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Energy-awareNodePlacementinWirelessSensorNetworksPengCheng,Chen-NeeChuahXinLiuDepartmentofElectricalandComputerEngineeringDepartmentofComputerScienceUniversityofCalifornia,DavisUniversityofCalifornia,DavisDavis,CA,95616Davis,CA,95616E-mail:{pcheng,chuah}@ece.ucdavis.eduE-mail:liu@cs.ucdavis.eduAbstract—OneofthemaindesignissuesforwirelesssensorNodesclosertothesinknodehaveheaviertrafficload,sincenetworksisthesensorplacementproblem.Inthispaper,wetheynotonlycollectdatawithintheirsensingrangesbutrelayformulateaconstrainedmultivariablenonlinearprogrammingdatafornodesfurtherawayaswell.Suchanunbalanceddataproblemtodetermineboththelocationsofthesensornodesandvolumeintroducesanunevenpowerconsumptiondistributiondatatransmissionpattern.Thetwoobjectivesstudiedintheamongdifferentsensornodes.Sincetrafficloadandpowerpaperaretomaximizethenetworklifetimeandtominimizetheconsumptionofeachnodearelocation-dependent,thenetworkapplication-specifictotalcost,givenafixednumberofsensorlifetimecanbelimitedbynodeswithheavierdataloadandnodesinaregionwithcertaincoveragerequirement.Wefirstthusgreaterpowerconsumption.Therefore,nodeplacementstudyalinearnetwork,andfindoptimalplacementstrategiesschemewillhaveconsiderableimpactonthenetworklifetime.numerically.Throughnumericalresults,weshowthattheoptimalnodeplacementstrategiesprovidesignificantbenefitOurcontributionsarethreefold.First,weformulateaoveracommonlyuseduniformplacementscheme.Furthermore,constrainedmultivariablenonlinearprogrammingproblemtowealsopresentaperformanceboundasabenchmark.Lastlywedetermineboththelocationsofthenodesandthedataextendtheresultstoamoresophisticatedplanarnetwork,andtransmissionpatternconsideringtwoobjectives:tomaximizeusenumericalresultstoevaluatetheperformanceofthethenetworklifetimeandtominimizetheapplication-specificproposedstrategies.totalcost,giventhenumberofsensornodes.Second,wepresenttwonumericallyoptimalplacementstrategiesandKeywords-NetworkLifetime;LinearNetwork;PlanarNetworkperformanceboundsforlinearnetworks.Finally,afterexploringandunderstandingthefundamentalsofalinearI.INTRODUCTIONnetwork,weextendtheresultstoamoresophisticatedplanarWirelesssensornetworks[1]arecomposedofagreatnetwork.numberofsensornodesdeployedinafashionthatmayTherestofthispaperisstructuredasfollows.InSectionII,revolutionizeinformationcollecting.Sensornetworksareweformulatetheproblemanddescribethesystemmodel.IndifferentfromotherwirelessnetworksduetothelimitationsonSectionIII,wepresentouroptimalstrategiesforlinearbatterypower,nodedensities,andhugedatavolume.Powernetworks.Heuristicboundsarecomputed,andnumericalconservationisaprimaryconcerninprolongingthelifetimeofresultsarepresentedinSectionIV.Weexploreplanaranetworkoperation.Manyapplications,suchasseismicnetworksandevaluateitthroughcomparisonsinSectionV.structuralanalysisandtrafficmonitoring,expectthenetworktoConclusionandfutureworkarefinallygiveninSectionVI.operateforalongtimeperiod,typicallyontheorderofafewyears.Thelifetimeofawirelesssensornetworkcouldbeaffectedbymanyfactors,suchastopologymanagement,MACII.SYSTEMMODELandroutingprotocoldesign,anderrorcontrolschemes.A.CommunicationModelDifferentmethodsforreducingpowerconsumptioninIthasbeenobservedthatcommunication-relatedpoweriswirelesssensornetworkshavebeenexploredintheliterature.usuallyasignificantcomponentofthetotalpowerconsumedinSomeapproachesweresuggested,suchasincreasingtheasensornetwork[1,2,4].Wewillmainlyfocusondistance-densityofsensornodestoreducetransmissionrange,reducingdependentandcommunication-relatedpowerconsumptioninstandbypowerconsumptionviasuitableprotocoldesign,andthispaper.Weassumethattheratiooftheotherpoweradvancedhardwareimplementationmethods[2].Algorithmsconsumptionstothetotalpowerconsumptionisonlyaconstantforfindingminimumenergydisjointpathsinanall-wirelessfactor.Thus,weonlyconsidertransmissionpowerinthisnetworkweredeveloped[3].Jointoptimizationofsensorpaper.ThetransmissionpowerPtosendastreamofdataatplacementandtransmissionstructurewasconsideredin[5]rateRcanbemodeledas:*r,wherewithspecifieddistortionbounds.However,thedatagenerationP=Rd2≤r≤4isthemodelisdifferentfromtheonediscussedinthispaper.pathlossexponent,dependingondifferentchannelmodels.Communicationoveralonglinkisseverelypenalized,becauseInthispaper,wewillexaminemany-to-onewirelesssensorpowerconsumptionoveralonglinkismuchhigherthanthenetworks,whereinformationcollectedfromallnodesistotalpowerconsumedoverseveralshortlinks,i.e.,aggregatedtoasinknode.Typicalapplicationsincludetrafficmonitoringanddatacollectioninwarehouses.Dataloadis()rrrr.(1)d1+d2+?+dn>>d1+d2+?dngenerallyasymmetricinmany-to-onewirelesssensornetworks. Wealsonoticefromthenumericalresultsthattransmissionsensingareaofeachnode,andthetotaltrafficloadthatnodeoverlonglinksdoesnotoccur.icarriesisi(Ln).WehaveB.SystemModelrL⎛L⎞Pi=i⎜⎟c(2)Wefirstconsideralinearsensornetwork,whichconsistsofn⎝n⎠.asetofsensor/aggregationnodesplacedalongalongand⎛E⎞narrowareawithasinknodeattheend.EachnodecollectsT=min⎜0⎟i=1,2,?,n−1(3)⎜P⎟thesampleddatawithinitssensingrange,relayinginformationi⎝i⎠towardsthesinknodeforfurtherprocessing,asinFig.1.Sinceweplacethesensor/aggregationnodesinsuchawayTypicalapplicationsincludetrafficmonitoringandborderlinethatthetotalvolumeofthedatafromthewholeareawillbecontrol.Nodenisthesinknode.Notethateachnodealsoaggregatedtothesinknode,thelifetimeofalinearnetworkrelaysdatafornodesfurtheraway,i.e.,nodeialsorelaysthedefinedinthispaperistheperiodoftimefromthenetworkinitializationtothepointwhenthefirstnoderunsoutofenergydatacollectedbynodes1toi−1.Thiscanmodeldifferentwithoutanyothernodecoveringthesamesensingarea.Fortiersofahierarchicalsensornetworkwhereeachsensornodetheuniformplacement,nodesclosertothesinkcarrymorewithinaclusteronlysendsdatatoitsaggregationnodeandtherelayloads,consumemorepower,diemorequickly,andthusaggregationnoderelaysinformationtothesinknode.Foralimitthenetworklifetime.InSectionIV,weshowthatplacinghighertier,weneedtoconsiderhowaggregationnodesbuildanodesoptimallyprovidessignificantbenefitoveracommonlynetworkandrelaydatatoasinknode.Foralowertier,weuseduniformplacement.couldregardeachclusterasasensornetworkwheretheOnepossibleapproachtoextendthenetworklifetimeistoaggregationnodeisthesinknode.Hence,wewillinvestigateallocatemoreinitialenergytonodesclosertothesinknode,theapproachesthatapplytobothtiersunlessitisassumedthatconsideringtheimpactofunbalancedtrafficloadsontheaggregationnodeshaveinfiniteamountofenergyandeachnetworklifetime.However,suchaheterogeneousenergysensornodeisonlyonehopawayfromitsaggregationnode.allocationschememaybeinconvenientinproductionandLdeployment.Alternatively,dataaggregationorcompressionisanotherpossiblesolution.Reducedamountofdataloadcancertainlybeenergy-saving,prolongingthenetworklifetime.f1iHowever,thetrade-offbetweenaccuracyandpowerf13consumptionshouldbeconsideredwhendesigninganefficientôf12ôf23ôôô…ôdataaggregationmodel.12f2iinInthispaper,ourobjectiveistofindanoptimalnodeplacementanddatatransmissionschemesuchthatthelifetimef3nofasensornetworkcanbemaximizedwithagiventotalf2jnumberofnodes,assuminghomogeneousinitialenergy.ThealternativeobjectiveistominimizetheapplicationspecificFigure1.Alinearnetworkandpossiblerelayingpatternstotalcost,i.e.,totalpowerconsumption.EachsensorhasacertainamountofinitialenergyE0andasensingrangeD.LetdibethedistancebetweennodeiandIII.SENSORNODEPLACEMENT()i+1,i=1,?,n−1,andd0betheareacoveredbynode1.WeconsiderhomogeneoussensornodeswiththesameHereweconsiderageneralscenariowhereeachsensornodeinitialenergyE0.Letfijbetheamountofdatasentdirectlycontinuouslyorperiodicallycollectsconstantbitratedata,e.g.,fromnodeitonodejperunittime,wherei>d1+?+di.Thus,anodecommunicationoverlonglinksisnotdesirable.Accordingtoshouldonlyrelaydatatoitsnearestneighbortowardsthesinktheproblemsetup,maximizingthelifetimeisequaltonode.Bysolvingthisconstrainedmultivariablenonlinearminimizingthepowerconsumptionperunittimeforeachnode.programmingproblem,optimalsolutioncanbeobtainedforWeimposeanadditionalconstraintthatallnodesdieatthethisproblem.Wenameitoptimalstrategy2.sametime.Atanygiventime,theresidualenergyofallnodesiskeptthesamegiventhesameinitialenergy.AlthoughthisIV.PERFORMANCEBOUNDANDNUMERICALRESULTSmaynotbetrueforallcases,wecanconsideritasaheuristicsolution.Theproblemisreformulatedasthefollowing:A.PerformanceBoundWefirstintroduceaperformanceboundforthe⎛i−1⎞MinimizeP=c⎜∑d⎟dri=1,2,?n−1(9)optimizationproblems.Wedividethewholeareaintoblocksi⎜k⎟i⎝k=0⎠oflengthD,i.e.,thetotalnumberofblocksis⎣LD⎦.Wesubjectto:P1=P2=?=Pn−1(10)calculatetheminimumenergyneededtotransferthedataineachblocktothesinknode.Tobemorespecific,inorderton−1∑di=L(11)collectthedatafromthefirstblock(theblockfarthestawayi=0fromthesinknode),weneedtoplacethefirstnodeatapointtocollectdatafromthefirstblockoflengthD.Themaximum0
