Lifetime-Oriented Optimal Relay Deployment for Three-tier Wireless Sensor Networks

Transcription

1 Sensors & Transducers by IFSA Lfetme-Orented Optmal Relay Deployment for Three-ter Wreless Sensor Networs Bn Zeng, Lu Yao and Ru Wang Department of Management, Naval Unversty of Engneerng, WuHan, HuBe,, Chna Lbrary of Trangng Offce, Naval Unversty of Engneerng, WuHan, HuBe,, Chna Tel.: , fax: E-mal: Receved: 8 Aprl /Accepted: 9 July /Publshed: July Abstract: In ths paper we address the networ deployment problem, n whch we am to maxmze the lfetme of a sensor networ wth mnmum total energy consumpton by computng the optmal locatons of relay nodes wth energy consumpton rate (ECR) constrant and ther assgnment relatonshp wth sensor nodes. Frstly a mxed nteger programmng model wth fewer varables s proposed to formulate the relay deployment problem under the constrants of networ flows and ECR. Then a shortest path based heurstc algorthm s developed to gve the suboptmal soluton of the model by constructng an energy effcent three-tered herarchcal structure consstng of many power-lmted sensor nodes, a small set of relays, and multple BSs. Fnally the effectveness and performance of the proposed strateges are llustrated through smulatons. Copyrght IFSA. Keywords: Wreless sensor networs, Relay deployment, Energy effcency, Heurstc algorthm, Three-ter structure.. Introducton Wreless sensor networs (WSNs) have been used n a wde range of applcatons. In the networ scenaros, Sensor nodes (SNs), such as sensors and transducers are deployed at strategc postons wth fxed sensng and transmt energy, thus they can sustan a fxed length of lfetme. In addton to the deployment of SNs, one or multple base statons (BSs) s necessary to collect data from the sensng feld. However, due to geographc reasons, sometmes the BSs could only be establshed far away from the sensng feld, resultng n very low data recepton rate and hgh transmsson energy consumpton. To address ths problem, a small number of Relay nodes (RNs), as energy-lmted as SNs, can be placed between the sensng feld and the BS to forward data pacets. Here we consder a large scale mult-hop relay routng from SNs to the BSs. Therefore, the SNs, RNs and BSs buld up a threetered wreless networ n such applcatons. There s a renewed nterest n research on relayed communcaton networs [, ]. In ths paper, we consder three-tered wreless networs [, ] that can be used for a wde range of applcatons, such as dsaster area communcatons, envronment nformaton gatherng, etc. Such realstc scenaros share smlar characterstcs: tas-based SNs are dstrbuted on the desred spots for sensng and sendng local nformaton; RNs, placed between SNs and the BSs, receve nformaton pacets from SNs and forward them to the BSs; the BSs, whch s located dstant away from the sensng feld as n Fg., collects all the data from RNs and processes Artcle number P_8

2 the nformaton to mae a decson. The RNs are battery powered, are temporally placed to enhance the networ performance. As descrbed n [5], the locatons of SNs and the BSs are gven at the frst stage of networ deployment. The data rates of SNs are also nown, but may be dfferent for dfferent SN dependng on the specfc type of data sensed, whch s reasonable snce most of sensor networs gather data from SNs at a predefned perod round by round. The total energy consumed by a RN per round of data collecton s defned as energy consumpton rate (ECR) of a RN [, 7], whch can be gven a maxmum threshold n case t wll deplete energy too faster. If a RN s ECR s defnes as C, ts ntal energy s defned as e, ts lfetme LT = e /C. Therefore, t s mportant to consder ECR as a ey constrant n the lfetme-orented deployment. Relay node deployment for WSNs has been studed n varous contexts [8-]. The problem of addng relays to mprove the connectvty of multhop wreless networs was frstly addressed n [], A set of canddate ponts are gven and the avalable relays must be deployed n a smaller set of these canddate ponts. The set of relay locatons, are determned based on testng all the canddate ponts and choosng the combnaton, whch results n hgher connectvty measure. Obvously, ths scheme s very complex as the networ sze ncreases and s an NP-hard problem. Later [] further extended the problem by formulatng t as a sem-defnte programmng (SDP) optmzaton problem. Secondly they proposed a routng algorthm, namely, Weghted Mnmum Power Routng (WMPR) algorthm to ncrease the networ lfetme by effcent utlzaton of the deployed relays. On the other hand, there are several wors [, ] explctly consderng relay node placement to prolong networ lfetme, e.g., [] proposed two deployment strateges, namely, lfetme orented deployment and hybrd deployment to overcome the BECR problems and [] stresses on usng energy provsonng and formulates the jont problem of energy provsonng and RNs deployment nto a mxed-nteger nonlnear programmng problem (MINLP). Snce an MINLP problem s NP-hard n general, a heurstc algorthm s proposed to address ths problem. Fg.. A three-tered wreless networ. As we now, most of researches have focused on the deployment problem for one or two ter sensor networs ncludng multple BSs except [], whch deploys sns and relays to mnmze the deployment cost of BSs and RNs and to guarantee that all sensor nodes n the networ are double covered. But the lfetme of WSNs sn t consdered n []. Furthermore, snce relay nodes are responsble for data transmsson between a lot of sensor nodes and mult BSs, t s obvous that the energy constrant of RNs has serous mpact on the performance of large scale herarchcal sensor networs besdes other constrant. Although some wors have notced the mportance of relay and BSs energy constrant, to the best of our nowledge, ths paper s the frst to ncorporate the ECR constrant and networ traffc flow nto deployment problem and gves an effcent soluton. The man contrbutons of ths paper are as follows: frst, we present a three-tered wreless networ archtecture n whch RNs are added to overcome the long dstance communcatons between the SNs and the BSs layer and the RNs are energy constraned; secondly, a mxed lnear programmng model s defned and analyzed for relay node deployment and assgnment; thrdly, an effcent yet practcal soluton s proposed usng heurstc algorthms named by ; fnally, the smulaton results are presented to demonstrate that the algorthm outperforms other relay placement schemes.. Problem Formulaton We defne the deployment problem more precsely as follows: Gven a complete graph G=(N, A), where N={,, n} s the node set and A=NN s the set of drected arcs. N conssts of three subset N s (SNs set), N r (canddate relay locaton set) and N b (BSs set).there s a networ flow of f j assocated wth each par of nodes (,j)a. f j s the volume of the assocated networ flow whch can be estmated and controlled ntally. We do not assume that f j = f j snce the sensor reportng flow s not the same as the query flow. Also we are gve E j the transmsson energy of sendng one unt of data drectly from to j. E j s usually proportonal to the dstance between and j and therefore generally can be represented as Eucldean dstance multpled by traffc accordng to the energy model n []. Each flow n mult-hop has three separate components: collecton (sensor nodeto-relay), transfer (nter-relay), and upln (relay-to- BS). Each component has the respectve per unt energy cost coeffcent of,,. Thus the cost per unt flow for gatherng s E, where s a sensor node and s a relay. Smlarly nter-relay transfer has cost E l, where, l are both relays and upln has cost of E lj where l s a relay and j s a BS node. Usually, due to the nter-relay and relay-bs transfer

3 effcences, < and < s a transfer dscount factor, whle =. Ths paper manly studes the constraned relay deployment problem where the RNs can only be placed at a subset of canddate locatons whose number s defned as P. Now we present the formulaton of relay deployment (RDF) as below. Subject to: m j m mn f, j E jm jm N, m, N, j N, jm jm X Ns, m, Nr, m s j N, jm X m N s, m, N r, j N, j m f E C X N, X jm jm r b b b r () () () () (5) {,} N, () where the varable jm denotes the fracton of flow that transmts from node to BS node j va relay located at and m, N s s the ntal sensor node set and N b s the BS set, both of them are subset of N. the varable X s defned by f locaton s placed a relay X, (7) otherwse The per unt transmsson energy cost of jm flow s defned by Ejm E Em Emj, (8) where c s the energy consumpton rate threshold (ECRT) of node accordng to ts battery level. By ECRT, we try to guarantee the lfetme of each relay. In the above formulaton, Eq. () ensures that the total flow (f j ) from to j s transferred, whle Eq. () and Eq. () guarantee that transfers only occur va relays. Eq. (5) ensures that the ECR constrant s beng adhered to. Wth the deployment problem the relays are capactated. Thus the model not only decdes on the optmal locaton of the relays and the allocaton of sensor nodes to relays. The deployment problem can be furthermore formulated as a MILP (Mxed Integer Lnear Programmng) named by. The varables n our formulatons are: p as the number of RNs to be placed as relays; f the flow from node to relay ; f m the flow from node va relays and m; f mj the flow from node to BS j va relay m; mn Subject to: f m m E j f E f K mj mj M E f fj, j f m m, (9) () fmj f j, j, () m f m fmj f, j f f X,, j j fmj fj X m m, j, E f C X, X p, r () () () (5) (), f, f, X {,}, j, m, (7) mj m, Eq. () specfes the networ traffc from equals the traffc to BSs, Eq. () specfes the traffc from node to BS j s transferred by relays. Eq. () represents the dvergence equaton of networ flow from node. Eq. () and Eq. () ensures no flow travels drectly between SNs. Eq. (5) ensures that the energy constrants are beng satsfed. Eq. () specfes the maxmal number of relays could be placed, defned as p r, ths equaton can be removed accordng to the need of real applcaton. Note that ths formulaton has substantally fewer varables than a formulaton of RDF. RDF shows usage of O(n ) varables, whlst uses O(n ) varables. Thus we hope to solve much larger problems wth our formulaton.. Algorthm Descrpton Here we develop a heurstc algorthm to solve. Ths s motvated by the nowledge that, f there s no energy constrant on the relays, the shortest path algorthm can provde a good bass for

4 relay deployment problems (see [, 7]). Gven a set of relays wthout energy constrant, the shortest path algorthm such as Floyd wll optmally place relays to sensor networs. However, snce we have relay constrants for the, we can develop a heurstc method for relay selecton, the shortest path procedure and a reroutng procedure for flow that volates energy constrants. We set off wth an ntal placement of relays. To ths, we apply the shortest path algorthm. If the energy and flow constrants are satsfed at any stage, we have a feasble soluton for the and we record ts value. If not, we reroute excess flow usng a heurstc procedure. Snce the above approach s based by our ntal placement of RNs, we attempt a greedy swap procedure to nvestgate f other potental locatons (n the neghborhood of the placed RN set) yeld better solutons. We repeat ths process untl some termnaton crtera are satsfed. Furthermore, t s possble to use an exact multcommodty flow approach to perform the allocaton of canddate locatons to the placed RNs n an effcent manner. However, snce ths s a computatonally expensve procedure, we only apply t to the fxed number of best RN solutons (defned as l n our algorthm) found durng the heurstc approach. We start by creatng an ordered lst L, whch s a permutaton of all the canddate locatons. We refer to the locatons n L as canddate RN. Intally the canddates are raned n descendng order of ECRT for each locaton N r. We refer to the th element of L as L() for each N r. Defne S(L, s)={l(): s} where s N r. Intally the frst s locatons are taen as tral locatons. Tral locatons are locatons that are chosen to place RNs n a gven teraton of the heurstc. Suppose that at some teraton of the heurstc L={ } and s=, then S(L, s)={,,},.e., and are the tral locatons. We also defne v(s) to be the objectve value calculated by the heurstc (ths mght not necessarly be the true objectve value) correspondng to S= S(L, s). The algorthm below gves a descrpton of the heurstc. The number of candd date locatons for relay placement s denoted as p. Snce the number p s very large, we eep trac of the l best solutons found by the algorthm (l= n our smulaton), denoted as {S * } l where S * =(L *, s ), L * s the lst correspondng to the th best soluton and s s the number of relay locatons n the set. The man loop performs a descent n whch relay locatons are swapped one at a tme. In each teraton v * s the best soluton found so far. The fnal two procedures of the heurstc perform a search n the vcnty of the l best solutons and evaluate the exact objectve value for the l best sets of locatons found. Man begn ntalze L to be RNs n descendng order of ECRT L o =L for (= to l-) do z * = f (=l-) L=L * for (g= to p) do //swap every node wth the g th relay {S * } l, L,v * =Evaluaton(g, l) repeat //add a relay untl no mprovements v= v * p=p+ {S * } l, L, v * =Evaluaton(g, l) whle (v< v * ) f (=) then L =L o L =swap() {S * } l =Mnm() Multcommodty({S * } l ) end The followng paragraphs descrbe the procedures that are referred to above... Evaluaton of Relays Selecton Ths functon taes locatons n S(L, s), uses them as tral locatons and evaluates the locaton selecton usng a heurstc. Every other locaton s then swapped wth the tral locaton L(g) and the resultng selecton of locatons s evaluated usng the same heurstc. The relay locaton recevng the flow from to j s stored n r j. The shortest path dstance from to j s gven by d j. All flow s ntally routed along the shortest paths rrespectve of relay constrants. The flows are then adjusted by reroutng some of the flow away from RNs exceedng ther energy constrant, to obtan a feasble soluton. It s mportant to note that we always ensure that there are no duplcate solutons n the set of l best solutons. Ths s mportant for the effectveness of The Mnm and the Multcommodty procedure. {S * } l,l, v * =Evaluaton(g, l) begn repeat p+-l tmes d,s=createstruct(p, L) v= j d jf j f (a relay has exceeded t s ECRT constrant) then v=reroutng(l, L, r, d) f (v*>v) then v*=v f (v<v(s* l )) then update {S * } l L=Swap g, l+ L=SwapSeq l return.. Constructon of Three-ter Networ Structure Gven a set of nodes, ths procedure creates a networ wth three layers: sensor nodes n the bottom 5

5 layer, relay nodes n the centre layer and BS nodes n the top layer. The arc costs n ths networ are gven by the collecton (layer to layer ), transfer (layer to layer ) and upln (layer to layer ) costs. It then uses the Floyd Shortest Path algorthm to assgn nodes to RNs rrespectve of constrants. r j represents the successor of node, that s the RN whch transfers the traffc from to j. The shortest dstances from to j are returned n d j. Also note that ths algorthm has complexty O(pn ), where p s the number of tral RNs... Reroute of Networ Flow Reroutng s performed by removng RNs from the networ that have reached ther ECRT constrant and reroutng the excess flow va RNs that have not yet reached ther constrant. We use H to denote the set of RNs that have not yet reached ther ECRT constrant. The excess flow s rerouted va the cheapest alternatve n H (Note that t s possble for ths alternatve path to nclude two new relay locatons that was not used before). However ths procedure does not guarantee optmalty, snce the flow to be rerouted s chosen arbtrarly. Optmal solutons could be obtaned by solvng a lnear program whch s too computatonally expensve to perform for each teraton of the heurstc. Note however that we do solve the flow problem exactly for the l best sets. It should also be noted that f the energy consumpton rate of the RN placed n the locaton exceeds ts constrant then t s never selected as a potental locaton snce such a locaton s unlely to be n the optmal soluton. We use to denote the energy consumpton for collectng data flow by RN located at locaton. v=reroutng(l, L, r, d) begn d f j: rj H : C whle ( s.t. > C ) do for (, j) NN f ( r C j r j ) then =argmn th (c t +d tj ) r j mn{ j Cr j, C v=v+ r j r j = + f ( C ) then H=H-{} return.. Procedure of Swap } Ths process smply swap the node L() wth node L(j). So f L={,,,, 5,, 7, 8} after one applcaton of Swap(,5) we would now have L={5,,,,,, 7, 8}..5. Procedure of SwapSeq A SwapSeq s the followng sequence of Swaps: L= SwapSeq l begn for (= to p-l-) do L=Swap (l+, l++) return;.. Procedure of Mnm The mnm fnds l local mnma by usng a descent procedure startng from the l best solutons. The fnal solutons returned by the procedure are mnmal wth respect to the neghborhood operaton of swappng any selected RN locaton wth any non- RN locaton. For soluton S * we accept any mprovement, whle for other solutons S *,, S * l we use a steepest descent method. Note that the algorthm never searches the same neghborhood twce as {S * } l are always dfferent and because our mplementaton ncludes a chec to sp any of these f they were already searched n a prevous teraton of the repeat loop. {S * } l =Mnm() begn repeat M=l for (j= to M) do L j =L * j For (l=l * j- to l * j +) do f (j=) then L=L j for (g=l to ) do f (j>) then L=L j {S * } l, L, v * =Evaluaton(g, l) Untl no mprovement n {S * } l return.7. Procedure of Multcommodty Ths procedure taes the l best solutons found and solves the Lnear Programmng formulaton gven by wth the S accordngly for each soluton. That s we solve the LP for each of the l solutons usng the relay locatons that were found for each correspondng soluton. The lnear programs can be solved by CPLEX.. Experment The smulatons were performed n NS- and the rado model used by our smulatons can be seen n [8], n whch the energy consumpton of unt data

6 transmsson of between a dstance of d meters s gven by E t =E elec +E amp d, where E elec and E amp are the energy consumed by the electronc components of the sensor and the amplfer crcut, respectvely. Meanwhle, the recevng energy consumpton s gven by E r =E elec In the smulatons, E elec and E amp were confgured as nj/bt and pj/bt/m, respectvely. In addton, the total energy bound of each sensor and relay was confgured as J and 8 J, respectvely. The bandwdth of wreless channel was specfed as Mbps, and the length of reportng pacet was confgured to be 5 bt. The data reportng rates of SNs are generated accordng to unform dstrbuton n [,] pacets per smulaton step. The transmsson and sensng radus of relay nodes and sensor nodes were specfed as m, and the energy consumed n performng each sensng acton was specfed as 5 - J. The sensors were deployed accordng to Gaussan dstrbuton n a square feld measurng m and only de due to energy completon. We pc fve of them as BSs by usng -means clusterng algorthm [9]. Each sensor sends data to ts physcally closest BS. The canddate locatons for relay placement are dvded nto varous numbers of grds rangng from 5 to 5. Each relay allocates a certan fracton of ther energy capacty as ECR threshold for relayng traffc. Ths ECR threshold s the same for all relays n our smulaton. We call ths parameter C q... Impact of RNs Number In the frst smulaton, we remove the constrant of equaton () to compute the mnmal number of RNs needed to mnmze energy consumpton of networs, whch s mportant to decde the relay deployment cost of dfferent algorthms. The performance of s compared to the followng two methods; the frst algorthm adopted a Bnary Integer Lnear Programmng () model to optmally locate suffcent RNs to acheve mnmum energy consumpton n WSNs, whch s smlar as [] but removng sgnal to nose rato constrant. Ths algorthm ams to determne optmal locatons to nstall RNs n the target sensng feld and determne optmal route to forward sensng data pacet from SNs drectly to SNs or ndrectly va RNs wthout consderng the networ flow and ECR constrants. The second algorthm formulates the relay deployment problem as a nonlnear programmng problem and then propose an approxmaton algorthm to compute the optmal postons of RNs wth the optmal energy allocated to them such that lfetme of sensor networ can be mantaned by mnmum energy [] named by algorthm. Both of the methods do not consder the optmzaton for multple BSs. Fg. shows that the number of RNs ncreases as the number of SNs number when C q =. % and C q =.5 %. In the algorthm, n order to nstall RNs, the suffcent number and the sutable locatons are selected based on the dstrbuton of SNs n the sensng feld. In some area where SNs are out of transmsson range from other nodes, RNs s needed to receve and forward the pacet to BS. Thus, the algorthm needs a larger number of relay nodes than ether the other two algorthms. In the algorthm, the number of relay nodes ncreases proportonal to that of SNs snce the postons of the relays are determned regularly. The number of relays deployed n the algorthm s slghtly less than that n the algorthm snce the grd ponts at whch RNs are selected to cover the maxmum number of sensor nodes and optmzed for multple BSs (a) C q =. % (b) C q =.5 % Fg.. Varaton of RNs number wth SNs changes. Fg. shows how the number of RNs n the mddle ter networ changes wth dfferent canddate relay locatons. We see that the qualty of the soluton mproves wth the ntal number of canddate locatons that are consdered. At frst there s a sgnfcant mprovement, as the number of canddate locatons s ncreased (e.g. from 5 to to ). However, as the number of canddate locatons ncreases beyond a certan value, t does not yeld any sgnfcant mprovements n the soluton. Ths can be 7

7 shown n Fg., where the curves smooth after the ntal steep decrease n the number of nodes requred for the transfer. For a gven number of possble ntal locatons, the number of RNs requred to transfer the data of SNs ncreases wth the number of SNs. mnor. For example, the networ lfetme ncreased only 5 % f we deploy them randomly even RNs are deployed. On the other hand, the networ lfetme can be tmes f the relays are deployed n an effcent way, as demonstrated by the fgure. 7 NSs=5 NSs= 5 NSs= Number of Canddate Relay Locatons Fg.. Varaton of the number of RNs wth the number of canddate locatons. From the results we can see that dfferent number of RNs has some mpacts on the performance comparson, there exsts a mnmum number of RNs to guarantee the sensor networs worng well. The requred mnmum number of RNs vares wth the gven number of SNs, ther canddate locatons and data rates, and the used deployment strategy. Durng our smulaton analyss, we fnd that the algorthm always needs a lower mnmum number of RNs than the other two schemes. We thus computer an upper bound on the mnmum number of RNs requred by algorthm for a gven SNs number and ther locatons. We compute ths bound for each smulaton case and use the results as the default number of RNs n the remanng of ths secton. To nvestgate how these three algorthms perform n the case of the number of RNs s comparable to the number of SNs, we temporarly extend the communcaton range constrant of RNs ranged from m to 5 m. The results are shown n Fg.. It llustrates the smulaton results for dfferent networ sze wth dfferent number of extra RNs. Specfcally, X-axs represents the number of RNs that should be placed n the networ, and Y-axs denotes the normalzed networ lfetme (normalzed by the results of no relay deployment). The two curves show the acheved networ lfetme by applyng the three dfferent relay deployment schemes. Fg. (a) shows the results of the networ lfetme wth dfferent number of RNs when SNs are deployed. From these results we can see that f we can place RNs n an energy-effcent way, sgnfcant gan can be acheved even when only a small number of RNs are deployed. For example, when only % of relay nodes are deployed, the networ lfetme can be further extended more than 7 % by applyng the heurstc deployment method. We can also see that f we deploy nodes randomly, the gan s very Normalzed Lfetme 5 Random Normalzed Lfetme 5 Random (a) SNs= (b) SNs= Fg.. Normalzed networ lfetme wth dfferent number of RNs. Fg. (b) shows the results for a smaller networ sze wth SNs number s. From these results we can see that sgnfcant networ lfetme mprovement stll can be acheved by relay deployment. For example, when only % of addtonal relays are placed, the networ lfetme can be mproved by more than %. If we compare the results n Fg. (a) and Fg. (b), we can see that more networ lfetme mprovement can be acheved n a larger networ, where % addtonal relays can brng 7 % lfetme mprovement. Ths s because n larger networ, the energy hole around the BS s more sgnfcant. Ths also suggests that the proposed algorthm can effectvely allevate the energy whole problem. It can be seen that there are some small fluctuatons n the Fg.. Ths s because as the number of RNs ncreases, the margnal effects of the networ topology vary and that only a small number of RNs can be used to mprove the networ performance sgnfcantly. However, the curve trends of and are stll relatvely stable wth the performance mprovement only slghtly decreased. Also, n Fgs. and 5, whle performs roughly up to 5 tmes of wthout relay, rases 8

8 the gan up to tmes. Ths demonstrates the mportance of consderng the traffc patterns durng node deployment stages. Furthermore, the performance of s hgher than snce the ECR constrant can guarantee tres to fnd the more elgble locatons for relay deployment. Fg. 5 shows the results of the normalzed remanng energy (normalzed by the results of deployment) wth dfferent number of RNs. We can see that the and soluton have much less total remanng energy than, snce the energy consumpton of the former two algorthms s more balanced by assgnng more RNs to the SNs wth hgher traffc flows. Ths also explans that the remanng energy of ncreases much faster than the other two solutons. It s because deploy RNs wthout consderng the mpact of networ flow. Normalzed Remanng Energy Fg. 5. Normalzed remanng energy wth dfferent number of RNs. In Fg., the energy consumpton by RNs n three algorthms s compared wth smulaton steps. The energy cost spent by relay nodes per step n s much lower than that n, and s about the same as that n. Because n algorthm relay nodes send ther data to the BS va -hop or -hop communcaton, the energy cost s much hgher. In OERD and, relay nodes are permtted to send ther data to the BS va mult-hop relay communcaton. By ths way a large number of energy consumpton s decreased n relay nodes. In and, the amount of energy consumpton spent by relay nodes n s slghter smaller than that of n each step due to ts optmzaton of three ter networ. Average energy consumpton by RN(mJ) Smulaton Step Fg.. Average energy consumpton by RNs wth smulaton step... Scalablty wth We next nvestgate how our soluton performs wth dfferent number of SNs. Fg. 7 shows the results of the networ lfetme wth dfferent number of SNs. It s clear to see that our scheme performs much better than the other solutons. As the number of SNs ncreases, the lfetme of both and ncrease faster and s much hgher than that of. From the results we can see that the lfetme of frst ncreases and then decreases slghtly. We analyses that the reason may be that the energy whole phenomenon [] becomes more serous when the number of SNs ncreases. The energy whole problem can result n a case that the RNs close to the BS are depleted whle most of other RNs stll have most of the energy. As the number of SNs ncreases, more traffc wll accumulate close to the BS. Ths reduces the lfetme serously f the deployment s not aware of the traffc accumulatons such as the scheme. On the other hand, and our soluton successfully solve ths problem by usng algorthms deployng more RNs close to the BS. In addton, algorthm performs better than snce t assgns the RNs to SNs accordng to the networ flow and ts energy consumpton rate. Normalzed Lfetme Fg. 7. Normalzed networ lfetme wth dfferent number of SNs Fg. 8 shows the results of the total remanng energy wth dfferent number of SNs. As the number of SNs ncreases, all the three schemes show a smlar trend and are not very senstve to the number of SNs. As we expected, the soluton has the lowest remanng energy, whch s followed by soluton. performs worse due to wthout consderng the mpact of networ flow n ts relay deployment model. Fg. 9 compares the average transmsson energy of scheme to that of the other two schemes. As the number of SNs ncreases, the average transmsson energy decreases. Compared to the other schemes, the addtonal transmsson energy requred n our scheme decreases sgnfcantly as the number of SNs ncreases (see the lower plot n Fg. 9 whch shows the dfference n average transmsson energy). Fg. plots the varance of the remanng energy of the sensors after the lfetme expres. The varance 9

9 of the remanng energy n scheme s much smaller than the other two schemes, whch ndcates that the remanng energy of scheme reaches almost unform dstrbuton. Ths result satsfes the requrement of sensor networs snce we balance the networ flow among the RNs by reroutng method. On the other hand, hgher varance of the other two deployment schemes ndcates that the remanng energy of the sensors fluctuate serously, whch results n low energy effcency. Normalzed Remanng Energy Fg. 8. Normalzed remanng energy wth dfferent number of SNs. the run tme ncreases sgnfcantly when the number of canddate relays ncreases. Fg. shows the normalzed lfetme n the networ wth dfferent number of BSs (normalzed by lfetme of the networ deployed by wth one BS). Results are averaged over 5 smulaton runs. Smulaton results depct that the lfetme ncreases almost lnearly as the number of BSs ncrease. Comparng the results when the number of BS s 7, we can see that our proposed algorthm can ncrease the lfetme by % and 5 % compared to algorthms and, respectvely. Runnng Tme(s) 5 l=5 l= Number of Canddate RN Locatons Fg.. Runnng tme of wth dfferent l. Average Transmsson Energy Normalzed Lfetme Number of Sns Fg. 9. Comparson of the average transmsson energy wth dfferent number of SNs. Fg.. Lfetme wth dfferent number of BSs. 5. Conclusons Varance of Remanng Energy e- e- e- e-5 e- 8 8 Fg.. The varance of the remanng energy. We also vary the number of canddate relay locatons n the networs to show whether t has an mpact on the computaton complexty of. As depcted n Fg. for the -SNs networs, Ths paper proposes a novel relay nodes deployment algorthm under the constrants of networ flow and energy level for three ter wreless sensor networ. We assume that the postons of SNs can be predetermned by the sensor placement algorthm of the applcaton and the data reportng traffc patterns can be estmated too. The problem s then to select the optmal locatons of RNs together wth the optmal assgnment of senor-relay so that the energy consumpton of the networ can be mnmzed under the energy constrant of relays. In our heurstc algorthm that was used, the maxmum sensor assgned to the mnmum number of relays performs better n term of the energy consumpton wth respect to networ sze. The computaton complexty of s analyzed mathematcally and the performance s valdated through smulaton. The smulaton results have showed ts performance

10 advantage compared wth tradtonal algorthms. algorthm not only mnmzes the energy consumpton of sensor networs, but also save the number of RNs. Acnowledgements Ths wor s supported by the natural scence foundaton of HuBe under grant no.zry5. References []. S. Lee and M. Youns, Optmzed Relay Placement to Federate Segments n Wreless Sensor Networs, IEEE Journal on Selected area n Communcaton, Vol. 8, Issue 5,, pp []. A. Bhattacharya, A. Kumar, Delay constraned optmal relay placement for planned wreless sensor networs, n Proceedng of the 8 th Internatonal Worshop on Qualty of Servce (IWQoS), 9- October,, pp. -. []. M. Soltan, M. Male, and M. Pedram, Lfetme- Aware Herarchcal Wreless Sensor Networ Archtecture wth Moble Overlays, n Proceedngs of the IEEE Rado and Wreless Symposum, 5-8 February 7, pp []. C. Rahul Shah, R. Sumt, J. Sushant, B. Waylon, Data MULEs: modelng and analyss of a three-ter archtecture for sparse sensor networs, Ad Hoc Networs, Vol., Issue,, pp. 5-. [5]. W. Feng, W. Dan and L. Jangchuan, Traffc-Aware Relay Node Deployment: Maxmzng Lfetme for Data Collecton Wreless Sensor Networs, IEEE Transactons on Parallel and Dstrbuted Systems, Vol., Issue 8,, pp. 5-. []. C. Subramanan, G. Lapll, F. Kret, J. P. Pnell, I. Kostanc, Expermental and Computatonal Performance Analyss of a Mult-Sensor Wreless Networ System for Hurrcane Montorng, Sensors & Transducers, Vol., Specal Issue,, pp. -. [7]. U. Datta, P. K. Sahu, Sumt Kundu, Outage and Energy Performance of Layered CDMA Wreless Sensor Networ wth Space Dversty, Sensors & Transducers, Vol., Issue 7,, pp. -7. [8]. X. F. Han, X. Cao, E. L. Lloyd, Fault-Tolerant Relay Node Placement n Heterogeneous Wreless Sensor Networs, IEEE Transactons on Moble Computng, Vol. 9, Issue 5,, pp. -5. [9]. S. Msra, S. D. Hong, G. Xue, and J. Tang, Constraned Relay Node Placement n Wreless Sensor Networs to Meet Connectvty and Survvablty Requrements, n Proceedng of the IEEE INFOCOM, Aprl 5-7, 8, pp []. E. Zh Ang, T. Hwee-Pn Tan, K. G. Wnston, Routng and Relay Node Placement n Wreless Sensor Networs Powered by Ambent Energy Harvestng, n Proceedng of the Wreless Communcatons and Networng Conference, Aprl 5-8, 9, pp. -. []. S. Maruyama, K. Naano, K. Meguro, M. Sengou, and S. Shnoda, On locaton of relay facltes to mprove connectvty of mult-hop wreless networs, n Proceedng of the th Asa-Pacfc Conf. Commun. and 5 th Internatonal Symposym on Mult- Dmensonal Moble Commun.., 5-7 February, pp []. A. S. Ibrahm, K. G. Sedd, Connectvty-aware networ mantenance and repar va relays deployment, IEEE Transactons on Wreless Communcatons, Vol. 8, Issue, 9, pp. 5. []. X. Kenan, H. Hossam, T. Glen, W. Quanhong, Relay Node Deployment Strateges n Heterogeneous Wreless Sensor Networs, IEEE Transactons on Moble Computng, Vol. 9, Issue,, pp []. Y. T. Hou, S. Y, H. D. Sheral, S. F. Mdff, On energy provsonng and relay node placement for wreless sensor networs, IEEE Transactons on Wreless Communcatons, Vol., Issue 5, 5, pp [5]. L. Stanayah, K. N. Brown, and C. J. Sreenan, Multple Sn and Relay Placement n Wreless Sensor Networs, n Proceedngs of the Worshop on AI n Telecommuncatons and Sensor Networs (WAITS ), Montpeler, France, August, pp. -. []. E. L. Lloyd and G. Xue, Relay Node Placement n Wreless Sensor Networs, IEEE Transacton on Computers,, Vol. 5, Issue, 7, pp [7]. L. Stanayah, K. N. Brown, C. J. Sreenan, Faulttolerant relay deployment for node-dsjont paths n wreless sensor networs, n Proceedngs of the Wreless Days (WD),, pp. -. [8]. W. Henzelman, A. Chandraasan, and H. Balarshnan, An applcaton Specfc Protocol Archtecture for Wreless Mcrosensor Networs, IEEE Transactons on Wreless Communcatons, Vol., Issue,, pp. 7. [9]. J. Flathagen, P. E. Engelstad, Constraned-based Multple Sn Placement for Wreless Sensor Networs, n Proceedng of the IEEE 8 th Internatonal Conference on Moble Adhoc and Sensor Systems (MASS),, pp []. C. Promma and S. Modhrun, Optmal Networ Desgn for Effcent Energy Utlzaton n Wreless Sensor Networs, Journal of Computer Scence, Vol. 8, Issue,, pp []. S. C. Ergen, P. Varaya, Optmal Placement of Relay Nodes for Energy Effcency n Sensor Networs, n Proceedng of the IEEE Internatonal Conference on Communcatons, Istanbul, Turey, - December, pp []. J. L, P. Mohapatra, Analytcal modelng and mtgaton technques for the energy hole problem n sensor networs, Journal of Pervasve and Moble Computng, Vol., Issue, 7, pp. -5. Copyrght, Internatonal Frequency Sensor Assocaton (IFSA). All rghts reserved. (