B Ma DahMing Chiu John CS Lui Vishal Misra Dan Rubenstein tbmaeecolumbiaedu dmchiuiecuhkeduhk csluicsecuhkeduhk misracscolumbiaedu danreecolumbiaedu Abstract Internet service providers ISPs must interconnect to provide global Internet connectivity to ID: 86721
Download Pdf The PPT/PDF document "Interconnecting Eyeballs to Content A Sh..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.
2complexity),allowingustospecicallyfocusonhowtherolesofthecontentandeyeballISPs,andthevariousrelationshipstheyhavewiththeirrespectivecustomersimpacttheirprotability.Ourresultsare:Weobtainclosed-formShapleyrevenuesforallISPsandgiveabilateralpaymentimplementationintermsofthepercentageofISPcustomerrevenues.Weshowthatwhencustomersareinelastic,theShapleyrevenueisseparable:eacheyeballISP'srevenueisproportionaltoitscustomersize,andisindependentofothereyeballISPs'sizes.EacheyeballISPcontrolsd=(d+1)fractionofthegeneratedrevenue,wheredisthenumberofconnectedcontentISPs.WequantifythemarginallossforaneyeballISPwithinelasticcustomerdemand.WeshowthatthepercentageofrevenuelossforaneyeballISPisinverselyproportionaltothesquareofthenumberofcontentISPsitcurrentlyconnectsto.Weshowthatwhencustomersareelastic,contentISPsandeyeballISPshavethesameroleinrevenuedistribution.Underacompletepartitetopology,therevenueratioofbothgroupsofISPsequalstheinverseoftheratioofnumberofISPsineachgroup.WebelievethatthebilateralpaymentsolutiongivesaguidelineforpaidpeeringagreementsforISPstonegotiatebasedonthecharacteristicsofcustomerdemand,contentdistributionandISPtopologies.II.SHAPLEYVALUEANDPROPERTIESHere,webrieyintroducetheconceptofShapleyvalueanditsuseunderourISPrevenuedistributioncontext.Wefollowthenotationsin[5].WeconsideranetworksystemcomprisedofasetofISPsdenotedasN.N=jNjdenotesthenumberofISPsinthenetwork.WecallanynonemptysubsetSNacoalitionoftheISPs.Eachcoalitioncanbethoughtofasasub-networkthatmightbeabletoprovidepartialservicestotheircustomers.Thenetworksystemisdenedas(N;v;E).EdenotesthesetofdirectedlinksbetweentheISPs.ThegraphG=(N;E)denestheISPtopologyofthenetwork.WedenoteGSasthesubgraphofGinducedbyS,denedbyGS=(S;ES),whereES=f(i;j)2E:i;j2Sg.GSistheISPtopologyformedbythecoalitionS.Wedenotevastheworthfunction,whichmeasuresthemonetarypaymentsproducedbythesub-networksformedbyallcoalitions.Inotherwords,foranycoalitionS,v(S)denestherevenuegeneratedbythesub-networkformedbythesetofISPsS.Inparticular,vmeasurestheaggregateend-paymentseachISPinacoalitionobtainsinaspecictopologyasv(S;ES)=Xi2SPi(S;ES);(1)wherePi(S;ES)istheend-paymentcollectedbyISPiinacoalitiontopologyGS=(S;ES).Toavoidtheredundancyinthenotation,wedropESanddenotev(S)astheworthfunctionforanyxedtopology.Throughtheworthfunctionv,wecanmeasurethecontributionofanISPtoagroupofISPsasthefollowing.Denition1:ThemarginalcontributionofISPitoacoalitionSNnfigisdenedasi(v;S)=v(S[fig)�v(S).ProposedbyLloydShapley[6],[7],theShapleyvalueservesasanappropriatemechanismforISPstosharerevenues.Denition2:TheShapleyvalue'isdenedby'i(N;v)=1 N!X2i(v;S(;i))8i2N;(2)whereisthesetofallN!orderingsofNandS(;i)isthesetofplayersprecedingiintheordering.TheShapleyvalueofanISPcanbeinterpretedastheexpectedmarginalcontributioni(v;S)whereSisthesetofISPsprecedingiinauniformlydistributedrandomordering.TheShapleyvaluedependsonlyonthevaluesfv(S):SNg.TheShapleyvaluesatisesabunchofdesirableefciencyandfairnessproperties[5].Weshowedin[5]thattheShapleyvaluemechanismalsoinducesglobalNashequilibrathataregloballyoptimalforroutingandinterconnecting.Inourpriorwork,weassumedanoraclethatperformedglobalrevenue(re)allocationbasedontheShapleyvalue.Thatassumptionhoweverhasclearpracticalandregulatorylimitations.Inthispaper,wefocusonISPinterconnectingandrevenuedistributionamongstpeers.Weassumetheroutingcostsarenegligiblecomparedtotherevenueobtainedfromprovidingservices.Nevertheless,ourframeworkcanalwaysbeextendedtoincludeanorthoganaldirectionofroutingdecisionsandcosts.III.THEISPMODELWefollowthecategorizationofISPsbyFaratinetal.[1]astwobasictypes[1]:contentISPsandeyeballISPs.ThesetofISPsisdenedasN=C[B,whereC=fC1;;CjCjgdenotesthesetofcontentISPsandB=fB1;;BjBjgdenotesthesetofeyeballISPs.WedenoteQasthesetofcontentsprovidedbythesetofcontentISPC.EachcontentISPCiprovidesasubsetofthecontentsQiQ.Foreachcontentq2Q,wedeneapopularityfactorkqforthatcontent,whichisusedtoquantifytherelativeamountofdemandthatend-usersaregoingtodownloadthiscontent.IfonlyonecontentisprovidedbyallcontentISPs,wedenotethepopularityfactorsimplyask.Weassumeasizeofxoftotalend-customerpopulation 5Theorem1showsthatundertheinelasticdemand,theShapleyvaluesoftheISPscanbedecomposedlinearlyasafunctionofcustomersizesfxjg.EacheyeballISPBj'sShapleyvalueisproportionaltoitsowncustomersizexj,andisindependentofthecustomersizesofothereyeballISPs.Further,thisShapleyvalue'Bjcanbedecomposedastwoparts:afractiondBj=(dBj+1)oftheeyeball-siderevenue xjandfractionsdqBj=(dqBj+1)ofthecontent-siderevenuekqxjgeneratedbyeachcontentq.Consequently,contentISPscollecttheremainingrevenue.AllcontentISPsthatconnecttoBjevenlyshare1=(dqBj+1)ofeyeball-siderevenue xj.The1=(dqBj+1)ofthecontent-siderevenuekqxjisalsoevenlysharedbythesubsetofcontentISPswhichprovidecontentq.Wedenetij;i2C;j2BasabilateralpaymentfromISPitoISPj.Thefollowingcorollarygivestheclosed-formbilateralpaymentsthatimplementtheShapleyvaluerevenuedistribution.Corollary1(BilateralPayments):ThebilateralpaymentsbetweenanylinkedpairofISPs,i.e.(Ci;Bj)2E,thatimplementtheShapleyvaluearethefollowing:tBjCi= xj (dBj+1)dBj=PBj (dBj+1)dBj;tCiBj=Xq2Qikqxj dqBj+1=Xq2QidqBj dqBj+1PBj;qCi:Corollary1implementstheShapleyvaluerevenueforISPsusingbilateralpayments.Eachpaymentcanbeexpressedasfractionofthedirectpayment(PCiforacontentISPandPBjforaneyeballISP)ofanISP.EacheyeballISPBjtransfers1=(dBj+1)ofitsdirectpaymentPBjtoconnectedcontentISPs.PBj;qCidenotesthefractionofdirectpaymentPCigeneratedbyBjrequestingcontentq.Therefore,eachcontentISPCi,however,onlykeeps1=(dqBj+1)ofitsdirectpaymentPBj;qCiforeverycontentqprovidedtoBj.Corollary2(MarginalRevenue):SupposeallcontentISPsprovideasetQofcontents.LetK=Pq2Qkq.Consideranyde-peeringofapairofISPs,i.e.removing(Ci;Bj)2EfromEtoformE0.ThemarginalrevenuesoftheISPs,denedasi='i(E0)�'i(E),arethefollowing:'Bj='Ci=�( +K)xj dBj(dBj+1)=�1 d2Bj'Bj(E);'Cl=2( +K)xj (d2Bj�1)dBj8Cl:(Cl;Bj)2E0;'Cl=08Cl:(Cl;Bj)=2E;'Bl=08Bl6=Bj:Corollary2showstherevenueeffectonthepairofde-peeringISPsaswellasotherISPs.Themarginalrevenuelossofade-peeringeyeballISPBjisinverselyproportionaltothesquareofdBj,whichisthedegreeofconnectivitytothecontentISPs.Forexample,ifBjonlyconnectstoonecontentISP,themarginalrevenueis�'Bj(E),whichmeansthatwhenthelinkisdisconnected,therevenuelossis100%oforiginalShapleyrevenue.Similarly,itloses1=n2ofitShapleyrevenueifitdisconnectsoneofitsnlinks.Thisresultimpliesthatwhenaneyeball,controllinginelasticcustomerdemand,connectstomorecontentISPs,itsmarginallossbydisconnectinganyofthecontentISPsdecreasesinverselyproportionaltothedegreeofconnectivity.V.ELASTICCUSTOMERDEMANDInthissection,weconsideranelasticcustomerdemandmodel.Weassumethatthetotalpopulationsizeofend-customerisx.ConsideranycoalitionSN.LetS=CS[BSforsomeCSCandBSB.WedenethecompletebipartitegraphofthecoalitionSas~ES=f(Ci;Bj):Ci2CS;Bj2BSg.Wefurtherassumethatifthetopologyofsystemis~ESforsomeSN,thecustomersizeofaneyeballISPBjisthefollowing:xj=x jBSjifBj2BS,0otherwise.ThiselasticdemandassumptionimpliesthatwhensomeeyeballISPsleavethesystem,theircustomersarere-distributedevenlytotheremainingeyeballISPs.ItmodelsaperfectelasticdemandwhereuserscanchooseanyoftheeyeballISPswithequalprobability.Wedonotputanyassumptiononthecustomerre-distributionwheneyeballISPsdisconnectindividuallinkstocontentISPs. 7 Fig.4.ShapleyrevenuedistributionbetweeneyeballandcontentISPs. Fig.5.Shapleyrevenuedistributionforeacheyeball/contentISPwithinelastic/elasticdemands.Figure5comparesrevenuesacrosselasticandinelasticsettings.ThenumberofeyeballISPsisxedat5,andthenumberofcontentISPsisvariedonthex-axis.IndividualISPrevenuesforthetwocases(elasticandinelasticcustomers)areplottedalongthey-axisforboththecontentISPandtheeyeballISP.Theguresupportsseveralinterestingobservations:WhenjCSj=jBSj,thesymmetrydesribedaboveresultsincontentaneyeballISPsevenlysplittingrevenue.Thissituationholdsforboththecaseofelasticandinelasticcustomers.WhenjCSjjBSj,contentISPrevenuesarelargerwheneyeballcustomersareelasticincomparisontowhencustomersareinelastic.ThereverseistrueforeyeballISPrevenues.WhenjCSj&#x]TJ/;༔ ; .96;& T; 10;&#x.516;&#x 0 T; [0;jBSj,thesituationreverses,withcontentISPrevenuesbeinglargerwhencustomersareinelasticthanwhenelastic.Theaboveobservationshavesomeinterestingimplications.Inanenvironmentwherethecontentmarketisdominatedbyasmallsetofplayers,andeyeballISPsarenumerous,eyeballsbenetfrominelasticity,i.e.,theyshoulddiscouragecustomersfrombeingabletomoveeasilyfromoneeyeballtoanother,suggestingthateyeballISPsarebetteroffmonopolizingcustomersinregions.Incontrast,ifthecontentmarkethasmanymoreISPsthantheeyeballmarket,eyeballISPscanincreasemarketsharebyfacilitatingcustomermovementbetweenthem,e.g.,ISPssharecoverageofregions.VII.CONCLUSIONInthispaper,weexploreISPpeeringsettlementsinthecontextofsharingrevenueamongeyeballandcontentISPs.OursolutionisbasedontheShapleyvalueconceptwhichprovidesvariousfairnessandincentivestotheISPs.OurresultsshowthattheShapleyvaluerevenuedistributioncanbeimplementedbybilateralpaymentbetweenanypairofeyeballandcontentISPs.Ourresultsrevealthat1)underinelasticcustomerdemand,themarginalrevenuelossofaneyeballISPfromde-peeringtoacontentISPisinverselyproportionaltothesquareofnumberofconnectedcontentISPs,and2)underinelasticcustomerdemandwithcompletebipartitetopology,therevenueratiobetweenthegroupsofeyeballandcontentISPsisinversetoratioofnumberofISPsineachgroup.Comparingwithrevenueunderinelasticandelasticcustomerdemand,weobservetheconditionswhereeyeballISPscanbetteroffbymonopolizingsmallregionsorsharingcoverageofregions.Inpractice,thisbilateralimplementationoftheShapleyvaluegivesaguidelineforISPstonegotiatepartialpeeringagreementsandforregulatoryinstitutionstoimposepricingregulations. 9BythebalancedcontributionpropertyoftheShapleyvalue,thefollowequationholdsforallm;n=1;2;.'B(m;n)�'B(m�1;n)='C(m;n)�'C(m;n�1):(11)Wewanttoprove('B(jCSj;jBSj)=jCSj jBSj(jCSj+jBSj)( +k)x;'C(jCSj;jBSj)=jBSj jCSj(jCSj+jBSj)( +k)x:FortheboundaryconditionjCSj=jBSj=1,'B(1;1)='C(1;1)=1 2( +k)x,whichsatisestheaboveequations.Weuseproofbyinduction.Supposetheaboveequationssatisfyfor(jCSj;jBSj)=(m�1;n)and(jCSj;jBSj)=(m;n�1).Thebalancedpropertyequationbecomes:'B(m;n)�(m�1)( +k)x n(m�1+n)='C(m;n)�(n�1)( +k)x m(m+n�1):'B(m;n)�'C(m;n)=(m�n)( +k)x mn:PuttingtheaboveequationtogetherwithEquation10,weobtain('B(m;n)=m n(m+n)( +k)x;'C(m;n)=n m(m+n)( +k)x:Finally,wecanextendtheaboveresultsformultiplecontentsusingtheadditivitypropertyoftheShapleyvaluetoreachTheorem2.