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Market-basedNetworkFormationforanAdHoc,P2PWirelessNetworkYasUlloriYamamoto·SchoolofInformationStudies,SyracuseUniversityMinistryofPublicManagement,HomeAffairs,PostsandTelecommunications5495-1-502Ooyaguchi,Saitama996-0934JAPANyayamamo@syr.
eduJunseokHwangtSchoolofInformationStudies,SyracuseUniversity4-291,CenterforScienceandTechnologySyracuse,NY13244-4100USAjshwang@syr.
eduAbstractInanadhoc,arbitrarilyformedpeertopeer(P2P)networksystem,eachusercanselectoneoftheservicesofferedbymultipleneighborstationstohaveanaccesstothenetwork.
Everyuserhasapreferencefunctiontodetermineaservicetouse,whichisdescribedasatotalwillingnesstopaybasedonthebandwidthandthedurationofusingaservice.
Inourstudy,wedevelopedamarket-basedmodelforausertodetermineaserviceinordertomaximizetheuser'ssurplus.
Ourmodelallowsastationtoconnectanotherstationwithoutreconnectionaslongasitwantsorpossible.
Byemployingourmodel,stationsofprovidingaservicecanofferacompetitivepricingbasedondurationsofconnectionssuchasadiscountfortheiruserstouseitlonger.
Thepricingofthiskindisalsopreferableforbothusersandproviders.
Inaddition,basedonourmodel,wedevelopedanalgorithmforastationtodetermineawayofmakingaconnectiontothenetwork.
WesimulatedsomescenariosofadhocP2Pwirelessnetworksbyusingthealgorithm.
WefoundthattheformednetworkismoreefficientthanformerceaselesslyreconnectingnetworksintermsoftheconnectivitytogetacertainQoS.
Keywords:Market-basednetworks,P2Pnetworking,WirelessCommunications·Phone:+81(48)874-7233,Fax:+l(702)921-3399tPhone:+l(315)443-4473,Fax:+l(315)443-5806Theoriginalversionofthischapterwasrevised:Thecopyrightlinewasincorrect.
Thishasbeencorrected.
TheErratumtothischapterisavailableatDOI:10.
1007/978-0-387-35618-1_37C.
G.
Omidyar(ed.
),MobileandWirelessCommunicationsIFIPInternationalFederationforInformationProcessing200322YasunoriYamamoto1.
IntroductionDuetorapiddevelopmentofthewirelesstechnology,demandsonhigh-speedpersonalwirelessdatacommunicationshasincreased(In-ternationalTelecommunicationUnion,2000).
Onceintherangeofpropagation,individualuserscanaccesstheInternetwithoutanyca-blewherevertheyare,whethertheymoveornot.
Inthissituation,decentralizedadhocP2Pnetworksaremoresuitablethancentralizedstaticnetworksystems.
Thosenetworksalloweverystationtobecomeanetworkproviderforotherstationsandactasarepeater,sothatauseroutoftherangeofabasestationcouldaccessthenetworkviaanotherstation.
Weassumedthefollowingscenario.
Inanadhoc,arbitrarilyformedP2Pnetworksystem,eachuserselectsoneoftheservicesofferedbymultipleneighborstationstohaveanaccesstothenetwork.
Everyuserhasapreferencefunctiontodetermineaservicetouse,whichisdescribedasatotalwillingnesstopaybasedonthebandwidthandthedurationofusingaservice.
Inourstudy,wedevelopedamarket-basedmodelforausertodetermineaserviceinordertomaximizetheuser'ssurplus.
Inourmodel,astationcanconnectwithanotherwithoutareconnectionaslongasitwantsorpossible.
Thisfeatureallowsstationstoprovideacompetitivepricingsuchasadiscountplanfortheiruserstoconnectwiththemlonger.
Inordertorealizeit,usersarepreviouslyinformedofcostsaccordingtothedurationofaconnectionbyprovid-ingstations.
Thepricingschemeofthiskindbringsbenefitstobothofusersandproviders,sincemanyuserspreferafixedrateservicetothatofusage-basedcharging(Ohu,1999),whileproviderscangetanoptimalpricingtomaketheirprofitshigher.
Inspiteofmanystudiesofoptimalpricing,fewofthemtakeconsiderationofthisusers'preference.
Inaddition,basedonthemarket-basedmodel,wedevelopedanalgo-rithmofdeterminingawayofconnectingwiththenetwork.
Wesimu-latedsomescenariosofadhocP2Pwirelessnetworkformationsbyusingthealgorithm.
Asaresult,wefoundthatanadhocP2Pwirelessnet-workcanbeformedautonomouslybyusingthealgorithm.
Theformednetworkshowedbetterperformancethanceaselesslyreconnectingnet-worksintermsoftheconnectivity.
2.
RelatedStudiesSomestudiesproposedabiddingmethodtoallocateresource(i.
e.
,asellerallocatesresourcetothosewhovalueitmost)andusedagametheorytoshowanoptimalconditionunderwhichusersandasellermaximizetheirutilities.
Usersbideverycertainperiodoftimetobeallocated.
Arecentstudy(LazarandSemret,1998)introducedthePro-Market-basedNetworkFormation/oranAdHoc,.
.
.
23gressiveSecondPrice(PSP)mechanism,whichisderivedfromVickreyAuction(secondpricesealedbid)andgeneralizesit.
Resourceisallo-catedtobiddersaccordingtotheorderofthebiddingpricesuntilnomoreresourceisleft.
Thismechanismisunprecedentedinthatitap-pliestoagenericarbitrarilydivisibleandadditiveresourcemodelsuchasspectrumallocation.
Theirapproachdoesnotassumeanyspecificmappingofresourceallocationtoqualityofservice.
However,biddersaredefinedashavinganexplicitmonetaryvaluationofquantitiesofresourcewhichauctioneerdoesnotorcannotknowapriori.
Anotherapproach(AltmannetaI.
,2002)usedaMarkovmodel.
Inthemodel,anadministratoroffersseveraltypesofservicesatdifferentprioritylevels,andauserdecidesoneofthemtousebasedonhisorherjob'spriorityandofferedprices.
ApriceatapriorityleveldoesnotchangebutanactualQoSatthelevelvariesdependingoncircumstances.
Accordingly,userscanseeaQoSanditspriceofaservicewhendeciding.
Sincethisapproachisjoboriented,however,userscannotestimatetotalcostsfortheirconnections.
3.
AssumptionWeconsidertwomaintypesofnetworktopologywhenwedevelopapricingmodel:StarandP2P.
Startopologyisthatthereisanaccesspointusedbymultipleuserssimultaneously.
Currentcellularsystemisinthistopology.
P2Ptopologyisthattherearemultiplestationsandastationcanbeanaccesspointtotheothers.
Needlesstosay,thistopologyincludesStartopology.
Anadvantageofthiscanbeshownwhenthereisastationoutoftherangeofanaccesspoint,butanotherstationwithintherangecanbecomeaproxytothatstation.
Sinceweassumethatanyusercanalsobeanetworkprovidertoanother,wedonotcareaboutanetworktopologybutfocusonbehaviorsofusersandproviders.
Userspreferfixedrateserviceswhileprovidersseekmaximumprofits.
Weseekawayofprovidingaconditionunderwhichbothplayerscangetsatisfied.
Aprovideroffersseveraltypesofservicesintermsofdurationofserviceandbandwidth(QoS).
Auserchoosesaserviceofferedbyneighborprovidersaccordingtohisorherpreference.
WeassumeaCDMAsystemtowhichourmodelapplies,whereusersareassignedorthogonalspreadingcodes.
Inthissystem,atransmittedpowerandalengthofcodesdetermineaQoS.
Asinastudy(Liuetal.
,2000),weassumeallcodeshavesamelength,andthereforeaQoSisdeterminedbyatransmittedpower.
Let#Li(O1(t),4>2(t),.
.
.
,4>N(t)and[kl(d),k2(d),kN(d),respectively.
Assum-ingthattheexponentiallydistributedservicedurationisnotaffectedby4>j(t),usersstartingaservicejattimetareexpectedtopayanaveragepriceof:1+00[1(T-t)1pj(t)=tTje-rj(T-t).
t4>j(v)dv·(1-kj(r-t))dr.
(4)LetPb(t)beaspotpricedeterminedbyhowscarcethespectrumresourceisattimet.
Pb(t)wouldbecomehigherif,forexample,thepropaga-tionconditionisworseornumberofuserswantingtouseitincreases.
Since4>j(t)canbeuniquelydeterminedbyPb(t)ifthediscountratesaregiven,weassumethatprovidersmanipulate[Pl(t),P2(t),···,PN(t)tomaximizetheirutility.
5.
CaseStudy5.
1.
Station'sBehavior(Withvs.
WithoutaDiscount)Asanexampleofcomparison,wetookthreeserviceplans4>i(i=1,2,and3)withandwithoutadiscountplankll.
Inaddition,wetookauser'spreferencetWIforthoseservicesasanexample,whichcanbedescribedasaGaussianfunction.
Inthissituation,theuser'ssurplusU(t)canbedescribedasfollows:U(t)=tWI(t)-kl(t)lot4>i(V)dv(i=1,2,3).
(5)Therefore,inthisexample,thedurationoftimetomaketheuser'ssurplusoptimalcanbefoundbysolvingthefollowingequation:dtwl(t)dr·dt=dtkl(t)104>i(V)dv1,2,3).
(6)s.
t.
(7)Figure1showshowthesethreepricingplansrequireausertopayac-cordingtothedurationofconnectiontime,andauser'spreference.
1kl(t)=1incaseofnodiscount.
26YasunoriYamamoto45.
0price40.
5WithoUldlJcouO36.
031.
527.
022.
518.
013.
59.
04.
5duration0.
00481216202428323640Figure1.
Comparisonofservices,andauser'spreference5.
2.
NetworkFormationAlgorithm.
Inordertomakeanetworkformationautonomic,wedevelopedanalgorithmforastationtodetermineawayofestablishingaconnectiontoanotherstationorgivingup.
Table1showsthealgorithm,whichemploysourmodeldiscussedinthisstudy.
Table1.
AlgorithmtomakeaconnectionP={},Q=U;Fori=1TotheendofexistingstationsnearbyCalculatethedistancedi;Forj=1TotheendofserviceswhichstationioffersQ=QU{QoSofServiceSij};P=Pu{PricingScheduleofServiceSij};End;End;FindaserviceSi*j*:surplussp(Si*j*)>sp(Sij)(i*I=-i,j*I=-j);IfSi*j*,;z<,.
I".
I.
':r-1I0,001tOOllOll!
tOOl0.
009D.
I1Itill0.
012tll.
ltOl4D.
I1ISRecIprocalTetaTimeFigure9.
ContinuativeConnectionsAverageNumberofActiveandInactiveStationsaveragenumbersofactiveandinactivestationstothereciprocaltotaltimestocompleteasimulation.
Asforthediscreteconnections,theaveragenumbersofactivestationsarefrom10.
6to22.
1whilethoseofinactiveonesarefrom2.
06to4.
40.
Ontheotherhand,concerningthecontinuativeconnections,thoseofactiveonesarefrom18.
6to32.
5andinactiveonesfrom0.
50to1.
12.
Thisresultindicatesthatmorestationscanhaveconnectionswhentheyarecontinuativethandiscrete.
Inotherwords,theconnectivityofanadhocP2Pnetworkimproveswhencon-2fromthetimeofthefirststationcomesuptothetimeofthelastonedisappears3stationhavingaconnection4stationnothavingaconnection5numberofconnectionsfromtheroottoastation(e.
g.
,astartopologynetworkhas1.
00ofitsaveragedepth.
)28YasunoriYamamototinuativeconnectionsareallowed.
Itshouldbenotedthattheaveragedepthsofbothsituationsarealmostidentical(1.
73and1.
84).
6.
ConclusionInourstudy,weintroduceadiscountfactor,andthereforefixedrateserviceswhichmanyindividualusers'preferencecanbedescribedinourpricingmodel.
Eachuserispreviouslyshownwithserviceplanswhichcompriseapricingandadiscountschedulebymultipleserviceproviders.
Afterthat,theusercandetermineaserviceplanandaserviceprovidertouse.
Besides,wedonotassumethateachserviceproviderpreviouslyknowstheusers'preferences,butinsteadassumethattheirdurationsoftimetousenetworksareexponentiallydistributed.
Inthisassumption,wegetanoptimalpricingmodel.
Inaddition,wedevelopedanalgorithmforeachstationtodeterminehowtomakeaconnectiontoanotherstationbasedonthesurplusforit.
Usingthealgorithm,wemadesimulationsandconfirmedthatanadhocP2Pwirelessnetworkcanbeformedautonomously.
Inaddition,oursimulationsshowedthatconnectivityofformednet-worksimprovesbyintroducingcontinuativeconnections.
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