IEEE TRANSACTIONS ON MOBILE COMPUTING Enabling Spectrum Sharing in Secondary Market Auctions - PDF document

2IEEETRANSACTIONSONMOBILECOMPUTINGtheirvaluefordifferentallocations,givenprobabilisticactivationpatterns,interference,andrequirementsforsharedvsexclusive-accessspectrum.Inclearingtheauction,wequantifyabidder'svalueforanallocationintermsofthefractionofthebidder'sdemandthatissatisedinexpectation.Forthispurpose,weconsiderlocalinterferenceviaaninterferencegraphandamodelforresolvingdevicecontention.Strategyproofnessisapropertythatmakessim-ple,truthfulbiddingoptimalforeachuser.Ausercanreporthistruevalueregardlessofthebidsandcharacteristicsofotherusers.Strategyproofnessisanimportantpropertyfordistributedsystemsbecauseitpromotesstability.Inanon-strategyproofalgorithm,asbidderslearntheymayhaveanincentivetokeepchangingtheirbids,whichimposescostsonthesysteminfrastructureInaddition,strategyproofnessremovesthestrategicproblemfacingbidders.Forevaluation,itbecomesvalidtoconsidertruebids,whichinanon-strategyproofauctionwouldleadtoanincorrectanalysis.Evenwithoutsharing,ndinganoptimalchannelassignmentinvolvessolvingagraphcoloringproblemandisNP-hard[20].Wethereforetakethecommonapproachofusingagreedyalgorithmtondachan-nelassignment.However,akeytechnicaldifcultyisthatunlikeinsettingswithoutexternalitiesastraightfor-wardgreedyallocationapproachfailstobemonotonic.Thefailureofmonotonicitymeansthatitispos-siblethatausercansubmitalargerbidbutreceivelessspectrum.Monotonicityiswellknownassuf-cientandessentiallynecessaryforanalgorithmtobestrategyproof(givensuitablepayments)[29].Inachievingmonotonicity,SATYAmodiesthegreedyalgorithmthroughanovelcombinationofbucketingbidsintointervalswhereintheyaretreatedequally(anideaemployedinGhoshandMahdian[16])andacomputationalironingprocedureusedtoperturbtheoutcomeasnecessarytoensuremonotonicity(anideaintroducedbyParkesandDuong[30]).ToevaluateSATYAweuserealworlddatasourcestodetermineparticipantsintheauction,alongwiththesophisticatedLongley-Ricepropagationmodel[3],andhighresolutionterraininformation,togener-ateconictgraphs.WecomparetheperformanceofSATYAagainstotherauctionalgorithmsandbaselinecomputations.Ourresultsshowthat,whenspectrumisscarce,allowingsharingusingSATYAincreasessocialwelfareby40%overpreviousapproaches.1.1RelatedWorkTherehasbeensignicantworkonspectrumauctionswherearegulatoryagency,suchastheFCC,leasestherighttospectrumacrosslargegeographicareas(see,e.g.[11],[12]).However,ourfocusonsecondary-marketauctions,whereanexistingownerofspectrum(whichcouldstillbetheFCC)wishestoresellittoalargenumberofsmalleruserssubjecttointerferenceconstraints.Mostapproachestosecondary-marketauctionspre-cludesharingamongauctionparticipants[8],[14],[17],[32],[34],[35].VERITAS[34]wastherstspec-trumauctionalgorithmbasedonamonotonealloca-tionrule,andthusstrategyproof.However,VERITASdoesnotsupportsharing.Theuseofaspectrumdatabaseinfacilitatingsecondarymarketauctionshasbeenproposed[19].Turningtosharing,Jiaetal.[23]envisionspectrumownersauctioningoffspectrumrightstoasecondaryuserwhenitisnotbeingusedbytheowner,andinvestigatehowrevenuecanbemaximized.Whilewinnerssharewiththespectrumowner,thereisnosharingamongbiddersintheauction.Gandhietal.[15]useanapproachthatallocatesmanysmallchannels,effectivelyenablingsharing.However,theiralgorithmallowssharingonlyamongbidderswhowantonlyaportionofachannel.Thus,itcannottakeadvantageofbidderswhoareonlyintermittentlyactive.Inaddition,theapproachisnotstrategyproofandthereisnoequilibriumanalysis,whichmakesitsefciencyandrevenuepropertieshardtoevaluate.ClosesttoourworkisthatofKasbekarandSarkar[24],whouseastrategyproofauctionandprovideforsharing.Butratherthanpro-videastructuredbiddinglanguagethedesignallowsbidderstoexpressarbitraryexternalities,andtheirproposedapproachisintractable.Theissueofexternalitiesinauctionshasbeencon-sideredmoregenerally.Jehieletal.[22]considersitua-tions,suchasthesaleofnuclearweapons,wherebid-derscarenotjustaboutwinningbutaboutwhoelsewins.Butthesettingsdonotincludecombinatorialallocationproblems.Anumberofpapershavecon-sideredexternalitiesinonlineadvertising(e.g.[10],[16]).However,thiswork(andsimilarlythatofKrystaetal.[26]ontheproblemofexternalitiesingeneralcombinatorialauctions)isnotdirectlyrelevant,astheexternalitiesinspectrumauctionshaveaspecialstructure,ofwhichSATYAtakesadvantage.2CHALLENGESINAUCTIONDESIGNInthissectionwedescribethechallengesthatarisewhendesigningaspectrumauctionthatpermitsshar-ingwhilebeingstrategyproofandprovidinggoodrevenuepropertiestotheseller.First,wediscussthegeneralformofanauctionandintroducethenotionofstrategyproofness.Second,wepresentaresultduetoMyerson[29]thatprovidesageneralframeworkfordesigningstrategyproofauctionsthroughtheuseofamonotoneallocationrule.Finally,weintroducethenotionofareserveprice,astandardapproachtoincreasingtherevenuefromanauction.Auctionsareaclassicapproachtoallocatingre-sourcesamongstparticipantswithcompetingneeds 4IEEETRANSACTIONSONMOBILECOMPUTING3THEMODELOFSHAREDSPECTRUMANDEXTERNALITIES3.1UserModelInordertondopportunitiestoshareamonghet-erogeneoususers(e.g.,auserwithawirelessdevice,oraTVstation),weneedalanguagetodescribetherequirementsofeachpossibletypeofuser.Ourmodelusesdiscreteintervalsoftime(calledepochs),withauctionsclearingperiodicallyandgrant-ingtherighttouserstocontendforaccesstoparticu-larchannelsovermultipleepochs2.Theultimateallo-cationofspectrumarisesthroughrandomactivationpatternsofusersandinterferenceeffects,anddependsonspecicsofthemedium-accesscontroller(MAC)contentionprotocol.TheeffectofthisMACprotocolismodeledwithinSATYAindeterminingtheallocation.Theinterferencebetweenusersandtheirassociateddevicesismodeledthroughaconictgraph,G=(V;E),suchthateachuseriisassociatedwithavertex(i2V)andanedge,e=(i;j)2Eexistswheneverusersiandjwouldinterferewitheachotheriftheyarebothactiveinthesameepochandonthesamechannel.Weallowforbothexclusive-useand“willingtoshare”users,wheretheformermustreceiveaccesstoachannelwithoutcontentionfrominterferingdeviceswhenevertheyareactive,whilethelattercanstillobtainvaluethroughcontendingforafractionofthechannelwithotherinterferingdevices.Wesaythatachannelisfree,fromtheperspectiveofuseriinaparticularepoch,ifnoexclusive-useuserj,whointerfereswithiandisassignedtherighttothesamechannelasi,isactiveintheepoch.Formally,wedenotethesetofusertypesT.Eachtypeti2Tisatupleti=(xi;ai;di;pi;Ci;vi),where:xi2f0;1gdenoteswhethertheuserrequiresexclusive-useofachannelinordertomakeuseofit(xi=1)orwillingtosharewithanotheruserwhilebothareactiveonthechannel(xi=0).ai2(0;1]denotestheactivationprobabilityoftheuser:theprobabilitythattheuserwillwanttousethechannel,andbeactive,inanepoch.Forsimplicity,weassumethatactivationisdeterminedindependentlyineachepochwiththisprobabilityandthatusersareactivefortheentireepoch.Thisimplicitlyrulesoutbehaviorsuchaswaitingtotransmitinthenextepoch.Italsorulesoutcorre-latedperiodsofhighdemand,butseeSection5.5wherewerelaxthisassumption.di2(0;1]isthefractionaldemandofthechannelthatauserwhoiswillingtoshareaccessrequires2.Weareintentionallyvagueaboutthedurationofanepoch.Dependingonthesettinganepochcouldbeseveralminutesorseveralhours.Thekeyfeatureisthatuserdemandsshouldbestableforthedurationofanepoch.inordertoachievefullvaluewhenactive.Intu-itivelythisisthefractionofthechannel'scapacitythattheuserwouldliketousecontinuouslyforthedurationoftheepoch.pi0denotestheper-epochpenaltyincurredbytheuserwhenactiveandtheassignedchannelisnotfree.Bothexclusive-useandnonexclusive-useuserscanhaveapenalty.CiC=f1;2;:::g,whereCisthesetofchannelstoallocate,eachcorrespondingtoaparticularspectrumfrequency,denotesthechannelsthatuseriisabletouse(theuserisindifferentacrossanysuchchannel.)vi0denotestheper-epochvaluereceivedbytheuserinanepochinwhichitisactive,thechannelisfree,andinthecaseofnonexclusive-usetypes,theuserreceivesatleastasharedioftheavailablespectrum.Inthismodel,eachuserdemandsasinglechannel.WediscussanextensiontomultiplechannelsinSection4.4.ExamplesAuserwhowishestorunalow-power(local)TVstationonachannelwouldbeunabletoshareitwithotherswhenactive(xi=1),wouldbeconstantlybroadcasting(ai=1),andwouldhaveaverylargepenaltypisinceitisunacceptableforthebroadcasttobeinterruptedbysomeoneturningonanother(exclusive-use)device.Auserwithawirelessmicrophonecannotshareachannelwhenactive(xi=1),butisusedonlyoccasionally(ai=0:05)andhasasmallervalueofpisinceitmaybeacceptableiftheuserisoccasionallyunabletobeusedwhenthereisanotherexclusiveuseralsotryingtousethechannel.3Abiddermaywanttorunawirelessnetwork.Suchauserwouldhaveconstanttrafc(ai=1),consumealargeportionofthechannel(di=0:9),andmighthavealargepenaltysimilartoaTVstationforbeingcompletelydisconnected.How-ever,suchauseriswillingtosharethechannelwithothernon-exclusivetypes(xi=0),andwillpayproportionatelylessforasmallerfractionofthebandwidth.Abidderrepresentingadelaytolerantnet-work[21],whooccasionally(ai=0:2)wouldliketosendasmallamountofinformation(di=0:4)ifthechannelisavailable.Suchbiddersmighthavealoworevennopenaltyastheiruseisopportunistic.3.Indeed,itmightmakesensefromanefciencyperspectivetohaveseveralsuchdevicesshareachanneliftheyinterferewitheachothersufcientlyrarely. 6IEEETRANSACTIONSONMOBILECOMPUTINGFormally,ifNaisasetcontainingiandtheactiveneighborsofiwithwhomisharesachannelintheallocation,andNf=fj2Najdjfg,thenuserireceivesashareoftheavailablebandwidthonthechannelequalto,sharei(Na;t)=min di;maxf2[0;1]1�Pj2Nfdj jNa�Nfj!(5)Theusereithergetsthefulldemanddior,failingthat,thefairshare(whichthemaxintheequationdetermines).Ifallusershavethesamedemanddi,thisreducestoeacheitherthefulldemandbeingsatisedifdi1=jNajorreceivinga1=jNajshareofthechannelcapacityotherwise.Ifsomeusersdemandlessthantheirfairshare,theremainderissplitevenlyamongtheothers.Inourexample,supposeusers1-3areallactive.Iftheysharethechannel'scapacityequally,eachgetsaonethirdshare.However,thisismoreofthechannelthanuser3actuallywants(d3=0:2).Thisleaves0:4availableforusers1and2.Ingeneralthisfairsharecanbecalculatedbyawaterllingstylealgorithm,whichisessentiallytheroleplayedbythemaximumin(5),whiletheminimumensuresthatnousertakesmorethanhedesires.Thisformulaisanapproximationinseveralways.ItassumesthatTDMAdoesnotresultinanylossofcapacityandtheimplementationisperfectlyfair(atleastinexpectation),whichmaynotbetrueinprac-tice.Further,thefractionmyneighboractuallyusesmaydependonhisneighbors,andtheirneighbors,andultimatelyontheentiregraph,soourcomputa-tionactuallygivesalowerbound(ifdesiredTDMAcouldenforcethislowerboundallocationbyleavinggapsintheschedule).Wechoosethisformulabecauseitisrelativelysimple,butourresultsarenottiedtoanyparticularmodelofaMACaslongaswecancalculatethevalueofshareforthemodelofinterest.WediscussthisfurtherinSection4.5.IncompletinganexpressionforEA[SijF;t],weadopti(A;c)todenotethesetofneighborsofionconictgraphGthat,inallocationA,areallocatedchannelc.Inparticular,i(A)denotesthesetofneigh-borsallocatedthesamechannelasi.Theprobabilitythataparticularset,N0i(A)isactiveinanyepochis,activei(N0;t)=0@Yj2N0aj1A0@Y`2i(A)�N0(1�a`)1A(6)Inourexample,theprobabilitythatanyparticularsubsetofusers1-3isactiveis0:125.Fromthis,auser'sexpectedshareofthechannel,giventhattheuserisactiveandthechannelisfree(wheretheexpectationiscomputedwithrespecttorandomactivationpatternsofinterferingneighbors)isgivenby,EA[SijF;t]=8�&#x]TJ ;� -1;.93; Td;&#x [00;:0ifPri(FjA;t)=01ifxi=1;ando.w.PN0i(A)activei(N0;t)sharei(N0;t)(7)Thetwospecialcasescoverexclusive-useusers(whoalwaysreceivetheirfulldemandwhenactive,conditionedonthechannelbeingotherwisefree),andusersforwhomthechannelisneverfree(forwhomwearbitrarilydeneittobe0,becausethevalueinthiscaseturnsouttobeirrelevant).Ingeneral,computingEA[SijF;t]requirestimeex-ponentialinthenumberofneighborsi(A)withwhichisharesachannel.Inmakingthispractical,sharingcanbelimitedtosomevaluernneighbors,andthecalculationcanbecompletedintimethatscalesasO(2r).Alternatively,itmayturnoutthatrisalreadysmallduetothenatureoftheconictgraph.Indeed,inourexperimentsusingpracticalmodelsofsignalpropagationwedidnotneedtoimposesuchalimitationevenwithhundredsofusersparticipatingintheauction.Weconcludethissectionwithafewremarksabouthowtheaianddiaffectauser'sexpectedvalue.Thevaluationviisinterpretedasthevalueperactiveepoch,soaiiseffectivelyjustamultiplierontheentirevaluationtoconvertittoaperepochvaluation.Thus,insomesensewearereallyaskingtheusertoreportaperepochvaluationinafactoredform,whereonehalfofthefactorcanbeveried,similartothewayonlineadvertisingauctionscanbeframedintermsofper-clickorper-impressionbids.Foranyxedallocation,increasingdimakesauser(weakly)lesshappyaboutsharingachannel.Inparticular,therealwaysexistssomedibelowwhichtheuserisperfectlyhappytosharesincehewillgetasmuchofthechannelashedesiresregardless.Abovethis,hewillbecomeprogressively(strictly)lesshappy,althoughhiseffectisnon-linearbecauseinourmodeluserscareaboutthefractionoftheirdemandsatisedratherthantheabsoluteamount.Againhowever,wecouldinsteaduseafactoredrepresentationandsolicitbidsthatareperunitbandwidthperepoch,whichwouldmakedijustanupperlimitontheamountofbandwidthobtained.4AUCTIONALGORITHMTurningtothedesignofSATYA,weassumethattheonlycomponentofauser'stypethatcanbemisreportedisvi,theper-epochvaluewhenactive,andwhenachievingtherequiredshareofthechannel(andwithexclusive-useiftheusercannotshare).4Itisreasonablethatmostoftheothercharacteristics,such4.Thismakestheauctionanattributeauction,where,inadditiontothebid,theauctioneerknowssomeadditionalcharacteristicsabouteachbidder[6]. 8IEEETRANSACTIONSONMOBILECOMPUTINGOnceusersareassignedtobucketstheyareas-signedchannelsgreedily,indescendingorderofbuck-ets.Theorderofassignmentacrossuserswithinthesamebucketisdeterminedrandomly.LetKidenotethebucketassociatedwithuseri.Achannelcisconsideredtobeavailabletoallocateuseriatsomestepinthealgorithm,andgiventheintermediateallocationA,if,thechannelcisinCi;assigningiwouldnotcauseanexternalitytoaneighborfromahigherbucket:forallj2Ni,withKj�Ki,X`2fj(A;c)[figgd`1(9)and,thecombineddemandsofiandtheneighborsififromhigherbucketsassignedtocarelessthan1:di+Xj2i(A;c);Kj�Kidj1(10)Werefertothesecondconditionasrequiringthatthedemandsofeachneighborofuserifromahigherbucketbesatised.Thethirdconditionrequiresthatthedemandofuseriissatised.Thisdoesnotpre-cludeallocationswheresomeuserhasE[SijF;t]di.Itsimplyrequiresthat,insuchcases,theuserissharingwithothersintheuser'sownbucket.Supposeiisthenextusertobeconsideredforallocation.SATYAwillidentifythechannelforwhichassigningitothechannelhasthemaximummarginaleffectonthetotalvalueofallcurrentlyallocatedusersalongwithuseriitself.Todoso,foreverychannelcthatisavailabletotheuser,andincluding?(andthusnotallocatinganyspectrumtotheuser),SATYAestimatestheexpectedvaluetosomeuserjafterassigningitocasej(A;b)=(Kj)Prj(FjA;b)EA[SjjF;b] dj�aj
pj(1�Prj(FjA;b))(11)Thisestimatediffersfromtheuser'sactualbidbyassumingthateachuserinagivenbucketsharesthesamevalue.Thisisimportantforachievingmono-tonicity,becauseweneedtoensurethedecisionforauserdependsonthebucketassociatedwithauser'sbidvalueandnotinmoredetailonauser'svalue.Giventhis,useriisassignedtothechannelthatmaximizesthesumoftheexpectedbidvaluesofeachuseralreadyallocatedandincludingitsownvalue,andwithoutleavinganyuserwithanegativeexpectedvalue.Theoptimalgreedydecisionmightallocate?touseri,andthusnospectrum.Intheeventofatie,theuserisassignedtothelowestnumberedamongthetiedchannels(includingpreferring?,allelseequal).Afterallusersinabucketareassignedchannels,thereisanironingstepinwhichmonotonicityoftheallocationisveried,andtheallocationperturbedifthisfails.Recallthatmonotonicityviolationsoccurwhenthegreedyallocationmakesa“bad”decisionfortheuserandwouldmakeabetteronehadtheuserbeenconsideredlater.Bucketingpreventsusersfrombeingabletomovethemselveslaterwhilestayinginthesamebucket,buttheycouldstilllowertheirbidenoughtodropintothenextbucket.Toruleoutthispossibility,theironingprocedurere-runstheal-locationprocedureforeachuserwiththeuserplacedinsteadinthenextlowerbucket.Ifthiscounterfactualshowsthatthenalallocationwouldbebetterfortheuser,thenthereisapotentialmonotonicityviolation,andtheprovisionalallocationismodiedbychangingtheassignmentsoftheneighborswithwhomtheusersharedachannelto?.Checkingonlythenextbucketissufcientbecauseiftheusercanbeassignedinanylowerbuckethecanbeassignedinthenextbucket. Algorithm1High-levelSATYAAlgorithm Generatearandompermutationofbidders//BucketedAllocationforallBucketskfromhighesttolowestdoforallUsersiinbucketkorderedbydoAssignuseritoavailablechannelthatmaxi-mizes(bucketestimated)socialwelfare.//IroningforallBucketskfromlowesttohighestdoforallBiddersiinbucketkorderedbythatareassignedachannelwherereceivelessthantheydemanddoRerunallocationprocedureforbucketkwith-outallocatingtoi.ifthereisstillachannelavailableforiafterallocatingothersinbucketkthenCancelallocationsofi'sneighborsinbucketkassignedtothesamechannelinreverseorderofuntilireceiveshisfulldemand.ChargeallbiddersassignedchannelstheirMyersonprice. ThisalgorithmisoutlinedasAlgorithm1,withamoredetailedpresentationavailableinthetechnicalreport[25].Asanillustration,oftheeffectsofbuck-etingandironing,considertheproblematicexamplefromFigure1.IfuserAisoriginallyinalowerbucketthanuserB,Bwillbeassignedrsttochannel1,leavingAtobeassignedtochannel2.IfAraiseshisbidtobeinahigherbucketthanB,hewillbeassignedtochannel1.WhenBisconsideredchannel1willnotbeavailable(Bwouldbecausinganexternalitytoaneighborinahigherbucket),soBwillnotbeassignedachannel.Thusbucketinghasavoidedapotentialviolationofmonotonicity.NowsupposethatAraiseshisbidtobeinthesamebucketasBandthe 10IEEETRANSACTIONSONMOBILECOMPUTINGAnotherareaofexibilityindeningSATYAisintheroleofthepermutation.Ratherthanarandomperturbation,anymethodthatdoesnotdependonuserbidscanbeused.Somenaturalpossibilitiesincludeorderingusersbytheirdegreeintheconictgraph(sothatuserswhointerferelessareallocatedrst),orderingbyacombinationofactivationproba-bilityanddemand(sothatuserswhouselessspec-trumareallocatedrst),consideringexclusive-useuserslastsincetheyimposemuchlargerexternalitiesonthosewithwhomtheyshare,orevenadaptivelyorderingeachbucketbasedonthestateafterprocess-ingpriorbuckets.Weleavefurtherexplorationofthisdirectionforfuturework.4.5SATYA'suseofaMACAsmentionedinSection3.2,weuseasimplemodeltocalculatewhathappenswhenusersshareachannel.Oursimplemodelcanbereplacedbyamoresophis-ticatedmodelfrompriorworkonTDMA[31],[33].ItcanalsobeextendedtoincludepriorworkthathasexploredthecapacityofCSMAbasedwirelessnetworks(e.g.,[27],[28],[36],[37])aslongas,inexpectation,havingmoreneighborsdecreasesauser'sshareofthechannel.Thismodelcanalsobeextendedinotherinterestingways.Forexample,wecouldaddforeachuseriaparameter`i,suchthatifhereceiveslessthanan`ifractionofthechannelitisuseless.Thissimplyrequiresdeningthesharetobe0ifitwouldbelessthan`i.Wecouldalsomodelapplicationsthatrequireareliablechannelwhentheyareactivebyusingaminimumratherthananexpectationin(7).Forimplementationperspective,theprimaryre-quirementforSATYAisforausertostoptransmittingwhenitisanotheruser'sturn(inthecaseofexclusive-useusers).ThisisnotuniquetoSATYAandis,forexample,requiredofdevicesthatusewhitespaces.However,asmallchangeisrequiredtoauser'snetworkstacktoseektotransmitonlywhentheuserwinstheauction(andthereforeisallowedtocontendforachannel).Thiscanbeimplementedanywhereinthesoftwarestack.5EVALUATIONInthissectionwecomparetheperformanceofSATYAtoVERITAS.SinceVERITASdoesnotpermitshar-ing,wemodifyitslightlyandimplementVERITAS-S,whichpermitssharingaslongastherearenoexternalitiesimposed(i.e.sharingispermittedonlywhenthecombineddemandsofusersthatwishtosharedonotexceedthecapacityofthechannel).WealsoimplementGREEDY,aversionofSATYAwithoutbucketingandironingthatprovideshigheroverallef-ciency.GREEDYisneitherstrategyproofnormonotone.Thus,bidsneednotmatchtheirtruevalues.However,tosetashighabaraspossible,weassumetheydoso.Sinceitgetstoactonthesameinformationbut UserType Act.Prob. Value Penalty Demand Exclusive-Continuous 1 [0,1000] 10000 1 Exclusive-Periodic [0.05,0.15] [0,1000] 5000 1 Sharing-High 1 [0,1000] 10000 [0.3,1] Sharing-Low [0,1] [0,1000] 5000 [0.3,1] TABLE1MixofusertypesusedintheevaluationhasfewerconstraintsthanSATYA,GREEDYservesasanupperboundforourexperiments.Parameters:AsshowninTable1,allourexperimentsusefourclassesofusertypesbiddingforspectrum,eachofwhichisoftheformdescribedinSection3.1.Notethat,inthetable,wewehavenormalizedthevaluessothetablereectstherangeofaiviratherthantherangeofvi.Eachclassrepresentsdifferentapplications.Forexample,aTVstationservingalocalcommunityisauserwhowantsexclusiveaccessforalongperiodoftime.Awirelessmicrophoneisanexampleofauserwhowantsexclusiveaccessbutforshortperiodsoftime.Alow-costruralISPisanex-ampleofaSharing-Highuserwhoexpectstoactivelyusethespectrumbutcanpotentiallytoleratesharing,andaregularhomeuserisanexampleofaSharing-Lowuserwhosespectrumaccesspatternvaries.Note,eachclassofusersmayhavedifferenttransmitpowersandcoverageareasthantheothers.SinceourgoalistoevaluatetheefcacyofSATYAinexploitingoppor-tunitiesforsharing,weassign5%ofthetotalusersasexclusive-continuous,15%exclusive-shared,30%Sharing-High,andtheremaining50%Sharing-Low.Withlargerpercentagesofexclusiveusers,thereislittleopportunityforsharingandSATYAiseffectivelyjustVERITAS-Smadelessefcientsincereportsarecoarsenedviabucketing.Methodology:Eachauctionalgorithmtakesasinputaconictgraphfortheusers.Togeneratethisconictgraphinarealisticmanner,weimplementandusethepopularLongley-Rice[2]propagationmodelincon-junctionwithhighresolutionterraininformationfromNASA[1].Thissophisticatedmodelestimatessignalpropagationbetweenanytwopointsontheearth'ssurfacefactoringinterraininformation,curvatureoftheearth,andclimacticconditions.Weusethismodeltopredictthesignalattenuationbetweenusers,andconsequentlytheconictgraph.WeusetheFCC'spubliclyavailableCDBS[13]databasetomodelthetransmitpower,location,andcoverageareaofExclusive-Continuoususers.Note,thatthisinformationaswellasthesignalpropagationpredictionsaresensitivetogeographicareas.Wemodelthepresenceofallothertypesofusersusingpopulationdensityinformation.Usersarescat-teredacrossa25milex25mileurbanareainarandomfashionbyfactoringinpopulationdensityinformation.Sinceeachclassofuserhasadifferentcoveragearea,wedeterminethatapairofnodesconictsifthepropagationmodelpredictssignalre-ceptionhigherthanaspeciedthreshold. 12IEEETRANSACTIONSONMOBILECOMPUTING (a)SocialWelfare (b)SpectrumUtilization (c)SatisfactionFig.4.Effectofvaryingthenumberofusersintheauction(comparedtoVERITAS-S,VERITAS,andGREEDY). (a)AllocatedUsers (b)SocialWelfare (c)AllocatedUsersforSATYAFig.5.Effectofvaryingthenumberofchannelsauctioned(comparedtoVERITAS-S,VERITAS,andGREEDY).tion.TheresultsshowninFigure5demonstratethefollowingtrend:asthenumberofauctionedchannelsincreasesthegapinperformanceamongthealgo-rithmsreduces.Thisissimilartohavingfewerbiddersparticipateintheauction;withmorechannels,thereisareducedneedforsharingandallalgorithmsperformsimilarly.AsFigure5(a)shows,SATYAisstillabletoassignmorebiddersthanotheralgorithmsuntilabout20auctionedchannels.Similarly,inFigure5(b),weseethatSATYAoutperformsVERITASby20-60%insocialwelfareupuntilabout10channels.5WealsovarythenumberofusersandthenumberofchannelssimultaneouslyandtheresultsforSATYAareshowninFigure5(c).Weseethatasthenumberofusersincreases,SATYAtakesadvantageoftheincreasedopportunityforsharingandallocatemoreusers.Hence,themaintakeawayisSATYAprovidessub-stantialbenetswhenthenumberofchannelsmakesspec-trumscarce.5.3MeasuringRevenueWeconsidersocialwelfarethemostimportantmea-sureofperformance:amarketthatndssuccessinthelongrunwillallocateresourcestothosethatndthemostvalue.However,inoursettingrevenuemayalsobeimportanttoprovideanincentiveforcurrentspectrumownerstoparticipateinthesecondarymar-ket.First,wemeasurethetotalrevenueobtainedasa5.Weomitgraphsforspectrumutilizationandsatisfactionforthisandlaterexperimentsforlackofspace;theydemonstrateasimilartrend. Fig.6.Impactofrevenue,asafunctionofnumberofusers.functionofthenumberofusersbiddingforspectrumwithoutreserveprices.WedonotincludeGREEDYinthisanalysisbecauseitisnotstrategyproofanditisnotclearwhatuserswillbidandthuswhattheactualrevenuewouldbe.AsseeninFigure6,therevenueobtainedbySATYAandismuchlowerthanVERITASforsmallernumbersofusers.WeomitVERITAS-Sfromthegureforreadability,butitsperformancealsosuffers.Paradoxically,thisisadirectconsequenceofsharingincreasingefciencybymakingiteasiertoaccommodateusers:iftheywouldbeallocatedwithabidofzerotheydonothavetopayanythinginastrategyproofauction.Toimproverevenue,weinstitutereserveprices.WhileMyerson'sapproachinprincipleallowsustocomputetheoptimalreserveprice[29],oursituationissufcientlycomplicatedthatwesimplyempiri-callydetermineareasonableuniformreserveprice.VERITASexploredasimilaropportunitytoincrease KASH,MURTY,ANDPARKES:ENABLINGSPECTRUMSHARINGINSECONDARYMARKETAUCTIONS13 (a)Revenue (b)AllocatedUsers (c)SocialWelfareFig.7.Effectofreservepriceswith300usersonrevenue,usersallocatedspectrum,andsocialwelfare.revenuebylimitingthenumberofchannelsavailable.TheresultsfromasimulationthatvariesthereservepricesisshowninFigure7for300biddingusers.Figure7(a)showsthatwithareservepriceof0(i.e.noreserveprice)VERITASperformsbetterthanSATYAandVERITAS-Sintermsofrevenue.Asthereservepricebeginstoincrease,therevenuederivedfromallthreeauctionsincreases.However,ataroundapricearound700(dependingonthealgorithm),revenuebeginstodecrease.AsseeninFigure7(b),thisisbecausesignicantlyfewerusersareallocatedbytheauctionandsocialwelfaredecreases(Figure7(c)).Basedontheseresults,weuseareservepriceof400andrepeattheexperimenttomeasurerevenuebyvaryingthenumberofbidders.Weusedaxedreservepriceforconsistency;inpracticeitcouldde-pendonthenumberofusersandbeindividualizedforeachuser.AsFigure6shows,thisincreasesrev-enuefortheauctioneersignicantlyforallalgorithms.Theincreaseismostpronouncedwith50users(notshownbecausetheimprovementissolarge)whererevenuegoesfromessentiallyzerotoapproximatelytenthousand.SATYA,whichwithoutareservepricelostrevenuebybeingtooefcientinallocatingusers,benetsslightlymorethanVERITAS.Withalargenumberofusers,thereservepriceisessentiallyir-relevantbecauseoftheamountofcompetition;with550usersthegainisbelow12%.5.4SATYA'sPerformancewithMultipleChannelsSATYAisalsocapableofallowinguserstobidformultiplechannelsintheauction.Toillustratethis,werananexperimentwherewevariedthenumberofchannelsthateachuserbidsforaswellasthenumberofusersintheauction.Todoso,weinterpreteduserswithdi=1asrequiringsomexednumberofchannels(asopposedto1fullchannelinpreviousexperiments).Userswithlowervaluesofdirequiredproportionallyfewerchannels.Figure8(a)comparestwodifferentmodesofchannelallocationproposedin[34],strict:whenausereithergetsthenumberofchannelsitrequestsforornothing,andpartial:ausercangetfewerthanrequestedchannels.Thetotalnumberofchannelsauctionedwasxedto26,whileuserswithdi=1required5channels.Partialallocationsresultinslightlymoreallocatedusersthanstrict,whichiswhatwewouldexpectsincestrictallocationsareconstraintsthatarehardertosatisfy.Figure8(b)showsthatincreasingthethenumberofchannelsdemandedbyusers(thelabelsonlinesreectthedemandwithdi=1)reducesthenumberofwinnersaswouldbeexpected. 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PLACEPHOTOHERE IanKashreceivedtheBSdegreeincom-putersciencefromCarnegieMellonUniver-sityin2004,andtheMSandPhDdegreesincomputersciencefromCornellUniver-sityin2007and2010respectively.HeisaresearcherintheNetworks,Economics,andAlgorithmsgroupatMicrosoftResearchCambridge. PLACEPHOTOHERE RohanMurtyreceivedtheBSdegreeincomputersciencefromCornellUniversityin2005,andthePhDdegreeincomputersci-encefromHarvardUniversityin2011.HeisaJuniorFellowintheSocietyofFellowsatHarvardUniversity. PLACEPHOTOHERE DavidParkesreceivedtheMEngdegreeinengineeringandcomputingsciencefromtheUniversityofOxfordin1995andthePhDdegreeincomputerandinformationsciencefromtheUniversityofPennsylvaniain2001.HeistheGordonMcKayProfessorofCom-puterScienceattheSchoolofEngineeringandAppliedSciences,HarvardUniversity.