as the mnmum resdual battery capacty among all nodes n the network, wth respect to tme expressed n days, for the analysed mechansms, for a node densty of 0.3 nodes/m 2 n case NUC-NUE. Startng from the same ntal battery charge, lfetme s shown to be much shorter f data are processed by fxed nodes, than n the solutons found by centralzed optmzaton algorthm and DLMA. Furthermore, early death of nodes could be avoded programmng nodes to run DLMA agan when they reach a threshold battery level, so that they can reduce ther burden and extend ther lfetme. Of course, runnng centralzed optmzaton algorthm agan when a node s battery level s crtcal should be much more dffcult due to ts hgher complexty and to ts centralzed nature. VI. CONCLUSIONS In ths paper we have studed the deployment of dstrbuted applcatons n WSNs and proposed a framework of decentralzed lfetme maxmzaton for WSNs whch mnmzes the mpact of the applcatons on the network lfetme. The resultng DLMA algorthm based on gossp has been descrbed and mplemented to perform smulaton n realstc scenaros. The results have been compared wth alternatve solutons, showng an mprovement wth respect to fxed nodes mechansms such as data processed only by the Coordnator or by Cluster Heads. DLMA algorthm s outperformed by the global optmzaton algorthm, whch however presents a hgher computatonal complexty and s unable to react quckly to network changes. REFERENCES [1] V. Pllon and L. Atzor, Deployment of dstrbuted applcatons n wreless sensor networks, Sensors, vol. 11, no. 8, pp. 7395 7419, 2011. [2] S. Sngh, M. Woo, and C. Raghavendra, Power-aware routng n moble ad hoc networks, n Proc. ACM MobCom, 1998. [3] F. Lu, C. Tsu, and Y. J. Zhang, Jont routng and sleep schedulng for lfetme maxmzaton of wreless sensor networks, IEEE Transactons on Wreless Communcatons, vol. 9, no. 7, pp. 2258 2267, July 2010. [4] B. Calhoun, D. Daly, N. Verma, D. Fnchelsten, D. Wentzloff, A. Wang, S. Cho, and A. Chandrakasan, Desgn consderatons for ultra-low energy wreless mcrosensor nodes, IEEE Transactons Computers, vol. 54, no. 6, pp. 727 740, June 2005. [5] S. C. Ergen and P. Varaya, Optmal placement of relay nodes for energy effcency n sensor networks, n Proc. IEEE ICC, 2006. [6] J.Tang, B. Hao, and A. Sen, Relay node placement n large scale wreless sensor networks, Computer Communcatons, vol. 29, no. 4, pp. 490 501, Feb. 2006. [7] W. Henzelman, A. Chandrakasan, and H. Balakrshnan, An applcaton-specfc protocol archtecture for wreless mcrosensor networks, IEEE Transactons on Wreless Communcatons, vol. 1, pp. 660 670, October 2002. [8] D. Shah, Gossp algorthms, Foundatons and Trends R n Networkng, vol. 3, no. 1, pp. 1 125, 2009. [9] S. Boyd, A. Ghosh, B. Prabhakar, and D. Shah, Randomzed gossp algorthms, Informaton Theory, IEEE Transactons on, vol. 52, no. 6, pp. 2508 2530, 2006. [10] M. Franceschell and A. Gasparr, On agreement problems wth gossp algorthms n absence of common reference frames, n Robotcs and Automaton (ICRA), 2010 IEEE Internatonal Conference on. IEEE, 2010, pp. 4481 4486. [11] M. Franceschell, A. Gua, and C. Seatzu, Load balancng over heterogeneous networks wth gossp-based algorthms, n 2009 Amercan Control Conference, St. Lous, Mssour, USA, Jun. 2009. [12] J. Lu, C. Tang, P. Reger, and T. Bow, A gossp algorthm for convex consensus optmzaton over networks, n Amercan Control Conference (ACC), 2010. IEEE, 2010, pp. 301 308. [13] R. Van Renesse, Y. Mnsky, and M. Hayden, A gossp-style falure detecton servce, n Proceedngs of the IFIP Internatonal Conference on Dstrbuted Systems Platforms and Open Dstrbuted Processng. Sprnger-Verlag, 2009, pp. 55 70. [14] Z. Cheng, M. Perllo, and W. Henzelman, General network lfetme and cost models for evaluatng sensor network deployment strateges, IEEE Transactons on Moble Computng, vol. 7, no. 4, pp. 484 497, Aprl 2008.