I. J. Communcatons, Network and System Scences, 008,, 05-06 Publshed Onlne May 008 n ScRes (http://www.srpublshng.org/journal/jcns/). Analyss of Lfetme of Large Wreless Sensor Networks Based on Multple Battery Levels Ruhua ZHANG, Zhpng JIA, Dongfeng YUAN School of Computer Scence and Technology, Shandong Unversty, Jnan 5006, P.R.Chna School of Informaton Scence and ngneerng, Shandong Unversty, Jnan 5000, P.R.Chna -mal: ruhua_zhang@sdu.edu.cn Abstract Due to the lmted transmsson range, data sensed by each sensor has to be forwarded n a mult-hop fashon before beng delvered to the snk. The sensors closer to the snk have to forward comparatvely more messages than sensors at the perphery of the network,and wll deplete ther batteres earler. Besdes the loss of the sensng capabltes of the nodes close to the snk, a more serous consequence of the death of the frst ter of sensor nodes s the loss of connectvty between the nodes at the perphery of the network and the snk; t makes the wreless networks expre. To allevate ths undesred effect and maxmze the useful lfetme of the network, we nvestgate the energy consumpton of dfferent ters and the effect of multple battery levels, and demonstrate an attractvely smple scheme to redstrbute the total energy budget n multple battery levels by data traffc load. We show by theoretcal analyss, as well as smulaton, that ths substantally mproves the network lfetme. Keywords: Wreless Sensor Networks, nergy ffcent, Network Lfetme, Battery Level. Introducton Sensor network applcatons have recently become of sgnfcant nterest due to cheap sngle-chp transcevers and mcro-controllers. Because sensor nodes are batterypowered, and ther operatonal lfetme should be maxmzed, one of the most mportant desgn crtera for ths type of network s energy effcency. Confrmng the mportance of the problem, many aspects of the problem have been extensvely studed [ 4]. Medum access control (MAC) layer technques [] [3] am to conserve battery energy by turnng the recever off whenever t s not needed. It s clear that the energy problem cannot be completely solved at any one sngle layer [4]. The motvaton for our work stems from the observaton that n a sensor network, the sensor nodes closer to the snk have to relay more packets than the ones at the perphery of the network. We assume that ths ncrease n workload results n an ncrease n energy consumpton, the nodes close to the snk wll de frst, leadng to a premature loss of connectvty n the sensor network. To allevate ths undesrable effect, we study the energy consumpton of dfferent ters, and demonstrate a scheme to redstrbute the total energy budget for the sensor network, the lfetme of the network can be sgnfcantly mproved over the case where all sensors have a unform lfetme. The optmal soluton s formulated theoretcally and valdated va smulatons. About ths problem, n [5 9], non-unform node deployment s exploted as an alternatve manner to get over the effect of non-unform energy depleton. The basc concept s that dfferent node denstes are assgned to dfferent sub-regons tryng to balance the communcaton load of each sub-regon. Some works specfcally consder the scenaro for concentrc subregons (rngs); the node densty of a rng s determned based on the number of hops to the snk, whch s roughly approxmated to be the same for all locatons n a rng n [5 7]. In [8], the mbalanced energy utlzaton of a WSN was analyzed based on the hop counts, and the authors accordngly proposed a non-unform node dstrbuton dependng on the hop-count to mprove the long-term connectvty. In [9], the energy-hole problem was dscussed n a more general form for a rectangular sensng area wth multple data snks at dfferent Copyrght 008 ScRes. I. J. Communcatons, Network and System Scences, 008,, 05-06
ANALYSIS OF LIFTIM OF LARG WIRLSS SNSOR NTWORKS 37 BASD ON MULTIPL BATTRY LVLS locatons. Another approach, heterogeneous deployment, overcomes the communcaton load unbalance problem by usng two types of sensors, low energy sensors and hgh energy sensors, to construct a herarchcal network structure [0]. However, ths scheme rases the deployment and mplementaton complexty and cannot be easly appled. The remander of the paper s organzed as follows. Frst we present the network model and the energy consumpton model n Secton. Secton 3 provdes a mathematcal formulaton that attempts to estmate the average lfetme of a sensor network and analyzes the desgn problems. We provde the smulaton results n secton 4. We conclude the paper wth a summary and dscusson of future work n Secton 5. pockets and wll de frst. If the spatal dstrbuton of nodes s close to unform, then the traffc load s equally dstrbuted spatally. ach frst ter node wll relay roughly the same amount of traffc, and all frst ter nodes wll de at tmes very close to each other, after the network s frst put nto operaton. Once all of the frst ter nodes are dead, no other node wll be able to send data to the snk, and the lfetme of the network wll be over.. nergy Consumpton Model nergy consumpton models of the rado llustrated by Fgure. In [] a model for rado energy consumpton s gven for energy per bt sngle hop (e b ) as: K bts Transmtter eta lectroncs eb etx + erx () e e d + e (-) Amplfer α tx ta te d Recever lectroncs K bts Fgure. Sensng feld We assume that sensed data s collected n a perodc manner; ths perod (nterval P seconds) conssts of the sensng of the data and the transmsson of one packet contanng the data sensed to the snk. We assume that each sensor has a constant amount of raw data pocket (b s bts) to sense and send n nterval P. ete eta Fgure. Rado energy consumpton model where e tx and e rx are the transmtter and recever energy consumptons per bt, respectvely, e te s the energy per bt needed by the transmtter electroncs, e ta s the energy needed to successfully transmt one bt over one meter, d s the dstance from transmtter to recever and α s a constant whch depends on the attenuaton the sgnal wll suffer n that envronment. Consder a crcular sensng feld wth the radus R L meters, a total of N sensor nodes are unformly dstrbuted wthn the feld. The snk node s n the center of the feld. The transmsson radus R of the sensor nodes assumed to be fxed. We dvde the sensng feld nto T ters, Tcelng (R L /R). Fgure shows the doughnut-lke dstrbuton of nodes [9]. In such a crcular feld, consder the set of nodes close to the snk at the center that can communcate drectly wth t. We refer to these one-hop neghbors of the snk as the frst ter of nodes. Smlarly, the two-hop neghbors of the snk wll be the second ter of nodes, etc. It s clear that the frst ter nodes relay the largest amount of data erx 3. Analyss and Numercal Results 3.. stmaton of Network Lfetme We defne ter as the set of the nodes that can reach the snk n hops ( T ). We consder the energy budget as the man cost functon, s the sum of the energy avalable at the nodes of ter, so T () N s the number of nodes at ter. Wth the assumpton of a unform densty: N (( ) N) / T (3) F s the total number of data packets, they are relayed to the snk by all nodes at ter ; each data packet s generated by one sensor node at ters + T. j ( ( ))/ (4) j F N N N T T Copyrght 008 ScRes. I. J. Communcatons, Network and System Scences, 008,, 05-06
38 R.H. ZHANG T AL. In ter, nodes relay all data pockets generated by nodes at ters j( < j T), and nodes at ter generate and send all data pockets, let relay and gen denote ther energy consumed, respectvely; e s s the energy spent sensng per bt; b s s data pocket sze. So we get the relaton wth energy consumpton and tme t. Thus relay + (5-) gen (/ t p) Fbe (5-) relay s b (/ t p) Nb ( e + e ) (5-3) gen s s tx tnbs( eb( T ) + ( es + etx)( )) (5) T p L s the lfetme of the nodes at ter, t can be determned by consderng the energy consumpton. Usng (5), we can get: PT L Nb T e e e s(( ) b + ( )( s + tx)) (6) In accordance wth all the above consderatons, we defne the lfetme of the network as the mnmum of the lfetmes of ts ters: L mn L (7)... T In ths case, each node wll start wth the same energy, namely /N; then, the energy at each ter s Hence, (6) becomes N ( ) (8) N T P L T N be s b + Nbs( es + etx) Snce the term (T - )/(-) s monotonously decreasng wth for T, L the lfetme of ter s monotonously ncreasng wth. In other words, the lfetme of the network L s equal to the lfetme of the frst ter: P L L N( T ) be + Nb ( e + e ) s b s s tx (9) (0) It s obvous that when the lfetme of the frst ter has expred, the whole network has expred; the nodes n other ters have stll remanng energy. Usng (8) and (9), the resdual energy of other ters rest : res ( T ) eb + ( )( es + etx) ( ) b + s + tx [( ) ] T T e e e () The above equatons can also help us determne a reasonable energy allocaton for all nodes. One possble crteron s to let the all ters have the same-targeted lfetme. Thus by balancng energy allocaton, by usng () and (6), we can maxmze the network lfetme for a gven fxed amount of energy. So we get the relaton: L L L () T ( T ) eb + ( )( es + etx) ( T ) eb + es + etx Usng () and (), we get the relaton: + + (4 3 ) / 6 ( ) (( T ) eb es etx) 3 T T T eb + T es + etx (3) (4) If we allocate the energes at dfferent ters accordng as (3) and (4), we can maxmze the network lfetme; all ters energes wll be depleted at the same tme. 3.. Desgn Problems From the above, how to allocate the energes n dfferent ters s practcal mportance to the network desgners. A reasonable alternatve problem specfcaton would provde, nstead of the total budget, the unform battery level b u for each node. In that case, the lfetme of the network would be ndependent of the total number of nodes N. The only topology relevant quantty would be the number of ters T. It wll be useful n nodes energy allocaton. Accordng to (0), t s obvous that when the lfetme of the frst ter and, therefore, the whole network has expred, the nodes n other ters have stll not expended ther battery energy. The energy consumpton for nodes at dfferent ters can be easly obtaned from a consderaton of (0) and (). The hypothetcal lfetme of ter s L ; but, t s actually expendng energy for only the lfetme L of the network. After that, communcaton stops, and there s no more expendture of energy. Thus, the rato of battery energy b actually consumed by a node n ter to the unform battery level b u that t started wth s: T b e ( ) e L b + es + etx C (5) b L ( T ) e + e + e u e b s tx We call the ratos C the deal allocaton ratos, because deally each node would be allocated only the amount of battery t would actually consume durng the lfetme. The farther out a node, the lower the fracton C of ts battery that t has consumed. The unconsumed energy s wastage of the total energy budget. The broad desgn goal s to redstrbute ths energy budget nonunformly so as to ncrease the lfetme of the whole Copyrght 008 ScRes. I. J. Communcatons, Network and System Scences, 008,, 05-06
ANALYSIS OF LIFTIM OF LARG WIRLSS SNSOR NTWORKS 39 BASD ON MULTIPL BATTRY LVLS network. 3... Problem In many practce applcatons, a desgner would have several known battery capactes to choose from e.g., AAA, AA, C and D. Then, the followng problem can be formulated. Gven k avalable battery levels b >b > >b k >0, assgn the battery level for each ter of nodes n a sensor network, such that the total battery budget s mnmzed subject to maxmzng the lfetme L of the network. Two alternatve flavors of the above problem can be artculated: (a) all nodes n any gven ter are constraned to be assgned the same battery level, and (b) dfferent nodes of the same ter can be assgned dfferent battery levels. Thus, we are requred to obtan one unque battery level b for ter n Problem A; every node n ths ter should be assgned ths battery level. For problem B, we can provde more than one battery level for each ter accompaned by the proportons of the total number of nodes n that ter that should be assgned each battery level. Below, we address problem A frst. The maxmum network lfetme s obtaned when all nodes have the maxmum battery level b. Thus, the frst ter of nodes should have batteres of capacty b, and the maxmum lfetme of the network wll be L L ( b ) (6) where, by L (b) we denote the lfetme of ter (gven by (6)) f each node n ter ntally has a battery capacty b. The same maxmum lfetme as n (6) may be obtaned wth a lower budget by assgnng lower battery levels to nodes n the hgher ters (n ters wth <<T); however, f the next smallest capacty sze s too small, then the lfetme of the network would be reduced because nodes n hgher ters wll deplete ther batteres before the nodes n the frst ter. Gven b, the deal level of battery that each node of ter should have s obvously C b, where C s the deal allocaton ratos gven by (5), so that ter wll have exactly the same lfetme as ter. In short, for each ter, n order to maxmze the lfetme of the network and then condtonally mnmze the total battery budget, we need to make sure that we assgn the battery sze b j to ter such that b j+ <C b <b j. If the deal level s less than the mnmum provded battery level b k, then that mnmum level must be used n that ter nstead; n ths case some battery wll ndeed reman unconsumed at the end of the lfetme. Now, f we consder problem B, we have the added flexblty of mxng the provded battery levels. Frst, we pck the hghest battery level b for ter as before: ths maxmzes the network lfetme. Now we predct the deal battery levels for each ter as before usng (5); but now, nstead of pckng the next hghest avalable level from the avalable ones, we am at attanng ths deal level exactly as the effectve battery level by mxng the two provded battery levels n the approprate rato. In case the desred battery level s exactly equal to one of the provded battery levels, no mxng s needed. How to mx the same ter nodes wth the dfferent battery levels? Usually, we would provde two battery levels to a ter. If we pck battery level b for ter, the deal level of battery that each node of ter should have been C b. We pck two battery levels b and b - for ter from avalable battery levels such that b <C b <b -. If we specfed proportons f and f for the two levels wth f +f, then the effectve battery level of ter would be gven by b f +b - f, such that, bf + b f Cb (7) So we get the relaton: b Cb f b b Cb b f b b 3... Problem (8) (9) In the above problem, mnmzng the battery budget s a secondary goal of the optmal desgn. It s also possble that the battery budget may be strctly a constrant for the desgn. If the total cost of the batteres used for a partcular network s upper bounded by a total battery budget and the battery capactes are fxed and gven, we can formulate the followng problem: Gven k avalable battery levels b >b > >b k >0, and a total energy budget, assgn the battery level for each ter of nodes n a sensor network, such that the total lfetme L of the network s maxmzed. As wth Problem, we can conceve of two alternate problems, Problems A and B, n whch the nodes n any ter are constraned to have the same battery level, or mxng s allowed, respectvely. We consder Problem A frst. As the soluton to Problem A, we assgn the battery levels at dfferent ters wth the maxmum lfetme unconstraned by total battery budget. Assume that L (b j ) s pre-computed lfetme for each ter and each battery level b j. Intalze current network lfetme L c to L (b ). Whenever the total battery Nb becomes less than or j equal to the battery budget, the algorthm s termnated. If the current total battery exceeds, repeatedly perform the followng. Fnd the ter such that the dfference L c L (bj+) s mnmzed. The ter wll be assgned the next lower battery level from the one t s currently assgned, that wll result n the mnmum reducton of the lfetme. Note that ths mnmum Copyrght 008 ScRes. I. J. Communcatons, Network and System Scences, 008,, 05-06
40 R.H. ZHANG T AL. dfference may well be zero at some teraton. Increment the current level for ter by and the update the network current lfetme to the new lfetme of ter. Recalculate the total battery used. When the total battery frst falls below the budget, the algorthm wll stop wth an optmal soluton. Problem B turns out to be a modfcaton of Problem B, where the total battery budget s now a hard constrant. Accordngly, we take the followng approach to solve t: frst solve Problem B on the same parameters, gnorng the battery budget. If the total battery budget t of ths soluton does not exceed, then ths s the desred soluton. If nstead t >, then obtan a new set of effectve battery levels for each ter by scalng the battery levels by a factor of / t : these are the new desred battery levels. A specal case arses when some of these new desred battery levels are less than the mnmum provded battery level b k. In ths case the battery levels for the nner ters have to be reduced to allow the outer ters to have battery level b k, further reducng the lfetme. In consderng these problems, any such algorthm would be executed not by the nodes themselves but offlne durng network desgn. In all realstc cases of deployment, most nodes wll have postons n the approprate annular regons, but some randomness wll be ntroduced; lfetme wll be then somewhat reduced from that acheved n the deal case, but the deal lfetme s a good ndcator of actual lfetme n such cases. 4.. Base Case Fgure 3. The energy consumpton at defferent ters 4. Smulaton Results To valdate the results presented n the prevous secton, we decded to smulate the wreless sensor network n several scenaros. For smplcty reasons, we wll assume that perfect schedulng s acheved at the MAC layer and routng layer. Any two nodes at a dstance less than the transmsson radus can communcate wth no errors; any nodes at a dstance larger than the transmsson radus cannot communcate. We consdered a network of N 500 nodes, whch corresponds to a fve-hop route for the perpheral nodes (T5), we assume that the total energy of the network s bounded by 40000 joules n each case. ach node generates one data packet every mnute; the sze of pocket s 04 bts. Fgure 4. The resdual energes at dfferent ters Table. Smulaton parameters Parameter Transmtter crcutry, ete Recever crcutry, erx Transmt one bt over one meter, eta Sensng energy per bt, es Bts sense per sensor, bs Value.34 µј/bt.34 µј/bt 7.8 nј/bt/m.75µј/bt 04bts Table shows the values of the parameters n ths sample crcut and the propagaton envronment []. Fgure 5. The allocatng energes rato at dfferent ters wth maxmzng the network lfetme Usng (5), we get Fgure 3. It depcts the energy consumpton at dfferent ters, because the frst ters relay the most data pockets, and consume the maxmum energes. The energy consumpton of the second ter, the thrd ter the ffth ter s ordnal decrease. The energy Copyrght 008 ScRes. I. J. Communcatons, Network and System Scences, 008,, 05-06
ANALYSIS OF LIFTIM OF LARG WIRLSS SNSOR NTWORKS 4 BASD ON MULTIPL BATTRY LVLS consumpton of the ffth ter s the mnmum; nodes at the ffth ter don t relay other data pockets. If each node wll start wth the same energy (namely /N), nodes at the frst ter depleted ther energes full out. Though nodes at other ters have the resdual energes, but ther data pockets can t be relay to the snk, the network becomes dsconnected; the lfetme of the network s the end. Usng (), we get Fgure 4. The resdual energes at dfferent ters aren t the same. The resdual energes at ffth ter are the most; the resdual energes at second ter are the least. For maxmzng the network lfetme for a gven fxed amount of energy, we wll balance energy allocaton at dfferent ters. Usng (3), we get Fgure 5. It depcts the allocatng energes rato at dfferent ters. If we allocate the energes at dfferent ters accordng as the rado wth Fgure 5, we can maxmze the network lfetme; all ters energes wll be depleted at the same tme. In the same parameters case, the network lfetme s 6.847 seconds and 494.8 seconds by the two energy allocaton schemes, respectvely. The lfetme of the network can be sgnfcantly mproved. n three deployment schemes, the frst ter lfetme s the shortest wth 7.34 P ntervals, so the whole networks lfetme s 7.34 P ntervals. In base case deployment scheme, energy effcency s 5.%; there s much resdual energy at dfferent four ters when the whole network has expred. In queston A deployment scheme, energy effcency s 89.6%. But avalable battery levels lmt, there are some resdual energes at dfferent ters when the whole networks has expred. In queston B deployment scheme, energy effcency s 98%. From the curve of queston B, we can know the lfetme of nodes n the frst, the second, the thrd, the forth s the same. Namely, the four ters energy all has expred when the networks lfetme has expred. 4.. The ffect of Multple Battery Levels On the assumpton that we can provde 5 battery levels, they are 578mAh, 000 mah, 000 mah, 500 mah, 50 mah, respectvely. For the base case, each node wll be assgned wth the same battery level 578 mah, the whole networks energy budget s 7767J. For the problem A and maxmzng network lfetme, the frst ter of nodes should have batteres of capacty 578mAh. Accordng to the deal allocaton ratos C, the second ter, the thrd ter, the fourth ter, the ffth ter of nodes should have batteres of capacty 656 mah, 868.7 mah, 47. mah, 05.7 mah, respectvely, but as avalable battery levels lmt, they have batteres of capacty 000 mah, 000 mah, 500 mah, 50 mah n applcaton, respectvely. Temporalty, the whole networks energy budget s 35.7J. For the problem B and two battery levels, unformty, the frst ter of nodes should have batteres of capacty 578mAh. Usng formula (8) and (9), the optmum s acheved when 66% of the nodes have 000 mah batteres, and 34% of the nodes have batteres wth 000 mah capacty n the second ter; 74% of the nodes have 000 mah batteres, and 6% of the nodes have batteres wth 500 mah capacty n the thrd ter; 89% of the nodes have 500 mah batteres, and % of the nodes have batteres wth 50 mah capacty n the fourth ter; All nodes have 50 mah batteres capacty n the ffth ter. Temporalty, the whole networks energy budget s 0.6J. Usng above battery deployment and the parameters n table, we can get fgure 6 and Fgure 7. They show the network lfetme of the dfferent ters. As can be seen, Fgure 6. The lfetme compare between the three schemes There s some resdual energy n ffth ter. Because avalable battery levels lmt, we can t deploy the deal approprate battery level. If offerng more battery levels, we can wn the energy effcency wth 00%. All nodes n the dfferent ters have expred at the same tme. Just from the lfetme of networks, the problem B deployment scheme s dealty, but calculatng the proporton of the mxng nodes s slghtly complex. In the practce applcaton, we can select one of the two schemes. Fgure 7. The lfetme compare between the two schemes Copyrght 008 ScRes. I. J. Communcatons, Network and System Scences, 008,, 05-06
4 R.H. ZHANG T AL. The network lfetme s further ncreased f more than two battery levels are consdered, as seen n Fgure 8. Accordng to the scheme n problem, battery levels were used for the smulaton. The same total energy budget 4000J was used for each smulaton. Fgure 8 show that the network lfetme wll ncrease wth the ncrease n the number of battery levels. In the same energy budget, the network lfetme wth dfferent battery levels wll ncrease 88%, 356%, 487%, 559% relatve to one wth one battery level, respectvely. Ths ndcates that most of the ncrease n the lfetme of the network can be acheved wth a relatvely more number of battery levels. The lfetme of the network decreases wth the ncrease n the ntal number of nodes. Ths s expected, as we already know a larger number of ters results n more battery wastage. 4.4. Dependency on Node Densty In ths secton, we study the effect of ncreasng the densty of the network on the lfetme of the network, whle keepng the network sze constant. Fgure 0 shows the dependency of the network lfetme on the node densty. As can be seen n Fgure 0, the node densty has no nfluence on the network lfetme as long as t remans unform. The reason s that the number of nodes n each ter wll ncrease n the same proporton wth the node densty; hence, the number of load flows carred by each node does not change. The lfetme of the network remans constant even f the densty of the network doubles or trples. Fgure 8. The ncrease n network lfetme wth the ncrease n the battery levels by the same energy budget at each battery level 4.3. Dependency on Number of Nodes Accordng to the scheme n problem, battery levels were used for the smulaton. The same total energy budget 4000J was used for each smulaton. Fgure 9 shows the dependency of the network lfetme on the ntal number of nodes. The densty of the network was kept constant, so the area of the network was proportonally ncreased wth the number of nodes. Fgure 9. Dependency of the network lfetme on the ntal number of nodes for three battery levels (constant densty) Fgure 0. Dependency of the network lfetme on the network densty for three battery levels (constant network area) 5. Conclusons and Future Work In ths paper, we have addressed a problem expected to occur n large, mult-hop wreless sensor networks. The nodes closer to the snk wll de before the nodes at the perphery of the network. The man dsadvantage of the expraton of the nodes close to the snk s that the network becomes dsconnected whle most of the nodes stll have a consderable amount of energy left. To allevate ths undesrable effect, we proposed an energy allocaton scheme, allocatng dfferent energy at dfferent ters by traffc. Wth ths strategy, we have shown that the lfetme of the network can be sgnfcantly mproved. Future work would explore smlar ssues, but MAC protocol wll be consdered. 6. References [] B.O. Prsclla Chen and. Callaway, nergy ffcent Copyrght 008 ScRes. I. J. Communcatons, Network and System Scences, 008,, 05-06
ANALYSIS OF LIFTIM OF LARG WIRLSS SNSOR NTWORKS 43 BASD ON MULTIPL BATTRY LVLS System Desgn wth Optmum Transmsson Range for Wreless Ad-Hoc Networks, n Proceedngs of ICC, vol., pp. 945 95, 00. [] W. Ye, J. Hedemann, and D. strn, Medum access control wth coordnated adaptve sleepng for wreless sensor networks, I/ACM Transactons on Networkng, vol., pp. 493 506, June 004. [3] T. V. Dam and K. Langendoen, An Adaptve nergy- ffcent MAC Protocol for Wreless Sensor Networks, Proceedngs of frst nternatonal conference an embedded networked sensor systems, pp. 7 80, 003. [4] R. Mn, M. Bhardwaj, N. Ickes, A. Wang, and A. Chandrakasan, The hardware and the network: Totalsystem strateges for energy aware wreless mcro sensors, n Proceedngs of the I CAS Workshop on Wreless Communcatons and Networkng, (Pasadena, CA), September 00. [5] S.C. Lu, A Lfetme-xtendng Deployment Strategy for Mult-Hop Wreless Sensor Networks, n Proceedngs of I Communcaton Networks and Servces Research Conference, pp. 53 60, May 006. [6] D. Wang, Y. Cheng, Y. Wang, and D.P. Agrawal, Lfetme nhancement of Wreless Sensor Networks by Dfferentable Node Densty Deployment, n Proceedngs of I Internatonal Conference on Moble Ad hoc and Sensor Systems (MASS), pp. 546 549, October 006. [7] X. Wu, G. Chen, and S.K. Das, On the nergy Hole Problem of Non-unform Node Dstrbuton n Wreless Sensor Networks, n Proceedngs of I Internatonal Conference on Moble Ad-hoc and Sensor Systems (MASS), pp. 80 87, October 006. [8] Y. Lu, H. Ngan, and L.M. N, Power-Aware Node Deployment n Wreless Sensor Networks, n Proceedngs of I Internatonal Conference on Sensor Networks, Ubqutous, and Trustworthy Computng (SUTC), pp.8 35, June 006. [9] J. Lan, K. Nak, and G. Agnew, Data Capacty Improvement of Wreless Sensor Networks Usng Non- Unform Sensor Dstrbuton, Internatonal Journal of Dstrbuted Sensor Networks, vol., no., pp. 45, Aprl 006. [0] J.J. Lee, B. Krshnamachar, and C.C.J. Kuo, Impact of heterogeneous deployment on lfetme sensng coverage n sensor networks, n Proceedngs of I Conference on Sensor and Ad Hoc Communcatons and Networks (SCON), pp. 367 376, October 004. [] W. R. Henzelman, A. Chandrakasan, and H. Balakrshnan, nergy effcent communcaton protocol for wreless mcrosensor networks, n Proceedngs of the Hawa nternatonal Conference on System Scences, January 000. [] R. Mn, M. Bhardwaj, N. Ickes, A. Wang, and A. Chandrakasan, The hardware and the network: Totalsystem strateges for energy aware wreless mcro sensors, n Proceedngs of the I CAS Workshop on Wreless Communcatons and Networkng, (Pasadena, CA), September 00. Copyrght 008 ScRes. I. J. Communcatons, Network and System Scences, 008,, 05-06