Frame ork for Reliable Routing in Mobile Ad Hoc Netw orks Zhenqiang Department of Electrical - PDF document

AFrameworkforReliableRoutinginMobileAdHocNetworksZhenqiangYeDepartmentofElectricalEngineeringUniversityofCalifornia,Riversidezye@cs.ucr.eduSrikanthV.Krishnamurthy,SatishK.TripathiDepartmentofComputerScienceandEngineeringUniversityofCalifornia,Riversidekrish,tripathi@cs.ucr.eduAbstract—Mobileadhocnetworksconsistofnodesthatareoftenvulnerabletofailure.Assuch,itisimportanttoprovideredundancyintermsofprovidingmultiplenode-disjointpathsfromasourcetoadestination.Werstpro-poseamodiedversionofthepopularAODVprotocolthatallowsustodiscovermultiplenode-disjointpathsfromasourcetoadestination.Wendthatveryfewofsuchpathscanbefound.Furthermore,asdistancesbetweensourcesanddestinationsincrease,bottlenecksinevitablyoccurandthus,thepossibilityofndingmultiplepathsisconsiderablyreduced.Weconcludethatitisnecessarytoplacewhatwecallreliablenodes(intermsofbothbeingrobusttofailureandbeingsecure)inthenetworkforefcientoperations.Weproposeadeploymentstrategythatdeterminesthepo-sitionsandthetrajectoriesofthesereliablenodessuchthatwecanachieveaframeworkforreliablyroutinginforma-tion.Wedeneanotionofareliablepathwhichismadeupofmultiplesegments,eachofwhicheitherentirelycon-sistsofreliablenodes,orcontainsapresetnumberofmul-tiplepathsbetweentheendpointsofthesegment.Weshowthattheprobabilityofestablishingareliablepathbetweenarandomsourceanddestinationpairincreasesconsiderablyevenwithalowpercentageofreliablenodeswhenwecon-troltheirpositionsandtrajectoriesinaccordancewithouralgorithm.I.INTRODUCTIONMobileadhocnetworksndapplicationinmanyeldssuchasmilitarydeployments,disasterrescuemissions,electronicclassrooms.Inthispaper,weprimarilylookatreliabilityintermsofprovidingrobustnesstonodefail-uresinadhocnetworks.Nodefailuresmaybeintermit-tent,i.e.,forshortperiodsorforlongperiodsoftime,andduetovariousreasons.First,sincethesenetworksarelikelytobedeployedinwirelessenvironments,thecom-municationsbetweentheadhocnodeswillhavetobeviaaharshfadingchannel.Thus,communicationsbetweenThisworkwassupportedbyDARPAundercontractnumber:FTNF30602-01-2-0535.nodeswouldtypicallyendureperiodsofintermittentfail-ureandasaconsequence,packetlosses.Itispossiblethatcertainnodesmightcompletelyloseconnectivityfortemporaryperiodsduetothefadingconditions.Onewayofovercomingthiswouldbetousesophisticatedantennasystemsormodulationmethods.However,manyoftheadhocnodes,ifnotmostofthem,wouldbeconstrainedbysize,processingandpowerlimitationsandthus,maynotpossesssuchcapabilities.Second,manyoftheadhocnodesarepowerconstrained.Duetobatterydrain,itispossiblethatsomeofthesenodesmightnotbeabletofunction.Suchaneffectmayresultinalongtermfailureifanode'sbatteryiscompletelydrainedorifitispossibletore-chargethenode'sbattery,thenodemightnotfunc-tionforintermittentshortperiods.Third,nodesinanadhocnetworkarevulnerabletocompromise.Compromisesareespeciallylikelyforunattendedsensornodesorhand-heldscarriedbypedestrians.Asimpleformofdenialofserviceistosimplycausenodefailures,eitherintermittentorlongterm.Multipathroutingisonewayofimprovingtherelia-bilityofthetransmittedinformation.Whilemultipathroutingmaybeusedforvariousotherreasonssuchasload-balancing,congestionavoidance,lowerfrequencyofrouteinquiriesandtoachievealoweroverallroutingover-head[1][2][3][4][5],ourobjectiveistoprimarilydesignamultipathroutingframeworkforprovidingenhancedro-bustnesstonodefailures.Ifonecouldprovidemultiplepathsfromasourcetoadestination,onecouldenvisionthetransmissionofredundantinformationonthevariouspaths(bytheuseofknowntechniquessuchasdiversityencoding[6])thatwouldhelpthereceiverinreconstruct-ingthetransmittedinformationevenifafewofthepathsweretofail.Bymultiplepaths,weimplymultiplenode-disjointroutesfromasourcenodetoadestinationnode.Ourrstgoaltowardsthisistodesignaroutingprotocolthatwouldallowustondmultiplenode-disjointpathsfromagivensourcetoadestination.Towardsthis,we makemodicationstotheAdHocDistanceVectorRout-ingProtocol(AODV)[7]whichisoneofthemostpopu-laradhocroutingprotocolstofacilitatethediscovery,andconsequentlytheuseofmultiplenode-disjointpaths.Wefoundthatthenumberofnode-disjointpathsfromasourcetoadestinationisdependentonthenodedensityintheadhocnetwork(asmightbeexpected).Furthermore,wefoundthatasthedistancebetweenasourceanditsdes-tinationisincreased,onecouldndnomorethanaverylimitednumberofpathsbetweenthem,evenatmoderatenodedensities(averagenodedegreeis6.7).Thisobserva-tionleadustobelievethat,onewouldrequireatleastafewoftheadhocnodestobemorereliable.Onecouldenvi-sionthatthesenodeswouldbeplacedinmovingvehiclesandcouldbelessconstrainedintermsofsize,processingandpower.Theywouldbephysicallymoresecureandro-busttocompromises.Thesenodes(typicallymuchfewerinnumberincomparisonwiththenormaladhocnodes)couldthen,beallowedtoparticipateinroutingalongmul-tipleroutesbetweenthesamesource-destinationpair.FortheeaseofnotationletuscallthesenodesR-nodes.Therevisedobjectiveisthentoconstructasequenceofre-liablesegmentsbetweenthesourceandthedestination.NodesthatjointwosegmentshavetobeR-nodes.Aseg-mentisdeemedreliableifitconsistsofeitherapresetnumberofpathsbetweenthetwoR-nodesthatitconnectsorifitismadeupofR-nodesentirely.Aconcatenationofreliablesegmentsiscalledareliablepath.WedescribetheconstructionofareliablepathindetailinSectionV.Thenextquestionthatarisesis:whereshouldtheseR-nodesbeplacedsothattheprobabilityofndingareli-ablepathbetweenanarbitrarysourceanddestinationisacceptable?Initially,weplacedtheseR-nodesatrandomlocationswithintheareaofinterest.However,wefoundthatthisdoesnothelpinachievinganacceptableprob-abilityofndingareliablepathbetweenasourceandadestination.Thus,weneedamoreintelligentwayofplac-ingtheseR-nodes.Furthermore,asthenodesintheadhocnetworkaremobile,theR-nodeswouldhavetoadaptivelymovesoastomaintaintheseadvantageouspositionswithrespecttotheothernodes.WeproposeamethodologytocontrolthetrajectoryofanR-nodebasedoninformationexchangedwithinalocalvicinityoftheR-node.WendbysimulationsthatplacingeachR-nodeatpositionsde-nedbyouralgorithm(whichisinfact,aversionoftherandomizedmin-cutalgorithm1[8])isaveryeffectivede-ploymentstrategyintermsofachievingahighprobabilitythatareliablepathisfoundbetweenanyarbitrarysourceanddestination.Theremainderofthispaperisorganizedasfollows.InThedetailsareprovidedinalatersection.SectionII,wereviewtherelatedworkonmultipathrout-inginadhocnetworks.Wedescribeourmodiedver-sionofAODV(wecallitAODVMforAODV-Multipath)inSectionIIIanddescribehowitndsmultiplenode-disjointpathsfromagivensourcetoagivendestination.InSectionIVwediscussthesimulationexperimentsper-formedwithAODVManddiscusstheobservedresultsintermsofperformance.WedescribethevariousstrategiesthatweconsiderfordeployingtheR-nodesandthemo-tivationfordoingsoinSectionV.InSectionVIwede-scribeoursimulationresultswithanewexperimentalsetupwithanadhocnetworkthatincludesasmallnumberofR-nodesanddiscusstheobservedresultsintermsoftheperformanceofthevariousdeploymentstrategies.WepresentourconclusionsinSectionVII.II.RELATEDWORKMultipathroutinghasbeenwellstudiedinwired[1][9][10]andwireless[2][3][4][5][11]networks.Mul-tipathroutinginMANETshasalsoreceivedsomeatten-tionrecently.DSR[12]andTORA[13]havetheabil-itytondmultiplepaths.InDSR,byusingtheinfor-mationreceivedfrommultipleroutequerieswhichmighttraversedistinctpaths,thedestinationcanattempttocon-structmultiplenode-disjointpaths.However,duetoitsinherentnature(asinAODV,describedinthenextsec-tion),DSRcanndonlyasmallfractionofthepossi-blenode-disjointpathsifusedwithoutanymodications.TORAbuildsandmaintainsmultipleloopfreepathsusingDirectedAcyclicGraph(DAG)rootedatthedestination;however,itdoesnotndnode-disjointpaths.Pathdisjointnesshasbeenstudiedin[2][3][5][11].In[2],theauthorshaveanalyzedtheperformanceimpactsofalternativepathroutingforloadbalancing.Nasipurietal.[3]studiedtheeffectofnumberofmultiplepathsandlengthsofthosepathsonroutingperformanceusingan-alyticalmodels.Leeetal.[11]proposedtheSplitMul-tipathRoutingprotocol(SMR),whichcanndanalter-nateroutethatismaximallydisjointfromtheshortestde-layroutefromthesourcetothedestination.Alloftheaboveprotocolsarebasedonsourcerouting.Distancevectorbasedmultipathroutingprotocolsareinvestigatedin[4][9][14].However,ofthese,AOMDV[4]istheonlyprotocolthatensuresthatthepathsareedge-disjoint.Themultipathroutingprotocolsdescribedabove,whicharebasedonsourcerouting,allowthesourcenodetocom-putemultiplenodeoredge-disjointpaths.Thesourcecandosofromthepartialtopologyinformationthatismadeavailablebymeansofmultipleresponsestoasingleroutequery.Withdistancevectorbasedprotocols,thetopol-ogyinformationthatanodecanobtainisfurtherlimited. Thus,itwouldbedifculttoconstructnode-disjointpathsfromasourcetoadestination.Linkstateroutingcanbeusedtogeneratemultiplenode-disjointpathsbuttheuseofsuchprotocolsrequireslargeoverheads[15].AODVisapopularroutingprotocolthatcreatesdistancevectorroutingtableson-demandanditrequiresaloweroverheadascomparedwithDSR[16].Thus,wechooseAODVasacandidateprotocolandmakemodicationstoit,tofa-cilitatethediscoveryofnode-disjointpathsfromasourcetoadestination.AlthoughtherehasbeenpriorworkonmodifyingAODVtocomputeedge-disjointpaths[4],tothebestofourknowledge,ourAODVMprotocolistherstmodiedversionofAODV,thathastheabilityofndingnode-disjointpaths.Furthermore,ourworkisthersttostudytherelationshipbetweenthenumberofnode-disjointpathsthatcanbefoundbetweenasourceandadestinationandthedensityofnodesinthenetwork.Ourobservationsleadustoconcludethatintheabsenceofanyinfrastructureitishighlyimprobablethatwecanndasatisfactorynumberofnode-disjointpathsevenatmod-eratedensities,especiallywhenthesourceandthedesti-nationarefarapart.Thus,weproposeaninfrastructurethatisfacilitatedthedeploymentofreliablenodes(thatwecallR-nodes),thatcanrouteonmultiplepaths,asde-scribedearlier.OurworkalsoinvestigatestheeffectofthelocationofR-nodesontheperformanceintermsofcomputingmul-tiplepaths.WeproposeadistributedprotocoltocontrolthetrajectoriesoftheR-nodessuchthatareliablerout-ingframeworkcouldbeprovided.In[17],atrajectorycontrolalgorithmwasproposedformobilegatewaysinadhocnetworks.Theobjectiveofthetrajectorycontrolalgo-rithmistodeterminewherethegatewaysaretobeplaced,relativetotheadhocgroupofnodesthatthegatewayservessuchthatcertainnetworkperformancemetricssuchasthroughputwasmaximized.Unlikein[17]whereinonewouldmostlikelyplacethegatewaysindenseregionswithinthenetwork,ourobjectivewouldbetoplacetheR-nodesinsparserregionsofthenetworkandcontroltheirtrajectoriessoastoincreasetheprobabilityofestablish-ingareliablepath(denedearlier)betweentwoarbitrarynodes.III.AD-HOCON-DEMANDDISTANCEVECTORMULTIPATH(AODVM)ROUTINGInordertofacilitatethecomputationofmultiplenode-disjointpathsfromasourcetothedestination,wechooseAODVasacandidateprotocolandmakemodicationstoittoenablethediscoveryofsuchpaths.First,thechoiceofAODVisbasedonpriorstudies[15]thatshowthaton-demandroutingprotocolsconsumeloweroverheadthanSourceDestinationLinks that are discardedLinks that are recorded in the routing tableFig.1.TheRREQpropagationprocedureinAODVpro-activeroutingprotocols.Second,ascomparedwithDSR(whichistheotherpopularon-demandroutingpro-tocol),AODVavoidsthehighsourceroutingoverhead.A.AODVWerstbrieydescribetheAODVprotocol.Weomitmostofthedetailsduetospacelimitations.Amorede-taileddescriptionofAODVmaybefoundin[7].AODVcombinestheuseofdestinationsequencenum-bersinDSDVwithanon-demandroutediscoverytech-nique.Ifasourceneedsaroutetoadestination,itinvokesanetwork-wideoodofarouterequestorRREQmes-sage.Inresponse,eitherthedestinationoranintermediatenodethatknowsaroutetothedestination,sendsaroutereplyorRREPmessagebacktothesourcealongthepathonwhichtheRREQmessagewasreceived.Intermediatenodesre-broadcasttheRREQmessageonlyif(a)theydonotknowaroutetothedestinationand(b)iftheyhavenotalreadyforwardedtheparticularRREQmessage.Oncearouteisestablished,itisusedbythesourcetosenddata.Ifalinkfails,thenodethatdetectsthelinkfailure(possiblythroughfeedbackfromthelinklayer),sendsarouteerror(RERR)messagetothesource,uponthereceiptofwhich,thesourcere-initiatesaroutesearch.Destinationsequencenumbersaretaggedontoallroutingmessagesandareusedtoindicatetherelativefreshnessoftheroutinginformation.SinceduplicateRREQmessagesarediscardedbyin-termediatenodes,itisprobablethat,someofthepossi-blenode-disjointpathstothedestination,mightneverbetracedduringthequeryprocess.InFig.1,thelinksindi-catedbythedashedlinesareneverreportedtothedestina-tionsincetheintermediaterelaynodesdiscardtheRREQmessagesreceivedontheselinks.Eventhoughtherearethreepossiblenode-disjointpathsfromthesourcetothedestination,AODVcanndonlyoneofthem.B.AODV-Multipath(AODVM)WeproposemodicationstotheAODVprotocolsoastoenablethediscoveryofmultiplenode-disjointpathsfromasourcetoadestination.InsteadofdiscardingtheduplicateRREQpackets,intermediatenodesarerequired Destination IDSource IDNeighbor ListHops To SourceExpiration TimerNeighbor IDDestination Sequence NumberDestination IDRoute ListSource Sequence NumberExpiration TimerLast Hop IDSource IDNext Hop IDHop Count(b)(a)Fig.2.(a)StructureoftheeachRREQtableentryinAODVM(b)StructureoftheeachroutingtableentryinAODVMtorecordtheinformationcontainedinthesepacketsinatablewhichwerefertoastheRREQtable.Foreachre-ceivedcopyofanRREQmessage,thereceivinginterme-diatenoderecordsthesourcewhogeneratedtheRREQ,thedestinationforwhichtheRREQisintended,theneigh-borwhotransmittedtheRREQ,andsomeadditionalin-formation(asshowninFig.2(a))intheRREQtable.Furthermore,intermediaterelaynodesareprecludedfromsendinganRREPmessagedirectlytothesource.WhenthedestinationreceivestherstRREQpacketfromoneofitsneighbors,itupdatesitssequencenum-berandgeneratesanRREPpacket.TheRREPpacketcontainsanadditionaleldcalled“lasthopID2”toindi-catetheneighborfromwhichtheparticularcopyofRREQpacketwasreceived.ThisRREPpacketissentbacktothesourceviathepathtraversedbytheRREQcopy,albeitinthereversedirection.Whenthedestinationreceivesdupli-catecopiesoftheRREQpacketfromotherneighbors,itupdatesitssequencenumberandgeneratesRREPpacketsforeachofthem.LiketherstRREPpacket,theseRREPpacketsalsocontaintheirrespectivelasthopnodes'IDs.WhenanintermediatenodereceivesanRREPpacketfromoneofitsneighbors,itdeletestheentrycorrespond-ingtothisneighborfromitsRREQtableandaddsarout-ingentrytoitsroutingtable(showninFig.2(b))toindi-catethediscoveredroutetotheoriginatoroftheRREPpacket(thedestination).Thenode,then,identiestheneighborintheRREQtableviawhich,thepathtothesourceistheshortest,andforwardstheRREPmessagetothatneighbor.TheentrycorrespondingtothisneighboristhendeletedfromtheRREQtable.Inordertoensurethatanodedoesnotparticipateinmultiplepaths,whennodesoverhearanynodebroadcastinganRREPmessage,theydeletetheentrycorrespondingtothetransmittingnodefromtheirRREQtables.WhenanintermediatenodethatreceivesanRREPmes-sagecannotforwarditfurther(itsRREQtableisnowempty),itgeneratesanRDERorRouteDiscoveryErrormessageandsendsthatmessagetotheneighborthatactu-allyforwardedtheRREPtothisnode.Theneighbor,upon
WeassumethattheIDofanodeisuniqueinthenetworkanditcanbethenode'sIPaddress.receivingtheRDERmessagewillnowattempttoforwardtheRREPtoadifferentneighborwhocanpotentiallyfor-warditfurthertowardsthesource.WelimitthenumberofRDERsthatanRREPmessagecanexperienceinordertopreventthegenerationandexchangeofalargenumberofsuchpackets3.WeseethatintermediatenodesmakedecisionsonwheretoforwardtheRREPmessages(unlikeinsourcerouting)andthedestination,whichisinfacttheorigi-natorofthesemessagesisunawareastohowmanyoftheseRREPmessagesthatitgeneratedactuallymadeitbacktothesource.Thus,itisnecessaryforthesourcetoconrmeachreceivedRREPmessagebymeansofaRouteConrmationmessage(RRCM).TheRRCMmes-sagecan,infact,bepiggybackedontotherstdatapacketsentonthecorrespondingrouteandwillalsocontainin-formationwithregardstothehopcountoftheroute,andtherstandlasthoprelaysonthatroute.AsintheAODVprotocol,weusesequencenumberstopreventloops.WhenasourcenodeinitiatesanRREQ,itincreasesitssequencenumber\n \r (representsnode'slatestsequencenumberknowntonode)andthedestination'ssequencenumber\r\r byone.ThesetwosequencenumbersareindicatedintheRREQpacketanddenotedby\r and\rrespectively.EachtimethedestinationnodereceivesanRREQpacket,itcomputesanewsequencenumber:\n\r !#"%$'&\r)(\r\n*,+.-(1)ThedestinationthengeneratesanRREPmessagethatcontainsasequencenumber\r0/,whichissetto\r\r.Lemma1UsingAODVM,ifaroute13254,...,2,...,2687isfound,where2isthe:9nodeonthepath,24isthesourcenode(theoriginatoroftheRREQquery)and26isthedestination,then22forany;and&#x;000;-=(=@?,i.e.,thereisnoloopinthisroute.Proof:WhenanodeforwardsanRREPpackettowardsthesource,itaddsanentryinitsroutingtabletoindicatearoutefromthedestinationtothesource.Assumethatthereisaloopontheroute,Withoutlossofgenerality,weassumethat2isontheloop.Thus,2wouldforwardthesameRREPmessagemorethanonce.WithAODVM,whenanodeforwardsanRREP,it“implicitly”informsallitsneighborsthatitisapartofthecorrespondingroute.Uponthereceiptofthismessage,thenode'sneighborsdeletetheentrycorrespondingtothetransmittingnodeintheirRREQtables.Thus,when2transmittedtheRREPmessageto2BA4,alloftheneighborsof2thatoverheardCInoursimulation(tobedescribedlater)wesetthislimittotwicethelifetime(TTL)oftheRREPpacket. theRREPwoulddeletetheentrycorrespondingto2intheirRREQtables.Thus,thesenodeswouldneverfor-wardanotherRREPto2.Ifanodefailedtooverhear2'sRREPmessage,itispossiblethatitmayforwardanRREPto2.However,uponthereceiptofthisRREP,since2isalreadyonanactiveroute,itcannotforwardtheRREPtoanyotherneighbor;2wouldsendanRDERmessagetotheparticularneighbor.Thus,theloopisprevented.Lemma2UsingAODVM,iftworoutes1D2\r ,...,24,...,2\n7and1@2\n ,...,2E,...,2\r7arediscovered,thesetworouteshavenocommonnodesexceptforthesource2\n andthedestination2\n,i.e.,thesetworoutesdonotcontainanycommonintermediatenodesandarehencenode-disjoint.Proof:Since,fromLemma1,anodeneverforwardsmorethanoneRREPinresponsetothesameRREQ,itisimpossibleforanodetoparticipateinmorethanoneroute.Thus,ifmultipleroutesarediscovered,theyshouldbenode-disjoint.OneofthedisadvantageswithAODVMisthatinterme-diatenodescannotusepreviouslycachedroutinginfor-mationtogenerateRREPmessages.TheRREPmessagesshouldalwaysbegeneratedbythedestinationnode.This,however,isnecessarysince,ifintermediatenodesgener-ateRREPs,itmightnotbefeasibletoguaranteethatthediscoveredroutesarenode-disjoint.IV.PERFORMANCEOFAODVMInthissection,weevaluatetheperformanceoftheAODVMprotocolanddiscusstheavailabilityofmulti-plenode-disjointpathswithvariousnodedensities.Weuseasimulationmodelbasedonns-2[18].TheMonarchresearchgroupinCMUdevelopedsupportforsimulatingmulti-hopwirelessnetworkscompletewithphysical,datalinkandMAClayermodelsinns-2.Thedistributedco-ordinationfunction(DCF)ofIEEE802.11forwirelessLANsisusedastheMAClayer.Theradiomodelusescharacteristicssimilartoacommercialradiointerface,Lu-cent'sWaveLAN.WaveLANisashared-mediaradiowithanominalbit-rateof2Mb/secandanominalradiorangeof250meters.Theperformancemetricsthatweareinter-estedinare:FTheaveragenumberofnode-disjointpathsthatarediscoveredperrouteinquiry.FTheprobabilitythatthenumberofnode-disjointpathsdiscoveredinanyrouteinquiryisnolessthanacertainpresetthresholdG.Inoursimulationswedisperseavaryingnumberofnodes(Case1:250nodes,Case2:350nodesandCase3:500nodes)uniformlyina2500mx2500mrectangularre-gion.Weusetherandomwaypointmodeltomodelnodemovements.PausetimeisalwayssettozeroandthespeedofthenodesisuniformlydistributedoverHI(-IJLKM.Ineachcase,wegenerate20differentscenarios.Ineachscenario,werandomlychoose500sourceanddestina-tionpairs.Thesimulationresultsaretheaverageofthese10000samples.SinceeveryRREPpackettriestondtheshortestpathfromthedestinationtothesource,notethatthenumberofnode-disjointpathsdiscoveredbyAODVMisnotthemaximalnumberofnode-disjointpathsthatcanbefoundbetweenthesourceandthedestination.However,withoutexpendingalargeamountofoverheadinordertoobtainthetopologyinformationoftheentirenetwork,itisim-possibletocomputeallthenode-disjointpaths.InordertoevaluatetheperformanceofAODVM,wecompareitwithanidealcase,inwhichthetopologyoftheentirenet-workisknownatthesourceandthesourcerstexecutestheshortestpathrstsearchalgorithm.Thenodesontheshortestpatharenowexcludedandthealgorithmisexe-cutedagaintocomputethenextshortestpath.Notethatthisnewpathisnode-disjointfromtherstpath.Thepro-cessisthenrepeateduntilnofurthernode-disjointpathscanbefoundbetweenthegivensourceanddestination.InFig.3theperformanceofAODVMiscomparedwiththatoftheidealcasewhilevaryingthedensityofnodesinthenetwork.InCases2andCase3,AODVMcanndatleast80%ofthepathsfoundintheidealcase,anditcanndatleast70%ofthepathsfoundbytheidealmethodinCase1.Thehigherthenodedensity,thehigherthispercentage.Thisisbecausethehigherthenodeden-sity,thehighertheprobabilitythatmultiplepathsexistbetweenthesourceandthedestination.Atlowernodedensities,theremayexistsome“bottlenecknodes”inre-gionsoflownodedensitybetweenthesourceandthedes-tination.Sincethesenodescanonlyroutepacketsonasinglepath,otherRREPshavetomakedetoursandndalternateroutes.However,wenotethatthereisalimitim-posedonthenumberofRDERsthatanRREPpacketcanexperience.Furthermore,someoftheRREQmessagesarelostduetocollisionsandhence,donotresultinRREPresponses.Duetotheseeffects,somealternatepaths(eveniftheyexist)mayneverbefound.Fig.4(andFig.5)plottheprobabilitythatthenum-berofnode-disjointpathsdiscoveredineachrouteinquirybyAODVMisnolessthan3(and4)versusthenumberofhops4ontheshortestpathbetweenthesourceandthedestination.FromFig.4,weseethattheprobabilitythatatleastthreepathsarefoundisalmost1inCase3,andisabove0.78inCase2.ButinCase1,thisprobabilitydropsquicklyasthedistancebetweentwonodesincreases.InNAmeasureofthedistancebetweenthetwonodes. 23456789102468101214Number of hops of the shortest path between two nodesAverage number of node-disjoint pathsCase 1 (250 nodes): AODVMCase 1 (250 nodes): Ideal searchCase 2 (350 nodes): AODVMCase 2 (350 nodes): Ideal searchCase 3 (500 nodes): AODVMCase 3 (500 nodes): Ideal searchFig.3.Averagenumberofnode-disjointpathsdiscoveredperrouteinquiry,forvariousnodedensities.23456789100.30.40.50.60.70.80.91Number of hops of the shortest path between two nodesProbabilityCase 1 (250 nodes)Case 2 (350 nodes)Case 3 (500 nodes)Fig.4.Probabilitythatthenumberofnode-disjointpathsdiscoveredisnolessthan3(OQPSR)perrouteinquiry,forvariousnodedensities.Fig.5,theprobabilitythatatleastfourpathsarefoundisabove0.77inCase3.InCase2,thisprobabilitydropsquicklyto0.5asthedistancebetweentwonodesincreasestoabout6hops.Itdropsbelow10%inCase1asthedis-tancebetweenthesourceandthedestinationis7hops.FromFig.3,Fig.4andFig.5wenotethatwhenthenodedensityishigh,wecanndanacceptablenumberofnode-disjointpathstoprovideareasonablelevelofro-bustnesstonodefailures.However,thenumberofnode-disjointpathsthatarediscoveredisverylimitedevenatmoderatenodedensities(forexample,Case1).Inordertorouteinformationreliablyincaseswherein,multiplenode-disjointpathsarenotavailable,acertainnumberof“reliablenodes”shouldbeplacedinthenetwork.Inthenextsectionwedescribethefunctionalityofthesereliablenodesanddescribeamethodologytocontroltheirtrajec-toriestoachievehigherroutingreliability.234567891000.10.20.30.40.50.60.70.80.91Number of hops of the shortest path between two nodesProbabilityCase 1 (250 nodes)Case 2 (350 nodes)Case 3 (500 nodes)Fig.5.Probabilitythatthenumberofnode-disjointpathsdiscoveredisnolessthan4(OTP8U)perrouteinquiry,forvariousnodedensities.V.AFRAMEWORKFORRELIABLEROUTINGIntheprevioussectionwesawthat,withoutexpendingalargeamountofoverhead,onecannotndasufcientnumberofnode-disjointpathsbetweenagivensourceandadestinationtoprovideareasonabledegreeofrobustnesstonodefailures.Thiswasespeciallytrueifthesourceandthedestinationwerefarawayfromeachother.Onecouldimmediatelythinkofndingedge-disjointpaths;how-ever,nodesthatareattheintersectionofmultipleroutesmightfailandthismightcausealltherouteswhichpassthroughsuchanodetofailsimultaneouslyuponthenode'sfailure.Thus,itisconceivablethatonewouldattempttodeploythosenodesthataremorereliablethanothersatjunctionsconnectingmultiplenode-disjointsegments(asegmentisapathbetweentwonodes,seeFig.6).Inthiswork,weproposethatasetofthesereliablenodesbedeployedinanadhocnetworkforthepurposesofincreasingreliabilityandsecurity.Thispropositionisnotunrealisticinthesensethatintypicaladhocdeploy-mentsonecanenvisionthepresenceofmultipletypesofnodes.Inabattleeldnetwork,onecouldhaveunreliablelowpowersensorsorhandhelds,whereastherecouldbethemorereliable,powercapableandsecurenodesthatarelocatedinatankoranyotherlargevehicles.Itisalsocom-moninsecurityresearchtoassumethepresenceofthesocalled“trustednodes”[19].Fortheeaseofdiscussion,werefertothesereliablenodesasR-nodes.Itwouldbenatu-rallyexpensivetodeployalargenumberoftheseR-nodesandtheR-nodeswouldconstituteasmallfractionoftheentireadhocnetwork.Thequestionthatwearetryingtoansweris:iftheobjectiveofdeployingtheseR-nodesisprimarilytosupportareliableroutingframework,then,whereshouldtheseR-nodesbepositionedandhowshouldtheirtrajectoriesbecontrolled?Beforewetrytoanswerthisquestionwerstdene whatwecallareliablepath.IntheabsenceoftheR-nodes,westatethatareliablepathexistsfromasourcetoadestinationifthenumberofnode-disjointpathsthatcanbefoundbetweenthissourceanddestinationisatleastequalinnumbertoapresetthresholdG.WhentheR-nodesaredeployed,thedenitionofareliablepathchanges.Ifonecanconcatenateasequenceofreliablesegmentsbetweenthesourceandthedestinationnode,thenthepathissaidtobereliable.Asegmentisdenedtobereliableifthenum-berofnode-disjointpathsthatcanbefoundbetweentheendnodesofthesegmentisatleastequalinnumbertoG,or,ifthesegmententiretyconsistsofreliablenodes.Notethat,whileconcatenatingreliablesegments,thenodesattheintersectionofsuchsegmentsoughttobereliable5.Asanexample,wehaveapathfromasourceVtoadestina-tionWinFig.6.ThevalueofGissettothree.TherearethreeR-nodesX4,XYEandXYZ.Weseethattheend-to-endpathfromVtoWmaybedeemedreliablesincewecanconcatenatethreereliablesegments,therstfromVtoX[4,thesecondfromX\4toXZandnallythelastfromXYZtoW.ItisimportanttopositiontheR-Nodessoastomaxi-mizetheirutility.Asthenodesinthemobileadhocnet-workmove,itmaybecomenecessarytomovetheR-nodesrelativetothemotionoftheothernodes.Ifthenetworkisdenseallover,itwouldbepossible(astheresultsindi-catedwithAODVM)tondareasonablenumberofpathsbetweenanyarbitrarysourceanddestinationpair.Asanexample,whentheaveragenodedegreewassetto13.5(Case3inSectionIV),AODVMwasabletondeightpaths,onaverage.Whenweconsideredalargesampleofsource-destinationpairsthatareseparatedbyaxedhopcountontheshortestpathbetweenthem,wefoundthattheminimumandthemaximumofthenumberofpathsthatarefoundbetweenallsuchpairsaresignicantlydiffer-entfromoneanother.Thus,thereasonwhywecouldnotndmultiplepathsbetweennodesthataredistantfromeachotherismostprobablybecauseofthepresenceofsparseregionsinthenetworkwhichactasbottlenecks.Ifwecouldplacethereliablenodesinthesesparseareas,itappearsasifwecouldcreatethedesiredreliablepaths.RandomlyplacingtheseR-nodesisnotlikelytoprovideuswithanyperformancegains(asweshallseelater).ByplacingtheseR-nodessuchthattheywouldinterconnectwiththemaximumnumberofadhocnodes(i.e.,haveamaximaldegree)wouldprobablynothelpeitherasweseeintheexampleinFig.7.InFig.7(a),theblacknodehasthelargestdegreeinthenetwork.InFig.7(b),theblacknodehasthesmallestdegreeinthenetwork.However,]Weassumethecommunicatingentitiesarereliableandhavemutu-allyauthenticatedthemselves.^_`abcdeSDRRR231segment 1segment 2segment 3RnodesNormal NodesUFig.6.Areliablepathbetweennodefandnodeg(OQP8R).hi(a)(b)Fig.7.(a)Themaximum-degreenode(theblacknode)isthebottle-necknodeinthenetwork.(b)Theminimum-degreenode(theblacknode)isthebottlenecknodeinthenetwork.eachnodehasanequalimportanceintermsofkeepingthenetworkconnected,i.e.,ensuringthatasinglepathex-istsbetweenanytwonodes.Ourobjectiveissimilar,i.e.,identifypositionsfortheR-nodessuchthattheprobabil-ityoftheexistenceofareliablepath(givenavalueofG)betweenanytwogivennodesishigh.Towardsthis,weuseamodicationoftherandomizedmin-cutalgorithmwhichwedescribeinthenextsub-section.A.Min-cutalgorithmandourmodicationPriortodescribinghowtherandomizedmin-cutalgo-rithmmaybeusedtodeterminewheretheR-nodesaretobeplaced,wedescribetherandomizedmin-cutalgorithm[8]inbrief.Letj&\nk(ml*beanundirectedweightedgraphwhichisconnected.Acutinjisapartitionoftheverticeskintotwonon-emptysetsVandV.Thevalueofacutisthesumoftheweightsoftheedgescrossingthecut.Iftheweightsofalltheedgesinjareone,thenthevalueofacutisthecountofthoseedgesthathaveoneend-pointineachofthetwosetsVandV.Themin-cutisthecut(s)withtheminimumcutvalueofallthepossiblecuts.Ifalltheedgesinjareofunitweight,themin-cutisthenumberofedgesthatmustberemovedfromjtoseparateitintotwopartitions.Thesmalleroneofthesetwopartitionsisthencalledmin-cutset.Acutofagivengraphcanbeobtainedbywhatiscalledthecontractionalgorithm.Thebasicideaofthecontrac-tionalgorithmistorandomlychooseanedge&on(p*injandreplaceverticesnandpbyanewvertexq;foreach 2rKs tn(pu,theweightofthenewedge&2(q*isthesumoftheweightsofedge&2(n*andedge&2(p*;therestofthegraphremainsunchanged.Thecontractionprocedureisrepeateduntilthereareonlytwonodesandoneedgeleft.Thecutvalueisthentheweightoftheedgethatconnectsthesetwonodes.Duringeachiterationofthecontractionprocedure,asingleedgeischosenandthetwonodescon-nectedbythisedgearecontracted.Thus,ifthereare?nodesinthegraph,thealgorithmtakesv&?E*time.Notethatthisrunningtimeisindependentofthenumberofedgesinthegraph.Itcanbeprovedthattheprobabil-itythatthemin-cutofagraphjisfoundbyasinglerunofthecontractionalgorithmisboundedbyw&?AE*[8].Ifwerepeatthecontractionalgorithmv&?Eyx{z|?*times,wecanexpectwithareasonableprobabilitythatsomeitera-tionsofthecontractionalgorithmndthemin-cut.Thus,inordertocomputethemin-cutvalueofagivengraphj,wewouldexpecttoincuraruntimeofv&?,}x{z|?*.InordertodeterminewheretheR-nodesoughttobeplaced,werequireeachnodetocomputethemin-cutofapartialgraph.Theobjectiveistodeterminehowvul-nerablethenetworkis,intermsofbecomingpartitionedifaparticularnodewasremovedfromthegraph(i.e.,asinfailure).Weassumethateachnodecanobtainapar-tialtopologyviewofthenetwork;morespecically,weassumethatitknowstheentiretopologywithinsome~hopsfromitself(~isasystemdesignparameter).Thenodethenremovesitselfandtheedgesincidentonitselffromthegraphrepresentingthispartialtopology6.Itthenrunsthemin-cutalgorithmwiththefollowingmodica-tion:Theoutermostlinksarecontractedrst,andthelinksthatareclosesttothenodearecontractedlast.Thisisdoneinanattempttoensurethatthemin-cutisanaccu-rateindicatoroftheimportanceofthecomputingnodeinkeepingthelocalizedtopologyconnected.Asanexam-ple,inFig.8(a),theblacknodeistheoneperformingthecomputations;onewouldlikethemin-cuttoinfact“pass”throughthelinksassociatedwiththeblacknode(shownbythedottedlines)asshown.Withouttherequirementthattheoutermostedgesbecontractedrst,themin-cutwouldprobablypassthroughoneoftheoutermostedges.InFig.8(a),withouttherequirement,themin-cutwouldpassthroughthelinkbetweennodesk4andkE,anditsvalueisone.Thishowever,doesnotreectontherela-tiveimportance(whichisofinterest)oftheblacknodeinkeepingthegraphconnected.Fig.8(b)through8(j)illustrateoneofiterationsofthecontractionalgorithmwhichndsacutvalueofthegraphClearlythisisdonetoestimatethevulnerabilityofthelocalizedneighborhoodintermsofbecomingpartitionedifthenodeperformingthecomputationweretofail.V10V1V2V3V5V6V8V9V4V7V1V2V3V4V11V6V1V2V3V6V8V4V7V10{V59, V }11VV1V2V3V11V6V4V7{V34, V }17V1V2V3V4V5V6V7V9V10V8V111111111111(c)(b)(d)(e)1111121211113(g)V3V4V146V111V3V4V141(h)111122(f)V3V4V11V13V61111111111111111111111(a)116V11216VV14(j)(i)mincut of the black nodeLinks connected with the black node are not counted.{V810, V }12V1113V{V615, V }16V{V1115V{V12, V }14V{V1418V{V , V }12 , V }13 , V }17Fig.8.Aniterationofthecontractionalgorithm.showninFig.8(a).Theinitialweightofeveryedgeisone.Ineachcontractionstep,anedge(wechoosethedashededgesasshown7)ischosenrst,amongtheout-ermostedges,andthetwonodesconnectedbythisedgearecontracted.Theinnermostedgesarechoseninthe-nalfewsteps.Finally(Fig.8(j)),onlyoneedgeandtwonodesareleft.Thevalueofthecutasdeterminedbythisiterationistwo.Sinceourmodicationdoesnotchangethenumberofnodesintheinputtopologyandtheonlydifferenceisinthecontractionsequenceofthenodes,thecomputationcomplexityremainsthesameasthatoftheoriginalmin-cutalgorithm,i.e.,v&?}x{z|?*,ifthereare?nodeswithin~hopsofthenodecomputingthemin-cut.If~issmall,thecomplexitymaybeexpectedtobefairlylow.Inthefollowingsub-sectionswedescribeacentralizedandadistributedapproachofusingtheabovemethod-ologytodeterminethebestpositionsforplacingtheR-nodes.Althoughacentralizedapproachisunrealisticwithinamobileadhocnetworksetting,itisusefulintermsofevaluatingthegoodnessofourdistributedalgo-rithm.€Thischoiceisarbitraryandisdonesimplyforillustrativepurposes.Wecouldchoosetheedgesinadifferentorderaswell. B.UsingacentralizedcontrollertodetermineR-nodeplacementInthecentralizedstrategy,weassumethatthetopologyinformationoftheentirenetworkisknowntoeverynode.Everynode'smin-cutvalueandmin-cutsetarecomputedaprioriwithrespecttoagraphofitslocaltopologyupto~hopsfromit.Asdescribedearlier,wethenplacetheR-nodesinthepositionsoccupiedbythenodeswiththelowestmin-cutvalues.Thiscentralizedstrategyrequiresastaticnetworktopologyandmobilityisnotallowed.Theperformanceintermsoftheprobabilitythatareliablepathisfoundbetweenanarbitrarilychosenpairofnodes,asachievedbythustheplacingofR-nodes,canbeusedasabenchmarktocomparewithourdistributedversionoftheR-nodeplacementalgorithm.C.ThedistributedR-nodedeploymentstrategyInthedistributedR-nodedeploymentstrategy,weas-sumethateachnodeinthenetworkhasinformation(byusingGPSorothertechniques)thatspeciesitsownco-ordinates.WefurthersupposethateverynodeperiodicallybroadcastsaHELLOmessagetoitsneighbors;informa-tionwhichspeciesthetopologyofthenode's~-hoplocalneighborhoodisincludedinthisHELLOmessage.If~issmall,wecanexpectthatwithinsomeshortnitetime,eachnodehasthecompleteinformationaboutthetopol-ogyofits~-hopneighborhood.R-nodestransmitHELLOmessagesaswell.InanR-node'sHELLOmessage,thereisaagthatisusedtoindicateitsmotionstatus:static(ifthisR-node'spositionhasbeendetermined)ordynamic(ifthisR-nodeisstillintheprocessofdeterminingwheretomove).Eachnormalnodecanthusconstructtwolo-caltopologygraphs,therstwiththestaticR-nodesandthesecondwithoutthestaticR-nodes.ThedynamicR-nodesarenotincludedineitherofthesetwographs.Anodeperiodicallycalculatesitsmin-cutvalueandthesizeofthemin-cutsetbasedonthesetwographs.NotethattheweightofadirectlinkbetweentwostaticreliablenodesissettoG.Alltheotherlinkshaveweightofone.Thecom-putedmin-cutvaluesandthecorrespondingmin-cutsetsizesarepiggybackedontothenode'sHELLOmessage.AnR-nodecomparesthemin-cutvalueandthemin-cutsetsizesofthenodesinits~-hopneighborhood,anditmovestotheproximityofthenormalnodethathastheminimummin-cutvalue.Ifthemin-cutvaluesoftwonodesarethesame,thereliablenodewillmovetotheproximityofthenodethathasalargermin-cutset.InordertopreventmultipleR-nodesfrommovingtothesamelocationatthesametime,beforeanR-nodemovestotheproximityofanormalnode,itsendsoutamotionre-questtothatnormalnode.TheR-nodedoesnotmoveun-tilitreceivesamotionconrmationfromthenormalnode.Someadditionalconstraintscanalsobeincorporated,suchasrequiringthatnotwoR-nodescanbetooclose8,andlimitingthenumberofR-nodeswithintherangeofapar-ticularR-node9.D.ModicationstoAODVMInordertoallowtheincorporationoftheR-nodesandtoallowthesenodestoparticipateinmultiplepaths,AODVMhastobefurthermodied.However,thechangesareverysimpleandlightweight.IneachRREPpacket,weincludewhatwecallarelia-bilityag.WhentheRREPpacketpassesthroughanin-termediatenode,thisagissettoRELIABLEonlyifthisintermediatenodeisanR-nodeandiftheoriginalvalueofthisagwasalsoRELIABLE.Otherwise,thisagissettoNORMAL.IfanintermediateR-nodecannotndanexthopR-nodetoforwardthisRREPpacket,itwillsplittheRREPpacketintomultipleRREPpacketsequalincounttothenumberofneighborsspeciedinitsRREQtable.AlloftheseRREPpacketsaremarkedNORMALandthenforwardedtothedifferentneighbors.IntheexampleinFig.6,letusassumethatGissettothree.Initially,nodeVgeneratesandsendsanRREQmessagetonode.UponreceivingtheRREQ10,nodegeneratesanRREPpacketandattemptstosendthispacketbacktoVviaXZ,XEandX4.WhenX4receivestheRREPmessage(markedRELI-ABLE),itisunabletoforwarditfurthertoareliablenode.Beingaware,thatithasactuallyreceivedthreecopiesoftheoriginalRREQfromthreenormaladhocnodes(bymeansofitsRREQtable),itthenmakesthreecopiesoftheRREPmessagereceivedfromXYE.ItthenmarksthesemessagesNORMALandforwardsonecopytoeachofthethreeneighbors.ThethreeRREPcopies,then,ndtheirwaytothesource.SinceGwasthree,andthreeRREPmessageswerereceived,thesourceinfersthata“reliablepath”isavailabletothedestination.E.EffectsofnodemobilityThemobileadhocnetworktopologychangesasnodesmove.Inordertomaintainthereliableroutingframework,theR-nodeswillhavetocorrespondinglymovetorevisedlocationsasthenetworkevolves.IfthemaximumspeedofmotionoftheR-nodesisthesame(orlowerthan)asthatofthenormalnodes,theywillnotbeabletomove‚Wespecifythisdistancetobe50minoursimulations.However,thiswouldbeasystemparameterthatcanbecongured.ƒThisisasystemparameteraswell.However,inoursimulations,wefoundthatifthisnumberissetto4,weobservethebestperformance.…„NoticethatonlyasinglecopyoftheRREQisreceivedbythedestination. quicklyenoughtonewstrategicpositionsinatimelyman-ner.Thus,arequirementwouldbethattheR-nodesshouldbeabletomoveatmuchfasterspeedsascomparedtoitsnormaladhocnodes.Thisisconceivablesinceasmen-tionedearliertheseR-nodesaretypicallypowerfulandhousedinlargevehiclesasopposedtobeingsensorsorbeingcarriedbypedestrians.VI.PERFORMANCEEVALUATIONOFR-NODEDEPLOYMENTSTRATEGIESInoursimulations,wefocusonCase1describedinsec-tionIV.Inthisscenario,250nodesaredeployedinarect-angularareaof2500mx2500m.WechoosethiscasetodemonstratetheeffectivenessofourR-nodedeploymentstrategyevenwhenthedensityofnodesinthenetworkismoderate.InalloursimulationexperimentswechooseG(thenumberofpathsthatwoulddeemaparticularseg-ment,madeupofnormaladhocnodes,reliable)tobeeither3or4.Thisnumberseemstobereasonableforthepopulationsizeconsideredandwewanttoavoidex-tremelylongpathsthataredifculttomaintain11.A.PerformanceofthecentralizedR-nodedeploymentstrategyWerststudytheeffectsoftheparameterk12ontheperformanceofthestrategyintermsoftheprobabilitythatareliablepathisfoundbetweenanarbitrarysourceanddestinationthatareseparatedbyaminimumhop-count(weshallrefertothisprobabilityas†forconvenience).Itisdesirablethat~shouldbesmallsinceotherwise,onewouldhavetodisseminatealargeamountofcontrolin-formationtoenableanodeobtainthistopologyinforma-tion.WeassumethattheR-nodesareplacedinaccordancetoourcentralizedmin-cutbasedstrategy.Fig.9showsthatthestrategyissomewhatinsensitivetothechoiceofk(withinareasonablesetofvaluesthatwecanexpect~totake).Tobemorespecic,theincreasein†whenkisin-creasedfrom2to4isnotsignicant(lessthan0.1inmostcases).Sincethecomplexityofthemin-cutalgorithmintermsofrunningtimeisv&?}xoz|?*,wechoosethelowervaluei.e.,~ˆ‡inallfurtherstudies.Wealsopointoutthatthismeansthatonlyasmallamountoftopologicalinformationisactuallynecessaryforachievingaconsid-erableimprovementinperformance(astobeseenlater).Next,wecomparetheperformanceresultsofthemin-cutbasedcentralizedR-nodedeploymentstrategywiththoseofseveralotherR-nodedeploymentstrategies.‰Thelongerthepath,thehighertheprobabilityofitsfailure.B
EachnodeisassumedtoknowthetopologyuptowithinŠhopsofitself.23456789100.40.50.60.70.80.91Number of hops of the shortest path between two nodesProbability10% of all nodes are R-nodesk=3, k=2k=3, k=3k=3, k=4k=4, k=2k=4, k=3k=4, k=4Fig.9.ComparisonoftheperformanceofthecentralizedR-nodedeploymentstrategyforvariousvaluesofOandŠ.FRandomstrategy:AstrategyinwhichtheR-nodesarerandomlydeployed.FDegreebasedstrategyI:AstrategyinwhichtheR-nodesareplacedintheproximityofnodeswiththeminimumdegrees.Towardsthis,werstsortthenodesinaccordancewithanascendingorderintermsoftheirdegree.Ifthereare?R-nodes,theyareplacedinthevicinityoftherst?nodesintheor-deredlist.Thisstrategyappearedtobeagoodchoiceinitiallysincewewouldexpectthattheminimumde-greenodesarethebottleneckswhenattemptingtondmultiplepaths.FDegreebasedstrategyII:Astrategyinwhichthenodeswiththeminimumdegreesareidentiedrstasinthepreviousstrategy;theR-nodesareplacedintheproximityofthehighest-degreeneighborsofthesenodes(oneneighborforeachnode).Wedothissincewerecognizethattheminimumdegreenodesmayinfact,beattheedgesoftheareathatwecon-siderandthebottlenecksmaybeduetothefactthatthesenodeshaveasinglelinktotherestofthenet-work.Throughthisstrategy,weattempttomakesuchlinksreliable.FromFig.10andFig.11weseethattherandomR-nodeplacementstrategydoesnothelpmuchinnd-ingareliablepathbetweentwoarbitrarychosennodeswhen10%ofthenodesareR-nodes.ItresultsinalmostthesameperformanceasthatachievedinacasewhereintherewerenoR-nodes.DegreebasedstrategyIandde-greebasedstrategyIIcanhelpinincreasing†,buttheachievedperformanceisstillinferiorascomparedwiththeperformanceofthemin-cutbasedstrategybyabout18%whenGˆ‹andby25%whenGŒ.Thesecom-parisonsprovethatthemin-cutbasedR-nodedeployment 234567891000.10.20.30.40.50.60.70.80.91Number of hops of the shortest path between two nodesProbability10% of all nodes are R-nodesMin-cut based strategyRandom strategyDegree based strategy IDegree based strategy IINo R-nodes are deployedFig.10.ComparisonoftheperformanceofthevariousR-nodede-ploymentstrategieswithO%P8R.234567891000.10.20.30.40.50.60.70.80.91Number of hops of the shortest path between two nodesProbability10% of all nodes are R-nodesMin-cut based strategyRandom strategyDegree based strategy IDegree based strategy IINo R-nodes are deployedFig.11.ComparisonoftheperformanceofthevariousR-nodede-ploymentstrategieswithO%PŽU.strategyisveryeffectiveanditoffersthehighestvalueof†amongalltheschemesconsidered,especiallywhenthenumberofdeployedR-nodesissmall.B.PerformanceofthedistributedR-nodedeploymentstrategyTheperformanceofthedistributedR-nodedeploymentstrategywithoutandwithnodemobilityarestudiednext.Weconsidertwocases.Intherstcase,allthenormalnodesarestatic,andonlytheR-nodesmovearoundandndtheiroptimalpositions.InitiallytheR-nodesarescat-tereduniformlyaswell.Inthelatercase,boththeR-nodesandthenormalnodesareallowedtomove.Therandomwaypointmodelisusedtomodelanormalnode'smobil-itypattern.ThespeedofthenormalnodesisuniformlydistributedoverHI(‡JLKM.ThemovingspeedoftheR-nodesis10m/s,andthetrajectoriesofthesenodesaredenedbythedeploymentstrategy.ThisisinlinewiththerequirementspeciedofR-nodesinsub-sectionV-E.234567891000.10.20.30.40.50.60.70.80.91Number of hops of the shortest path between two nodesProbability10% of all nodes are R-nodesk=3, distributed strategy without mobilityk=3, distributed strategy with mobilityk=3, centralized strategyk=4, distributed strategy without mobilityk=4, distributed strategy with mobilityk=4, centralized strategyFig.12.EffectsofmobilityonthedistributedR-nodedeploymentstrategy.Fig.12showsthatthedistributeddeploymentstrategy,intherstcase(withoutmobility),performsworsethanthecentralizeddeploymentstrategy.Thisisbecause,inthedistributedstrategy,theR-nodesdonothaveacentralcontrollerwhichcanprovideglobaltopologyinformation.Basedontheavailablelocalinformationthatisdissemi-nated,theywillhavetomovearoundandndtheirposi-tions.SomeofthepositionsthattheR-nodeschoosemaynotbetheoptimalonesfromtheglobalpointofview.Fur-thermore,thenetworktopologychangeswiththemove-mentofR-nodes,suchchangesmakeitmoredifcultfortheR-nodestondthebestpositions.FromFig.12weseethatthedistributedstrategy,per-formsonlyalittleworsewhenthereismobilityascom-paredwiththecasewhereinthereisnomobility(byabout5%atmostwhenG‹).TheR-nodescantracethetopol-ogychangesinatimelymannerinspiteofmobilityandadaptivelymodifytheirtrajectoriestondthebestpossi-blepositions.Thus,ourdistributedR-nodedeploymentstrategycanbeappliedinpracticalmobileadhocnet-works,inwhichthenormaladhocnodesareeitherstaticorhavepedestriantypemotion.VII.CONCLUSIONSInthispaper,ourobjectivewastoproviderobustnesstobothintermittent(orshortterm)andlongtermnodefail-uresinadhocnetworks.Thesefailurescouldbearesultofeitherfading,batteryfailureorcompromises.Thecom-putationanduseofmultiplenode-disjointroutescouldpotentiallyprovidesometolerancetonodefailures.Weproposedmodicationstoapopularadhocroutingpro-tocolAODV,toenablethecomputationofmultiplenode-disjointpathswithoutincurringtheoverheadgeneratedbylink-stateroutingmethods.Oursimulationresultsshow thatthenumberofnode-disjointpathsthatcanbefoundbetweenasourceandadestinationdependsonthedensityofnodesinthenetwork.Furthermore,wendthatevenatmoderatenodedensities(averagenodedegreeis6.7),thenumberofnode-disjointpathsthatmaybefoundareverylimited(around2ifthedistanceontheshortestpathbe-tweenthesource-destinationpairis7).Thus,weinferthatitisnecessarytopopulatethenetworkwithafewreliablenodesthatarephysicallymoresophisticatedintermsofbeingcapableofcombatingfading,possessingbetterbat-teriesandphysicallymoresecure.ThesenodeswhichwecallR-nodesaremainlyusedforcreatingareliableroutingframeworkwithintheadhocnetwork.WethenattempttoaddressthequestionofwheretheR-nodesaretobeposi-tionedwithintheadhocnetworkandhowtheirtrajecto-riesaretobecontrolledifanotionofroutingreliabilityistobeprovided.WedenereliablepathtocapturethenotionofroutingreliabilityandevaluatetheperformanceofR-nodedeploymentstrategiesintermsoftheprobabil-itythatareliablepathisfoundbetweenasourceandadestination.Weproposeastrategybasedontherandom-izedmin-cutalgorithm.Weshowthatourstrategyhasthebestperformanceintermsoftheabovedenedmet-ricascomparedwiththeotherpossiblestrategiesthatweconsidered,andthatitcancopewithdynamictopologychangesduetolowmobilitypatterns.Webelievethatthearchitectureproposedanddeveloped,isnecessaryandisaviableoptionforprovidingareliableroutingframeworkinadhocnetworks.ACKNOWLEDGMENTSTheauthorswouldliketothankChinyaRavishankarandMichalisFaloutsosfortheirvaluablesuggestionsandcomments.REFERENCES[1]N.F.Maxemchuk,“Dispersityroutinginstoreandforwardnet-works,”Ph.D.thesis,UniversityofPennsylvania,May1975.[2]M.R.Pearlman,Z.J.Haas,P.Sholander,andS.S.Tabrizi,“Ontheimpactofalternatepathroutingforloadbalancinginmobileadhocnetworks,”ProceedingsoftheACMMobiHoc,pp.3–10,2000.[3]A.Nasipuri,R.Castaneda,andS.R.Das,“Performanceofmultipathroutingforon-demandprotocolsinmobileadhocnetworks,”ACM/KluwerMobileNetworksandApplications(MONET),vol.6,no.4,pp.339–349,2001.[4]M.K.MarinaandS.R.Das,“On-demandmultipathdistancevectorroutinginadhocnetworks,”ProceedingsoftheInter-nationalConferenceforNetworkProcotols(ICNP),pp.14–23,Nov.2001.[5]K.WuandJ.Harms,“Performancestudyofamultipathroutingmethodforwirelessmobileadhocnetworks,”ProceedingsoftheIEEEInt'lSymposiumonModeling,AnalysisandSimulationofComputeandTelecommunicationSystems(MASCOTS),pp.99–107,2001.[6]E.Ayanoglu,I.Chih-Lin,R.D.Gitlin,andJ.E.Mazo,“Diversitycodingfortransparentself-healingandfault-tolerantcommuni-cationnetworks,”IEEETransactionsonCommunications,vol.41,no.11,pp.1677–1686,1993.[7]C.E.PerkinsandE.M.Royer,“Adhocon-demanddistancevec-torrouting,”ProceedingsoftheIEEEWorkshoponMobileCom-putingSystemsandApplications(WMCSA),pp.90–100,1999.[8]R.MotwaniandP.Raghavan,RandomizedAlgorithms,Cam-bridgeUniversityPress,1995.[9]S.VutukuryandJ.J.Garcia-Luna-Aceves,“Mdva:Adistance-vectormultipathroutingprotocol,”ProceedingsoftheIEEEIN-FOCOM,pp.557–564,2001.[10]W.ZaumenandJ.J.Garcia-Luna-Aceves,“Shortestmultipathroutingusinggeneralizeddiffusingcomputations,”ProceedingsoftheIEEEINFOCOM,pp.1408–1417,1998.[11]S.J.LeeandM.Gerla,“Splitmultipathroutingwithmaximallydisjointpathsinadhocnetworks,”ProceedingsoftheIEEEICC,pp.3201–3205,2001.[12]D.B.Johnson,D.A.Maltz,andJ.Broch,“Dsr:Thedynamicsourceroutingprotocolformultihopwirelessadhocnetworks,”AdHocNetworking,pp.139–172,2001.[13]V.D.ParkandM.S.Corson,“Ahighlyadaptivedistributedrout-ingalgorithmformobilewirelessnetworks,”ProceedingsoftheIEEEINFOCOM,vol.Kobe,Japan,pp.1405–1413,April1997.[14]J.RajuandJ.J.Garcia-Luna-Aceves,“Anewapproachtoon-demandloop-freemultipathrouting,”ProceedingsoftheInterna-tionalConferenceonComputerCommunicationsandNetworks,pp.522–527,1999.[15]S.R.Das,R.Castaneda,andJ.Yan,“Simulation-basedper-formanceevaluationofroutingprotocolsformobileadhocnet-works,”ACM/BaltzerMobileNetworksandApplications,pp.179–189,2000.[16]S.R.Das,C.E.Perkins,andE.M.Royer,“Performancecompar-isonoftwoon-demandroutingprotocolsforadhocnetworks,”ProceedingsoftheIEEEINFOCOM,vol.TelAviv,Israel,pp.3–12,2000.[17]M.Ahmed,S.V.Krishnamurthy,R.Katz,andS.Dao,“Trajec-torycontrolofmobilegatewaysthatfacilitaterangeextensioninadhocnetworks,”ComputerNetworksJournal(COMNET),toappear.[18]K.FallandK.Varadham,ThensManual,http://www.isi.edu/nsnam/ns/ns-documentation.html/.[19]S.Yi,P.Naldurg,andR.Kravets,“Security-awareadhocroutingforwirelessnetworks,”Proceedingsofthe2001ACMInterna-tionalSymposiumonMobileAdHocNetworking&Computing,vol.LongBeach,California,pp.299–302,2001.[20]E.M.RoyerandC.E.Perkins,“Areviewofcurrentroutingproto-colforad-hocmobilewirelessnetworks,”IEEEPersonalCom-municationMagazine,pp.46–55,April1999.