無線傳感器網(wǎng)絡(luò)能量?jī)?yōu)化設(shè)計(jì)

無線傳感器網(wǎng)絡(luò)能量?jī)?yōu)化設(shè)計(jì)

1案例4:德國(guó)兩,4.3.4與4.5inraftingraftingraftingraftingraftingraftingdrinci生物,ro無線通信的sensor網(wǎng)絡(luò)有更多的應(yīng)用，即無線通信的流暢行動(dòng)應(yīng)用，這也是一個(gè)適用的結(jié)果，即家庭成員的安裝、環(huán)境管理、安全和互聯(lián)網(wǎng)生活運(yùn)營(yíng)商。Sensorsarecapableofmonitoringawidevarietyofambientconditionssuchastemperature,pressure,andmotion.Becausesensorsarepoweredbybatteries,energy-efficientofsensorsisamainconcernandamoschallengingtaskforthedesignofwirelesssensornetworks.Inamulti-hopadhocsensornetwork,eachnodeplaysthedualroleofdataoriginatoranddatarouter.Afewnodes’malfunctioningcancauseseriousproblemsthatrequirereroutingofpacketsandreorganizationofthenetwork.Hence,powerconservationandmanagementhaveadditionaimportance.Recently,manyprotocolsandalgorithmsaboutenergy-efficiencyhavebeenproposed.AsreportedinRef.,thecluster-basedhierarchicalmodelisbetterthantheone-hopormulti-hopmodel.ArecentprotocolthaoptimizestheenergyefficiencyinsensornetworksisLowEnergyAdaptiveClusteringHierarchy(LEACH)LEACHisthearchitecturethatinafixedarea,theuniformlydistributedsensornodesareformingadaptiveclustersandrotatingclusterheadpositionsrandomlytoevenlydistributetheenergyloadamongthesensorsinthenetwork.Duetothelimitedenergyandotherresources,thenodeswillrepresentafeaturethatmaximizestheirownbenefits,whichmakethemnotpositivelyfollowthecommonassumptions.Thisfeatureissimilartotheauctiontheoryofageneralizedsecondbestsealedbidaction.Moreover,inadversaryenvironment,theremayexismaliciousnodesthatnotonlymayrejecttoreporttheirtrueenergybutalsomaydisturborevendestroythenetwork.Wecallthecharacteroftheformerself-interestorselfishness,andthelatermalice.Theselfishcharactercommonlyexistsinthecivilsensornetworks,whilethemalicemainlyexistsinmilitarynetworks.Inthispaper,weonlyconsidertheself-interestcharacterofsensornodes.Duetotheself-interestcharacter,thenodesmaynotreportheirenergytruthfullyandforwardtherelaydataactively,thatwillmakethenetwork’stopologychangefrequentlyThebehaviorofselfishnodescanbemodeledbygametheoryandtheselfishnodescanbecalledselfishagents.Toachievedesiredproperties,mostpapersassumethatnodescooperatewitheachotherbyfollowingthewell-definedprotocols,regardlessoftheselfishcharacterofnodes.InspiredbythegametheoryandmechanismdesigntheoryinRef.,westudytheselfishlyconstructednetworksbymodelingenergyreportasamechanismdesign,andbasedonthetrulyreportedenergy,formtheclusters.Inthisnon-cooperativegame,wedevelopsuchamechanismthatalignsthegoalsofselfishindividualsensorswiththeglobalgoalsoftheentirenetwork.Insuchanapproach,sensorswithinthenetworkareassumedtoberationalandnodesmakinglocaldecisionsincreasetheirownutility.Themechanismensurestheglobalgoalandmaximumnetworklifetimewhentheselfishsensorstruthfullyreporttheirenergy.2“非-cooperation”laheningOneofthemostcriticalissuesindesigningsensornetworkalgorithmsistominimizetheenergyconsumptionwhilemeetingcertainperformancerequirementssuchasdelayandthroughput,etc.Manyresearchershavefocusedonissueslikeenergyawarerouting,energysavingthroughactivationofalimitedsubsetofnodes,andproposedprotocolsandalgorithmsincludingenergyefficiency.Clusteringinwirelesssensornetworkisahottopic.Acluster-basedroutingprotocolgroupssensornodesinordertoefficientlyrelaythesenseddatatothesink.Eachgroupofsensorshasaclusterheadthatisaspecifiednodebeinglessenergy-constrained.Clusterheadsaggregatethereceiveddataandsendthemtothesink.Clusterformingisamethodthatminimizesenergyconsumptionandcommunicationlatency.ThreemostwellknownhierarchicaroutingprotocolsareLEACH,TEENandChain-based3levelPEGASIS.However,mostproposedapproacheshavetoomanyassumptionsonsensornodes.Forexample,nodesmusthavethesameinitialenergylevel,nodesarestatic,ornodesshouldhavemuchinformationaboutothernodes.Theseassumptionsarenopracticalinreality.OtherproblemssuchasinLEACHtheclusterheadiselectedbasedonaround-robinstrategyThisstrategywillchangethetopologyofclustersfrequentlybecausetheselectedclusterheadmayhaslessenergyEverytime,theclusterheadchangingproducesalargeoverheadsinceallthenodesinthisclusterhavetobenotified.Besides,mostoftheproposedclusteringprotocolsdonotconsidertheselfishnessofthenodes.Forapracticasensornetworksthatneedutmostcooperation,especiallythosethatarecontrolledremotely,theselfishnodeswilreluctanttotelltheirprivateinformation,suchastheirownenergy.Selfishnessinwirelessnetworksisstudiedonlyrecently.Mostapproachesfallintotwocategories:rewardingthecooperativenodesorpunishingnon-cooperativenodes.Bothcategoriesfocusondataforwardingstrategiesbetweennon-cooperationnodes.Inthenextsectionweextendtheideatotheclusterformation.Ourgoalistodesignanadaptive,energy-efficient,hierarchicalclusterformationalgorithmthatmaximizesthelifetimeofthesensornetworksbyselectingthemostpowerfulclusterheads.Theselfishnessofthesensornodesismodeledbygametheory,morespecifically,themechanismdesignismodeledbydesigningagamesuchthatselfishbehaviorofthenodesinducesapredictablestrategyprofile,andtheoutputfunctionforthispredictedstrategycorrespondstotheoutcome,calledsocialchoiceoptimum.Inotherwords,thegameshouldbedesignedinsuchawaythatchoosingthepredefinedstrategythatresultsinthesociachoiceoptimumisadominantstrategyforeachnode.Heredominantmeansthatnonodehasanincentivetounilaterallydeviatefromthestrategy.Ifallnodesselectadominantstrategyfromthestrategyprofile,thenthecombinationofeachnode’sdominantstrategyiscalleddominantstrategyequilibrium.Ourgoalofmechanismdesignistodefinerulessuchthatthesocialchoiceoptimumisdominant-strategyequilibrium.Therestofthepaperisorganizedasfollows.Section3introducesthebasicmechanismdesigntheory.InSection4,weproposetheclusteringalgorithmwithoutconsideringtheselfishnessofnodes,andanalyzethecompactofselfishnesstoclusteringperformance.Thenwegivetheclustermechanismdesignstrategythatcanbeappliedtoourclusteringalgorithm.InSection5,wepresentsimulationresultsaboutouralgorithmwithandwithoutheselfishnodes.Theresultsshowabetterclusteringperformancecanbeachievedwithourmechanismdesignstrategyforselfishnetwork.InSection6,wegiveconclusions.3n-t回歸系數(shù)Inthissectionweintroducesomestandardnotionsformechanismdesign.Wealsodiscussthedominanstrategyimplementationinquasi-linearenvironmentdescribedinRef..Assumetherearennodes,eachnodeihasitsprivateinformationti∈Ti(termeditstypeorenergy)thatmapstothemechanism’soutputspecificationo∈O,hereOisthesetofallowedoutputs.Eachnodeihasapreferencereavaluedfunctionvi(ti,o),calleditsvaluation.Definition1.AmechanismM=(O,P)iscomposedoftwoelements:Anoutputfunctiono(),andann-tupleofpaymentsp1,p2,…,pn.Specifically:1.ThemechanismdefinesafamilyofstrategiesSiforeachnodei.Nodecanchoosesi∈Sitoperformtheoutputfunctiono(s1,s2,…,sn).Themechanismdefinesapaymentpi=pi(s1,s2,…,sn)toeachnode;2.Whenthemechanismtransfersthepaymentpitonodeifortheoutputo,thenode’sutilitywillbeui=vi(ti,o)+pi.Thisutility*iswhatthenodeaimstooptimize;3.Wesayamechanismisanimplementationwithdominantstrategies(orinshortjustanimplementation)ifforeachnodeiandti,thereexistsastrategysi∈Si,calleddominant,suchthatforallpossiblestrategiesoftheothernodess-i,simaximizesnodei’sutility.i.e.,foreveryis′∈Si,ifwedefineo=o(si,s-i)**,o′=o(is′,s-i),pi=pi(si,s-i),ip′=pi(is′,s-i),thenvi(ti,o)+pi≥vi(ti,o′)+ip′.Thenwesayforeachtupleofdominantstrategiess=(s1,s2,…,sn),theoutputfunctiono(s)satisfiestheoutputspecification.Thesimplesttypeofmechanismsisthatthenodes’strategiesaresimplytoreporttheirtypesorenergy.Definition2.Wesaythatamechanismistruthfulif1.Forallnodei,andallti,Si=Ti,i.e.,thenodes’strategiesaretoreporttheirtrueenergy.(Thisiscalledadirectrevelationmechanism);2.Truthtellingisadominantstrategy,i.e.,si=tisatisfiesthedefinitionofadominantstrategyabove.Definition3.Wesaythatamechanismisstronglytruthfuliftruthtellingistheonlydominantstrategy.ThemostimportantimplementationofmechanismdesigniswhatisusuallycalledthegeneralizedVickrey-Clarke-Groves(VCG)mechanism(Vickrey(1961);Clarke(1971);Groves(1973)).TheVCGmechanismappliestothemechanismdesignmaximizationproblemswheretheobjectivefunctiong(o,t)issimplythesumofallnodes’valuations.Thesetofpossibleoutputsisassumedtobefinite.Definition4.AmaximizationmechanismdesignproblemiscalledutilitarianifitsobjectivefunctionsatisfiesDefinition5.Wesaythatadirectrevelationmechanismm=(o(t),p(t))belongstotheVCGfamilyifTheorem(Groves(1973)).AVCGmechanismistruthful.4ransmisonforasWeconsiderafullydynamicnetworkandallcommunicationbetweenclustersisthroughclusterheadssatisfyingthefollowingassumptions:(1)Thesinknodeislocatedinthecenterofthenetwork;(2)Allnodesinthenetworkhavedifferentenergylevelsandhavenolocationinformation;(3)Thenode’stransmissionradiusislineartoitsenergy;(4)Nodescanadjustthepowerlevelfortransmissionandcanvarythetransmissionrange;(5)Linksareasymmetric.I.e.,nodeiwithhigherenergycanreachnodejthatisfallwithini’stransmissionradius,whilenodejmaynotreachnodeibecauseofitslowenergy.WemodelthewirelesssensornetworkconsistingofasetofnodesN=(n1,n2,…,ni,…)thatareuniformlydistributedinasquarearea.Nodesshareacommonwirelesschannelbyusingomni-directionalantennas.Wedividethelarge-scalesensornetworkintoclusteredlayers.Allnodesaregroupedintoclusters.Eachclustervotesaclusterhead.Tosaveenergyanddecreasethedataredundancy,datashouldfirstaggregateincurrentclusterthenbesenttoalower-levelclusterheaduntilitreachesthesinknode.Asdatamovesfromahigher-leveltoalowerone,ittravelsgreaterdistances,thusreducingthetraveltimeandlatency.Afterinitializationofthesensornetwork,ouralgorithmformsclustersandchoosesoneclusterheadforeachclusterthathasthemaximumenergylevel.Inordertodetermineclusterheads,weneedamechanismtoreconfiguretheclusters.WeusetheideasofweightedclusteringapproachdescribedinRef..4.1receificity,清水景,其他相關(guān)文件whereKisaconstant,di,jisthedistancebetweennodesiandj,whichisalsothecommunicationradiusofnodei,andαisthedistance-powergradientvaryingbetweenoneandsixdependingontheenvironmentconditionsofthenetwork.Ourmechanismwillensurethenodetoreportitsmaximumtransmissionpowerwhenitperformstheclusteringalgorithm.Forsimplicity,weconsidertheidealconditioninEq.(1)thatcomesK=1,α=2forthedistance-powergradientofthefreespace.Accordingtothereceiversensitivity,eachnodehasaminimalreceivingpowerthatistheminimalsignalstrengthtoreceivesignals.Forsimplicityofouralgorithm,weassumeallnodeshavethesamereceiversensitivity,thusrecrecjreciPPPminmin,min,==.Ifnodej’sminimalreceivingpowerisrecjPmin,,toassurejreceivingmessagesfromnodei,nodei’stransmissionpowermustbegreaterthanaminimaltransmissionpowertranjiP→min,.ThusFromEqs.(1)and(2),wehaveOncenodejreceivesmessagefromnodei,itcancomputethenodei’sminimaltransmissionpowerbyEq.(3),anditsendsbackamessagetonodeitotelltheminimaltransmissionpoweraswellasitsdefaultpower.Thiscangreatlysavenodei’senergywhenitsendsdatatonodejusingtheminimaltransmissionpower.4.2cluder&非ighbocking/la服er/非igh-非igh-非igh-非好演化/非igh-非好演化非好關(guān)于“cluder-非關(guān)于cluder”/非igh-u.3.3.3.3.3.3.3.3.3.3inchister3.4和laraincisiphincisilit-laraincisiphincisi運(yùn)行國(guó)際,lartrainsiphinsiphinsiinceince.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.4.3.4.3.4.5.3.4.5.3.4.5.3.4.5.3.4.5.3.4.5.4.5.4.5.4.5.4.5.4.5.5.4.5.4.5.5.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.4.5.5.4.5.4.5.4.5.4.5.4.5.4.5.5.4.5.4.5.4.5.4.5.5.4.5.4.5.4.5.4.5.4.5.5.4.5.4.5.4.5.5.4.5.5.5.4.5.5.5.5.4.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.5.4.5.5.5.4.5.5.4.5.5.5Ahierarchicalclusteredsensornetworkispartitionedtoanumberofclusters.Nodeiworkingasaclusterheadisdenotedbychi.ThesetofallclusterheadsisdenotedbyCH,CH?N.CurrenthierarchyclusterheadsaredenotedbyasetofCHcur＿h(yuǎn)ier.AlltheclustersofthenetworkaredenotedbyasetofCandcurrenthierarchyclustersaredenotedbyasetofCcur＿h(yuǎn)ier.ThetotalnumberofnodesinCcur＿h(yuǎn)ierisdenoteby|Ccur＿h(yuǎn)ier|.WeuseΓasatemporarysetofstoresforcurrentcluster’smembernodes.Asensorj∈{N-CH}belongstoaclusterciifandonlyifdi,jisminimalamongalltheclusterheadsinCH.Theclusterheadofciischi.Itisclearthat|C|=|CH|.ThememberofclusterciisdenotedbyicM,CHNMiiccC-=∈?U.Nowwedescribeourclusterformationalgorithmindetail.Thealgorithmconsistsoftwostages.Intheinitialstagethesinknodeinitiatestheclusteringprocedure(Fig.1(a)).Hereweassumetherealwaysexistsneighborsofthesinknode.Thisisreasonablesinceweconsiderthenodestobeuniformlydistributed.Theclusterformationstagecanbedividedintotwosimilarsteps.Thefirststep(Lines1～8,Fig.1(b))isthefirsthierarchyclusteringprocess.Thenodethathasthelargestenergywillbeselectedastheclusterheadwithahigherpriority.Howeverthereisalsoanimplicitconditionthatthedistancebetweenthisnodeanditscurrentclusterheadshouldbefartherthanthedistancebetweenthisnodeandtheclusterheadoftheuplevelhierarchy.Whenchiisselectedasaclusterhead,itbroadcastsREQ＿ENERGYmessagetoallothernodestoindicateitsdefaultenergyPchidefaultandtransmissionenergyPchitraninthepacketheader.EachneighborjofchireceivingREQ＿ENERGYcandetectthereceivingenergyPjrecbythereceivedsignalstrengthindicator(RSSI).AccordingtothetransmissionenergyiPtranandminimalreceivingenergyPminrecofchi,neighbornodejcancomputeitstheminimatransmissionenergyPtranj→chi,minbyEq.(3).NodejthensendsbackREP＿ENERGYtochicontainingitsdefaultenergyandminimaltransmissionenergy.WhenchireceivesREP＿ENERGYfromallitsneighborsNBRchi,thealgorithmselectsthenodewiththemaximaldefaultenergyasthenexthierarchyclusterhead(Line13,Fig.1(b)).ThenclusterheadchisendsclusteringmessagetoNBRchitonotifytheneighborstojointhecurrentclusterci.Afterclusteringfinishes,thenetworkispartitionedbysomeclustersandseveralhierarchies.Duetothelargerenergyoftheselectedclusterheads,thetopologycankeepstableforalongtime.Andthetransmissionpowerwithinaclustercanbeminimizedbecausetheclustermemberscansenddatatotheirclusterheadsusingtheminimaltransmissionenergy.Sincemostofthepacketsaretransmittedfromclustermemberstoclusterheads,thisgreatlysavesenergy.Thusourclusteringalgorithmisenergy-efficient.Withthenodessendingandreceivingdata,someofthenodesmaybeenergy-depleted.Thenetworkneedsreclustering.Wedesignamonitoringprocesstodealwiththereclusteringprocedure.DifferentfromothertopologycontrolprotocolssuchasLEACH,whichusesaninitialpercentageofeachnodetobeaclusterheadandtheclusteringisexecutedcircularly,ouralgorithmisadaptive.Thereclusteringformationistriggeredwhenneededanditcanoperateinalocalarea.Whenanysensornodedetectsthatitsenergyistoolowtoprovideserviceduringthenetworkoperation,ourreclusteringprocesswillbetriggeredanditoperatesonlyinthecurrentclusterrange.Thisguaranteesthereclusteringprocesstakeslittletimeandrunsefficiently.Weinducethepossiblescenariosthatmaytriggerthenetworkreclusteringasfollows:(i)Ifaclusterheaddetectsitsenergytoolowtosustainthecluster,itwillsenditsneighbornodesamessagetorecluster,anditgivesuptheclusterheadposition.Allthenodesincludingtheclusterheadshouldindividuallyjoinotherexistingclustersorestablishanewcluster;(ii)Iftheclusterheadmovesoutofthecurrentclusterrangebutwithinanotherexistingcluster,thenitmustjointhenewclusterandbeacommonsensornode.Nodeswithincurrentclustermustreconstructanddefineanewcluster;(iii)Ifasensornodemovesoutofthecurrentclusterrangebutwithinanotherclusterrange,transferthesensornodetothelatercluster;(iv)Ifthesensornodemovesoutoftheexistingclusterrangeandisoutofrangeofanyotherexistingcluster,thendefineanewcluster.4.3重新定義squetsPreviousalgorithmisbasedonthenetworkwithhonestnodes.However,foranetworkwithselfishnodestherearisestheproblem:itmaynotbethebestinterestthatnodeipresentsitsemissionsignalstrengthcorrectly.Inreality,forselfishnodes,assertinglargerenergywillresultinahigherpaymentthatthenodereceives.Wediscusstheselfishnessinarealsensornetworkanddesignamechanismthatisfairlyenoughsothattheselfishnodeswilnottrytocheat.Ourgoalistodesignsuchamechanismthatcausesallnodestoacttruthfully,i.e.,torevealtheirtrueprivateinformation.WedesignourmechanismdesignframeworkasFig.2referencedfromRef..Theinputofourmechanismisavectorofstrategiess(t)=(s1,s2,…,sn)thatdependonthetruetypet.Theoutpufunctiono=o(s)correspondstoasocialchoicefunction(SCF),g(o,s).Thepaymentpicomputedbythemechanismistransferredtonodeithatincentsnodeitoreporther***trueenergy.Inthefollowing,weusetheeconomicmechanismdesigntheorytodesignthemechanismforselfishnetwork(Fig.2).AssumethetotalcostoftopologyformationisW.Thenodesvoluntarilycontributew1,w2,…,wnresourcesthacanbeconsideredastheenergyconsumed,andwiisproportionaltonodei’strueenergyPi.Assumenodesbenefifromthetopologywithfixedprofitsr1,r2,…,rn.Oncethetopologyisformed,nodeicangainvi=ri-winetprofitorpreferencevalue.Thusthenecessaryandsufficientconditionfortopologyformationis∑∈>Niiv0.Thatistosay,whethernodeicooperatesornot,herobjectiveistomaximizetheutility.Toensurethenodescooperate,wehavetomaximizetheirutility.Wedenotenodei’sreportedpreferencevaluebyv?i.Sincenodeimaycheat,v?imaynotequaltovi.AccordingtotheVCGmechanism,thetopologyisestablishedwhenthesumofallnodes’preferencevaluesisgreaterthanthesumofalltheircontributions.HenceOurmechanismmustbenefitforthosewhocooperatewithothers.Weassociatethisbenefitwithtransferpaymenttiforeachnode.tiisdeterminedbythefollowingequationwherehi()isanarbitraryfunctionofv?-iandisindependentofv?i.SubstitutingEq.(5)andEq.(6)inEq.(4)withEq.(5),wehavethepayofffunctionTheselfishnodeexpectstogetthetransferpaymentwhatevershecooperateornot.FromVCGmechanism,cooperationforanodeisadominantequilibriumstrategy.i.e.,eachnodewillincentivelytellhertrueenergy.Wecanformulateourresultsasfollows:Lemma1.Ifnodeiwantstojoinacluster,shemusttellhertrueenergyPi.Lemma2.Ifnodeihopesthetopologynottobeformed,shealsomusttellhertrueenergyPi.Weomittheproofoftheselemmasduetothelimitationofspaceofpages.Fromthelemmasweseethattruthtellingisadominantstrategy.Thuswehavethefollowingresult:Theorem.OurVCGmechanismistruthful.Tosimplifyourmechanism,wecandefinethearbitraryfunctionhi()asfollowsThenthetransferpaymentis:Thatmeansthemechanismwillpunishthosewhoseobjectivechangesthesocialchoiceobjective.Inotherwords,themechanismwillforcethenodesthatsatisfy(?)(∑∑?0)<Nii≠∈ijjvvtotransferpaymenttooumechanism.Becauseoftheselfishfeature,nonodewouldliketoreceivepunishment.Thenwhattheycandoistocooperatewiththeirneighbors.5通過sixremaining/rohsremaining表示活動(dòng)—SimulationandEvaluationWesimulateawirelesssensornetworkof1000and2000nodesusingMATLAB.Theheterogeneoussensorsareuniformlydistributedina1000×1000squaremetersareaandthesinknodeislocatedinthecenterofthenetwork.Weassigneachsensornodeadifferentrandomlygeneratedinitialenergyfrom0.3to0.5Joules.Anodeisconsidereddiedifitsenergylevelreaches0.Wealsoassumethatthechanneliscollisionfree.Inordertomeasuretheenergyconsumptionforcollectingsenseddatafromtheclustermembers,weusedthesameenergymodeintroducedinLEACH,usingradioelectronicsenergyEelec=50nJ/bit,radioamplifierenergyεamp=1000pJ/bit/m2and512bit-sizesenseddatapacket.Wesimulatethetotalenergyconsumedforhigh-densitysensornetworkwhenformingthetopology.Figure3showsourresultfor1000-nodeand2000-node.Thesensornodes’radiorangesarerandomlysetfrom150mto300m.Andthemaximumclusterradiusis300m.FromFig.3,itisclearthattheconsumedenergyforclusteringforLEACHincreasesgreatlywhentheclusterradiusincreases.HowevertheenergyconsumedforDEEHincreasesveryslowly.Forhigh-densitynetwork,energyconsumedforDEEHevendoesnotincreasewithclusterradiusincreasing.SoDEEHismoresuitableforlarge-scalenetwork.Whenselfishnodesexistinthenetwork,itisveryimportanttoassuretheselfishnodestocooperateandteltheirtrueenergy.Wesimulatetheselfishnodesasrandomlyreportingtheirlocalenergyfrom0to0.8Joules.Andweanalyzetheclusterheads’remainingenergydistributionaftertheclusteringprocedureends.Figure4showsthesimulationresultswithdifferentselfishnodesinthenetwork.Becauseoftheselfishnodesinthenetwork,theclusterheadsremainenergyoscillationsgreatly.Aseachnode’sinitialenergyisfrom0.3to0.5Joules,theremainingenergythatislowerthan0.3orgreaterthan0.5canbeconsideredasthedeclaredenergybyselfishnodes.Theselfishnodemayunderdeclareitsenergytosaveenergyoroverdeclaretobeaclusterheadtoacquiremorebenefitfromthemechanism.Bothofthetwodeclarationscancausethetopologyunstable.Ifanodeoverdeclaresitsenergyanditiselectedasclusterhead,sinceitsrealenergyislowitdepletesitsenergyquickly,andthecurrentclustermustreselectaclusterhead.Thismakesthetopologyalterfrequently.Ifanodeunderdeclaresitsenergy,ithardlybecomesaclusterheadalthoughithashighenergy.Thiswillconsumetheclusteringproceduremoreenergytoselecttheclusterhead.FromFig.4,wecanseeth