I J Communicaions, Newok and Sysem Sciences, 008, 3, 07-83 Published Online Augus 008 in Scies (hp://wwwscipog/jounal/ijcns/) On Enegy-Efficien Node Deploymen in Wieless Sesno Newoks Hui WANG 1, KeZhong LU, XiaoHui LIN 1 1 Depamen of Eleconic Engineeing, Shenzhen Univesiy, Shenzhen, China Supecompuing Cene, Shenzhen Univesiy, Shenzhen, China Email: {wanghsz, kzlu, xhlin}@szueducn eceived on July 15, 008; evised and acceped on Augus 6, 008 Absac In wieless senso newoks, senso nodes collec local daa and ansfe o he base saion ofen elayed by ohe nodes If deploying senso nodes evenly, senso nodes neae o he base saion will consume moe enegy and use up hei enegy fase ha educes sysem lifeime By analyzing enegy consumpion, a densiy fomula of deploying nodes is poposed The aio of whole enegy of senso nodes o enegy consumpion speed of senso nodes in evey aea can ge consisen if deploying nodes by he densiy fomula, heefoe sysem lifeime is polonged Analysis and simulaion esuls show ha when communicaion dominaes whole enegy consumpion and he monioed egion is big compaed wih adio ange of senso node, sysem lifeime unde his scheme can be 3/() imes of ha unde deploying nodes evenly, whee is adius of he monioed egion and is adio ange of senso node Keywods: Wieless Senso Newoks, Senso Node, Deploying Node 1 Inoducion ecenly, wieless senso newoks composed of lage senso nodes come o ealize [1 4] Senso nodes have vey limied pocessing and communicaion capabiliies Senso newoks ae muli-hop and senso nodes play a dual ole as boh daa geneaos and oues [5] Enegy is idenified as one of he mos cucial esouces in senso newoks dual o he difficuly of echaging baeies of housands of devices in emoe o hosile envionmens [6 8] eseaches show ha enegy consumpion of senso node is dominaed by communicaion [4,9] In a ypical senso newok, hee is a base saion in he newok Senso nodes sense envionmen, collec senso eading, pocess he daa and hen fowad he infomaion o he base saion An example of such applicaions is habia monioed [10] Senso nodes ae deployed in he habia and he base saion collecs daa fom senso nodes So infomaion of he habia can be achieved fom he base saion Because emoe senso nodes ansfeing daa o he base saion needs some close nodes o elay, daa seam densiy neae o he base saion is bigge If senso nodes ae deployed evenly, nodes neae o he base saion will consume moe enegy If close nodes use up hei enegy, ohe nodes can ansfe hei daa o he base saion and sysem lifeime of senso newok is ove Pesenly, hee s few eseach abou deploying nodes wih he pupose of polonging sysem lifeime Mos eseaches assumed ha senso nodes ae deployed evenly scaeed by aiplane o ohe ools in he monioed egion [11,1] So sysem lifeime of he senso newok can be long [13] eseached daa seam in wieless senso newok and showed ha daa seams of diffeen aeas aen balancing Daa seam of middle aea is dense while daa seam of bounday aea is spase This pape deeminaes aional scheme of deploying nodes by eseaching enegy consumpion in diffeen aeas o polong sysem lifeime The emainde of his pape is oganized as follows In secion, assumpions and base model ae given Secion 3 descibes how o deploy nodes in wieless senso newoks Secion 4 pesens some heoeic analysis and secion 5 pesens a compaaive pefomance evaluaion using simulaion This pape concludes wih secion 6
4 H WANG ET AL Assumpions and Base Model This secion pesens he basic model of he senso newok ha his pape ages The newok model makes he following assumpion: Wieless senso newok is lage-scale Thee ae many senso nodes and a base saion in he newok Monioed egion of he senso newok is a cicle which adius is The base saion is locaed in he cene of he cicle Senso nodes ae homology Iniial enegy of senso node is e Each senso node senses envionmen and ansfes local infomaion o he base saion Evens occu evenly in he monioed egion Daa geneaing speed is λ pe uni aea Senso nodes communicae wih he base saion by deliveing daa acoss muliple hops adio ange of senso node is Enegy consumpion of senso nodes ansmiing uni daa and eceiving uni daa is T and E especively Enegy consumpion no caused by communicaion is evenly disibued in he monioed egion Ohe enegy consumpion speed pe uni aea is W In above, we assume ha he monioed egion is a cicle fo he sake of analyzing easily Sysem lifeime is mosly opimized when he base saion is locaed in he cene Figue 1 Enegy consumpion in aea B elaying daa geneaed ouside aea B is λxdx (T + E ) + / Daa geneaing speed in aea B is π λxdx Enegy consumpion speed of senso nodes in aea B ansmiing daa geneaed in aea B is λxdx T Ohe enegy consumpion speed in aea A is So enegy consumpion of senso nodes in aea B is λ xdx (T + E ) + λ xdx T + The numbe of senso nodes in aea B is 3 Scheme of Deploying Nodes In his secion, we will deduce a densiy fomula of deploying nodes ha will polong sysem lifeime of wieless senso newoks In wieless senso newoks, he aio of whole enegy of senso nodes o enegy consumpion speed of senso nodes in evey aea should be consisen Thus moe senso nodes will be deployed in aea whee enegy is consumed soone As a whole, senso nodes in diffeen aeas will end o use up enegy a he same ime Theefoe sysem lifeime ges polonged fuhes Because we have assumed ha he monioed egion is cene symmey, node densiy should be only elaional wih disance o he base saion We denoe ρ() as node densiy of poin ha is fa fom he base saion Nex we analyze enegy consumpion in aea B in Figue 1 Aea B is a ing ceneed a he base saion ha inne adius is -/ and oue adius is +/ Because adio ange of senso node is, senso nodes ha ae fahe fom he base saion han +/ (ie senso nodes ouside aea B) ansfeing daa o he base saion needs some node in aea B o elay Daa geneaing speed ouside aea B is + / λxdx Enegy consumpion speed of senso nodes in aea B Copyigh 008 Scies ρ ( x) xdx So he whole enegy of senso nodes in aea B is ρ ( x) xdx e The aio of whole enegy of senso nodes o enegy consumpion speed of senso nodes in aea B should be a consan So following condiion is saisfied: ρ ( x) xdx e λ xdx (T + E ) + λ xdx T + =b whee b is a consan Because node densiy of each poin in aea B is almos equal So we appoximaely choose ρ() as aveage node densiy of aea B ie + ρ ( x) xdx ρ ( ) xdx So we can ge: ρ ( ) xdx e λ xdx (T + E ) + λ xdx T + =b Fom he above fomula, we can deduce: ρ ( ) = λ b[ (T + E ) ( / ) T ( + / ) E ] + bw e I J Communicaions, Newok and Sysem Sciences, 008, 3, 07-83
AN ENEGY-EFFICIENT SCHEME OF DEPLOYING NODES IN 43 WIELESS SENSO NETWOKS When / lage, we have -/, +/ So we ge: ρ( ) d, whee c =, ( T + E) λb d = λ( T + E) e Assume ha he numbe of all senso nodes is n, hen π ρ( ) d = n 0 We can deduce d = So we π (4 can obain node densiy of poin ha is fa fom he base saion: ρ ( ), whee c = π (4 λ ( T + E) Fom above densiy fomula, node densiy of close aea is bigge han ha of emoe aea I is consisen wih ou expecaion ρ() consiss of wo pas: and c, whee is evese wih disance o he base saion and c is a consan independen of disance o he base saion In he fomula of c =, λ(t+e) is enegy λ ( T + E) consumpion speed of senso nodes ansmiing and eceiving daa and W is ohe enegy consumpion speed If he popoion of ohe enegy consumpion speed is bigge, c is bigge and node densiies of he monioed egion end o be moe even Ohewise node densiies of he monioed egion end o be moe uneven This is because ohe enegy consumpion speeds in diffeen aeas ae close while enegy consumpion speeds of senso nodes ansmiing and eceiving daa in diffeen aeas ae diffeen 4 Analysis of Sysem Lifeime In his secion, we will analyze sysem lifeime unde deploying nodes by he densiy fomula deduced in las secion compaed wih deploying nodes evenly in wieless senso newok Fis analyze sysem lifeime unde deploying nodes by he densiy fomula ρ ( ) π (4 Because in his case he aio of whole enegy of senso nodes o enegy consumpion speed of senso nodes in evey aea is consisen, senso nodes in evey aea end o use up hei enegy a he same ime Then sysem lifeime appoximaes he aio of whole enegy of senso nodes o enegy consumpion speed of senso nodes in some aea Theefoe we can only analyze sysem lifeime of senso nodes in aea C which is less han fa fom he base saion Enegy consumpion speed of senso nodes in aea C is π λxdx ( T + E ) + π λxdx T + π Whole enegy of senso nodes in aea C is ρ( ) xdx = 0 3 ne(6 + 3c ) So sysem lifeime is: (4 ne c 3 (6 + 3 ) π (4 + 3 c)[ λ xdx (T + E ) + λxdx T xdx W ] + 0 0 Nex le s analyze sysem lifeime unde deploying nodes evenly Senso nodes ouside aea C ansfeing daa o he base saion needs some node in aea C o elay Because senso nodes ae deployed evenly, enegy consumpion speed of senso nodes in aea C is fases Theefoe senso nodes in aea C will use up hei enegy ealies When senso nodes in aea C use up hei enegy, he base saion can eceive any daa fom he senso newok and sysem lifeime is ove So sysem lifeime appoximaes he aio of whole enegy of senso nodes o enegy consumpion speed of senso nodes in aea C also Enegy consumpion speed of senso nodes in aea C is π λxdx ( T + E) + π λxdx T + π Whole enegy of senso nodes in aea C is lifeime is: ne ne So sysem π [ λxdx ( T + E) + λxdx T + ] The aio of sysem lifeime unde deploying nodes by he densiy fomula ha unde deploying nodes evenly is: ρ ( ) o π (4 6 + 3c 6 3c = +, (4 (4 3c + 4 whee and c ae fixed values Fom he above aio, we can see sysem lifeime unde deploying nodes by he densiy fomula is long han ha unde deploying nodes evenly When ohe enegy consumpion is lile and he monioed egion is big, ie c 0 and», he aio appoximaes o 3/() Because is a fixed value, he aio is bigge when he monioed egion is lage 5 Simulaion In his secion, we compae sysem lifeime unde deploying nodes by he densiy fomula poposed by his pape wih deploying nodes evenly by simulaion We adop ns-8 simulao [14] as expeimen plafom We use he following model fo ou simulaion sudy: MAC poocol is 8011 DCF adio bandwidh is 1 Mbps adio ange is 50 m Iniial powe of senso node is 10000 J Senso node s sending and eceiving powe ae 0660
44 H WANG ET AL W and 0395 W especively The size of packe is 64 B Ohe enegy consumpion of senso node is 0 The occuing of even in he monioed egion saisfies Poisson disibuion The speed of even occuing in aea is 001 m - s -1 Sensing daa of one even has 10 packes aveagely We simulae unde vaious sizes of he monioed egion Choose adiuses of he monioed egion be 00 m, 400 m, 600 m, 800 m, and 1000 m Fix aveage node densiy of he whole monioed aea be 1/(400π) m - So he numbes of senso nodes in vaious monioed egions ae 100, 400, 900, 1600 and 500 especively We choose sysem lifeime as he ime fom beginning o when aveage aio of even being successfully monioed by he base saion is unde a heshold of 90% Obseve sysem lifeime unde vaious simulaion condiions In ode o make esuls moe pecise, we simulae 10 imes fo each simulaion condiion and choose aveage value Table 1 shows sysem lifeime unde vaious condiions denoes adius of he monioed egion denoes adio ange n denoes he numbe of senso nodes α denoes sysem lifeime unde deploying nodes by he densiy fomula poposed by his pape β denoes sysem lifeime unde deploying nodes evenly The aio of sysem lifeimes unde hese wo schemes is nea o 3/ I s consisen wih analysis esul in secion 4 Figue shows compaison of sysem lifeimes unde hese wo schemes Sysem lifeime unde deploying nodes by he densiy fomula poposed by his pape is much longe han deploying nodes evenly Table 1 Sysem lifeime unde vaious condiions ( is 50 m) (m) n α(10 4 s) β(10 3 s) α/β 3/ 00 100 461 81 561 6 400 400 6 187 1140 1 600 900 147 086 1715 18 800 1600 108 047 89 4 1000 5085 030 86 30 sysem lifeime (10 3 s) Figue Sysem lifeime: deploying nodes by he densiy fomula vs deploying nodes evenly 6 Conclusions This pape deduces he densiy fomula ρ ( ) of deploying nodes in π (4 wieless senso newoks by analyzing enegy consumpion speeds in diffeen aeas The aio of whole enegy of senso nodes o enegy consumpion speed of senso nodes in evey aea can ge consisen if deploying nodes by he densiy fomula Then we analyze sysem lifeime unde his scheme of deploying nodes When communicaion dominaes whole enegy consumpion and he monioed egion is big compaed wih adio ange of senso node, sysem lifeime unde his scheme can be 3/() imes of ha unde deploying nodes evenly, whee is adius of he monioed egion and is adio ange of senso node Finally simulaion esuls validae his conclusion 7 Acknowledgemen The eseach was joinly suppoed by eseach gans fom Naual Science Foundaion of China unde pojec numbe 6060066 and 6077303, gan fom Guangdong Naual Science Foundaion unde pojec numbe 5010494 The wok has also go suppo fom Foundaion of Shenzhen Ciy unde pojec numbe QK00601 Coesponding auho: Ke-Zhong Lu (kzlu@szueducn) 8 efeences [1] I F Akyildiz, W Su, Y Sankaasubamaniam, and E Cayici, Wieless senso newoks: a suvey, Compue Newoks, 38(4), pp 393 4, 00 [] S Bown and CJ Seenan, A new model fo updaing sofwae in wieless senso newoks, IEEE Newok, 0(6), pp 4 47, 006 [3] L Cui, H L Ju, Y Miao, T P Li, W Liu, and Z Zhao, Oveview of wieless senso newoks, Jounal of Compue eseach and Developmen, 4(1), pp 163 174, 005 [4] J M Kahn, H Kaz, and K S J Pise, Nex cenuy challenges: mobile newoking fo sma dus, in Poceedings of he 5h Annual ACM/IEEE Inenaional Confeence on Mobile Compuing and Newoking, pp 63 70, 1999 [5] H S Kim, T F Abdelzahe, and W H Kwon, Minimum-enegy asynchonous disseminaion o mobile sinks in wieless senso newoks, in Poceedings of he 1s Inenaional Confeence on Embedded Newoked Senso Sysems, pp 193 04, 003 [6] Y Yang, V K Pasanna, and B Kishnamachai, Enegy minimizaion fo eal-ime daa gaheing in wieless senso newoks, IEEE Tansacions on Wieless Communicaions, 5(11), pp 3087 3096, 006
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