modelling user behaviour in networked gameskrasic/cpsc538a/papers/p212... · 2003-12-22 · have...
TRANSCRIPT
Modelling userbehaviour in networkedgames
TristanHendersonandSaleemBhattiDepartmentof ComputerScience
UniversityCollegeLondonGowerStreet
LondonWC1E6BTUK�
T.Henderson,S.Bhatti� @cs.ucl.ac.uk
June25,2001
Abstract
In thispaperweattemptto gainanunderstandingof thebehaviour of usersin amultipoint,interactivecommunicationscenario.In particular, we wish to understandthe dynamicsof userparticipationat asessionlevel. We presentwide-areasession-level tracesof the popularmultiplayernetworked gamesQuake andHalf-Life. Thesetracesweregatheredby regularly polling 2256gameservers locatedallover the Internet,and queryingthe numberof playerspresentat eachserver and how long they hadbeenplaying. We analysethreespecificfeaturesof the data: the numberof playersin a game,theinterarrival times betweenplayersand the length of a player’s session. We find significant time-of-day andnetwork externality effects in the numberof players. Playerdurationtimesfit an exponentialdistribution,while interarrival timesfit a heavy-taileddistribution. The implicationsof our findingsarediscussedin thecontext of provisioningandcharging for network quality of servicefor multipoint andmulticasttransmission.Thiswork is ongoing.
1 Introduction
In spiteof beinganactiveresearchareafor overa decade,multicasthasyet to seelarge-scaledeployment.This maybedueto a numberof factors,suchasthelack of compellingmulticastapplications,or thelackof a methodfor multicastserviceprovidersto chargefor a multicastservice[10]. We arein theprocessofdevelopingapricingschemewhichallowsefficientandpredictablechargingfor multicast(initial detailsofthisschemearedescribedin [15]). Oneproblemwith attemptingto chargefor multiple-sourceapplications,however, is the needfor predictableprices. If userssharethe costof a multiusertransmission,and thenumberof userschangesas usersjoin and leave the session,the price paid per userwill also change.We thereforeneedto understandhow usersbehave in multiuserscenariosif we are to engineerpricingschemesthat will provide stableand predictableprices. Models for userbehaviour are also useful indesigningpricing schemesfor maximisingobjectivessuchasaggregateutility or network utilisation,andfor understandingandproviding for network Quality of Service(QoS).
In a somewhat“chickenandegg” situation,the limited deploymentof multicastalsomeansthat thereare few sourcesof datafrom which a model for userbehaviour can be determined. A featureof ourintendedpricing schemeis thatit shouldbeindependentof theunderlyingnetwork protocols.Thus,thereis no reasonwhy a modelfor multipoint userbehaviour needbe determinedfrom IP multicastsessions.Fromanend-userviewpoint, thereis no functionaldifferencebetweenanIP multicastsessionandseveralunicaststreams,andsouserbehaviour shouldbesimilar in bothof thesemultipoint situations.Theremaybea differencein costandthis maybeusedasanincentive for theuseof multicast.
With theremoval of theabsoluterequirementfor nativeIP multicastsessionsin orderto providemulti-point communications,theproblemof creatinga modelfor multipoint behaviour becomesmoretractable.Therearemany existing,andpopular, multipoint applicationsthatuseunicastrouting,for example,online
1
chatapplicationssuchasInternetRelayChat(IRC), or multiusernetworked gamessuchasQuake. Wehave chosento examinethelatter to determineuserbehaviour, andthusto determinetherequirementsforpricing this behaviour andprovisioningnetwork resources.
This paperis structuredasfollows. We discussour motivation for choosinggamesasan applicationandnoteprevious work in Section2. Section3 describesthe methodologyusedfor gatheringdataandsummarisesour results. Sections4, 5 and6 analysethreeparticularaspectsof the data,namelysessionmembership,sessiondurationanduserinterarrival times respectively. Finally, Section7 concludesthepaperanddiscussespossibilitiesfor futureresearch.
2 Motivation
Multiplayer networkedgamesarecontributing to an increasinglylargeproportionof network traffic [22].Suchnetwork usageis likely to increasefurthernow thatconsolessuchastheSegaDreamcastandSonyPlaystation2 featureEthernetandmodemconnections.Gamesplayersarealreadywilling to pay extrato get an improvementin their playing experience,asevidencedby specialistgaminghardwaresuchasjoysticks,mice,mousepadsandevenfurniture.Gamepublishershaveproposedchargingplayersper-gamevia network delivery, ratherthanthecurrentpracticeof charging a one-off feefor thesoftware[25], or bycharging a fee pergamewith the opportunityfor playersto win money or prizes[29]. More interesting,from a networking point of view, is the existenceof modemsmarketedasbeingspeciallyoptimisedforgames[1], andsoftwaredesignedto determinenetwork characteristicsof potentialgamesserverssuchasdelay[13]. Thesedevelopmentsindicatethatgamesplayersareinterestedin network QoS,andwould bewilling to payfor theability to improveit.
The gamesthat we study hereareof the type commonlyreferredto asFPS(First PersonShooter)games.Playersconnectto a centralserverusingunicastUDP (or occasionallyTCP)flows. Themaximumnumberof playersthat canconnectto a server is setarbitrarily by the server administrator, accordingtotheamountof network traffic andCPUtime they wish thegameserver to consume(for thegamesstudiedhere,this figure is typically set to 16 or 32 players). Players’actionsaretransmittedfirst to the centralserver, which calculatesandmaintainsthe overall stateof the gameandthentransmitsthis statebacktotheplayers.Thegeneralobjectiveof mostof thesegamesis to explorea commonvirtual world andkill asmany of theotherplayersaspossible.
2.1 Previous work
Multicast sessionson the MBone arestudiedby Almeroth andAmmar [2]; thesesessionsareall single-sourceandperhapsdo not reflectthedifferentdynamicsof multiple-sourceapplications.Thereis a longhistoryof network andInternettraffic analysis(see[24] for asurvey). Themajorityof this,however, looksat packet-level andnetwork-level traces. In particular, Bangunet al. [3] andBorella [5] both study thetraffic patternsof multiplayergames,but donotexaminesession-level userdynamics,andlimit thestudiesto local areanetwork traffic only. Althoughtheremaybeinterestingrelationshipsbetweenthedataat thepacketandsessionlevels,for instancein termsof self-similarity, wedonotconsiderthesein thisstudy, butleave themfor possiblefuturework.
3 Methodology
AlmerothandAmmar [2] show that themonitoringof IP multicastsessionsis possiblethroughjoining asessionandthenwatchingothersessionmembersjoin andleave. This is impracticalfor networkedgames,however, sinceto join a gameimpliesparticipation.As mostpeopleareonly capableof playingonegameatatime,andonly for acertainnumberof hoursaday, thislimits thescopeof any datacollection.Althoughit is possibleto simulatea userthrougha scriptor program,such“bots” arefrowneduponby many gameserveroperatorsandgenerallyleadto theuserin questionbeingbarredfrom thatserver. Furthermore,thereis adataintegrity problemin thatuserbehaviour mightdependon thenumberof playersin agame,andsoby joining agameto monitorit, we mightaffect theresults.
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Somegameserversoffer a queryingmechanism,wherebyspecificvariablesaboutgamestatuscanberetrieved. Sincejoining and continuouslymonitoring gamesseemedimpractical,polling and queryinggamesservers at regular intervals was determinedto be the next bestoption. By polling servers anddeterminingthenumberof playersateachpoll, anapproximationof userbehaviour canbeobtained.Manynetworkedgamesalsoallow thequeryingof suchvariablesasplayers’nicknamesandtheamountof timethatthey havebeenplaying,andsothedurationof eachusers’sessioncanalsobeestimated.Theaccuracyof thismethoddependson thefrequency of polls. If thepollsaretoofarapart,thenany userswhojoin andleave betweenpolls will bemissed.If thepolls aretoo frequent,theamountof network traffic might haveaneffecton theserversandperhapsaffectuserbehaviour.
Datawerecollectedusing the QStattool [27], which is a programdesignedto display the statusofgamesservers,andwhich supportsa largenumberof onlinemultiplayergames.Of thesegames,thegameHalf-Life [14] wasdeterminedto bethemostpopulargame,andwasalsooneof thegameswhichsupportsthereportingof a player’sconnectiontime,andsoit waschosento concentrateon playersof this game.
A list of 2193 IP address/portpairs1 of machinesrunning the Half-Life daemonwasobtainedfroma “masterserver” at half-life.west.won.net. This list is composedfrom submissionsby serveradministratorsand/orautomaticregistrationby servers(dependingon the game). This list may alsobequeriedby usersthroughtheapplicationitself, or throughtheuseof someof theaforementionedprogramsfor determiningtheclosestor quickest-respondinggameserver.
ServerswerepolledusingQStatat regular intervals (Figure1). At eachpoll, the numberof players,their chosennicknamesandthe numberof secondsthat eachplayerhadbeenconnectedwereretrieved(exampleoutputfrom QStatis shown in Figure2). If a responsewasnot received from a server, groupmembershipwasassumedto bethesameasat theprevioussuccessfulpoll. Sincepolling tookplaceat theapplicationlevel, we could not detectsucheventsasunsuccessfuljoin attempts,asthesedo not registerin thegame.We werealsolimited in thatpolling takesplacefrom a centralmachineat UCL, andsoanynetwork failuresthatexistedsolelybetweenUCL andthegameservers(but not betweenthegameserverandtheplayers)wouldaffectour results.
SERVERGAMEPOLLING
USER USER
USERUSER
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QUERY (2 UDP pkts) −>
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MACHINE
Figure1: Datagatheringsetup
Servers Game Frequency DurationO-I 2193 Half-Life 30min 1 weekO-II 35 Half-Life 5min 3 daysO-III 22 Quake 5min 1 weekO-IV 3 Half-Life 5min 2 monthsO-V 3 QuakeIII Arena 5min 2 months
Table1: Observations
1It is not uncommonfor a singlemachineto run several serverson differentports;of our list of 2193servers,therewere1725uniqueIP addresses.
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NAME: Merlin TIME: 5710NAME: [F.u.T]The_LAW TIME: 5728NAME: MagNETo [FH] TIME: 2176NAME: TomiN TIME: 2409NAME: [DEM] Guybrush T. TIME: 8575NAME: [.HoF.]Ben Kenobi TIME: 1177NAME: [Thug]Tosh TIME: 142NAME: TDMT_Silvan TIME: 1540NAME: Gulzak TIME: 874NAME: [DBK]HannibalTC TIME: 954NAME: [STANDARD] Kill Demon TIME: 1085NAME: -=Phoenix=- TIME: 5593
Figure2: ExampleQStatoutput
Severalsetsof observationsweretaken; thedifferencesbetweenthese,andthe labelsthatareusedinthis paperto referto them,areshown in Table1. Thefirst setO-I usedthemasterlist of Half-Life servers.From this, the 35 most popularservers were selectedfor more detailedobservation over one weekendin O-II.
SetO-III used22Quakeservers,theaddressesof whichwerealsoobtainedby queryingamasterserver.Quake is an older game,introducedin 1996,which is why the numberof serversis so muchlower thanHalf-Life, whichfirst wentonsalein 1998.Quake, however, is oneof thefew gamesto allow thequeryingof players’IP addresses,which maybeusefulfor determiningthenetwork topologiesandspatialanalysisof games.Thesourcecodefor thegameis freelyavailable,sothissetof observationsmayproveusefulforfuturework.
Thelastpair of observations,O-IV andO-V, comefrom two setsof serverswhich MicrosoftResearchhavebeenrunningat their sitein Cambridge,UK. Usingapublic list of serversprovedto havedifficulties,sincesomeof the IP addresseson the list weredynamicallyallocated(for instance,usersrunninggameserverson dial-up machines).It would appearthat the masterlist doesnot updatefrequentlyenoughtoeliminatethese,andso many polls would endup targetingmachineswhich wereno longerrunning thegameserver. Of the original list of 2193addresses,we found that 265 of thesewerenever running theserverduringthecourseof ourpolls. Thegameusedin O-V, QuakeIII Arena, doesnotallow thequeryingof playerduration.For this setof datawe assumethateachplayerjoinedat thetime of thepoll at whichthey arefirst noticed;this figurethushasaninaccuracy of up to two poll periods.
3.1 Summary of observations
We observed a total of 1,757,539individual sessions(i.e., individual usersjoining and then leaving agame). Table2 shows someof the overall aspectsof the data. We were interestedin examining threespecificfeatures:thenumberof participantsin a game,theinterarrival timebetweenparticipants,andhowlonga playerremainedin a game.
4 Session membership
Figure3(a)shows thetotal numberof playersfor all theserversin O-I andO-III to O-V, aggregatedto aone-weekperiod.Figure3(b) shows thenumberof playersfor oneserver from O-IV, againscaledto oneweek.It canbeseenthatthenumberof participantsin agameexhibits strongtime-of-dayeffects,peakingin the middleof the day. Thestrongsinusoidalpatternin the correlogramsin Figures3(c) and3(d) alsoindicatesseasonalvariation.
It canbeseenfrom Figure3(a)thatmid-Tuesdayis anoutlier, with anunusuallylow numberof players.This might have beendue,for instance,to a breakin network connectivity. This outlier wasremovedbyreplacingthedatawith theaverageof thesamples24 hoursbeforeand24 hoursafter.
4
Total joins Averagejoins/server/hr
Medianinterarrival(sec)
Max interar-rival (sec)
Median du-ration (sec)
Max dura-tion (sec)
O-I 1510445 4.65 225 246171 1576 3165999O-II 69961 27.76 70 17309 1098 66738O-III 37037 10.01 118 51706 618 410699O-IV 23559 4.19 115 77843 612 2614737O-V 5872 1.04 300 76800 901 403201
Table2: Summaryof results
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Sincethetime-of-dayeffect is soclearlyevident, it is possibleto do a simpleseasonaldecompositionby subtractingeachobservationfrom themeanvaluefor all theobservationstakenat thattime of day[7].Theresultsof this areshown in Figure4, wherethehighersolid line representsthetime-of-dayeffect, thelowersolid line theremainder, andthedashedline theobserveddata.Threedaysarehigherthantheothers;these,asonemightexpect,areFridayto Sunday.
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4.1 Network externalities
It is acceptedthat thevalueof a groupactivity to an individual participantmaybe relatedto thenumberof participantsin thatgroup. This hasbeenquantifiedconjecturallyby engineersasMetcalfe’s Law (thevalueof a network is proportionalto n2, wheren is the numberof users[23]), or more recentlyas theGroup-FormingLaw (thevalueof theInternetis proportionalto 2n [28]). Economists,however, generallyreferto theseeffectsas“positiveconsumption”or “network externalities”: for example,Katz andShapirodefinenetwork externalitiesas“productsfor which theutility thata userderivesfrom consumptionof thegoodincreaseswith thenumberof otheragentsconsumingthegood.” [18] Network externalitieshavemostcommonlybeenstudiedin termsof standardisationandcompatibility (e.g.,thetake-upandacceptanceoffaxmachines[11]), althoughHenrietandMoulin [16] presentacostallocationschemefor networkswhereuserssharecostsaccordingto thenetwork externalitiesthatareaccrued.
Onewould expectthatmultiplayergameswould alsoexhibit network externalities.Thepurposeof anetworkedmultiplayergameis to participatewith otherpeople;if a userwishesto play againstelectronicopponentstherewould be lessneedfor the networked aspectof the game(unless,for example,a userwishedto playagainsta farmorepowerful computersuchasthefamouschessmatchesbetweenKasparovandIBM machines).In general,however, it is reasonableto assumethatagivenparticipantin anetworkedgameis takingpartbecausethey wish to interactwith otherremote,humanusers,and,therefore,thattheirutility is derived,to someextent,from theexistenceandnumberof theseotherusers.
Figure5 shows thetemporalACF (autocorrelationfunction)of thecorrecteddatafrom Figure4, afterremoving the time-of-dayeffect; this shows the degreeto which the numberof playersin a subsequenttime perioddependson the sessionmembershipin the previous period. It canbe seenthat the level ofautocorrelationis high, even for a large numberof time periods. Thus,asexpected,thereappearto besomenetwork externalityeffects.
Having observedthetime-of-dayandnetwork externalityeffects,weanalysedthesessionmembershipdatausingtime-seriesanalysis.ARIMA (Autoregressive IntegratedMoving Average)models,introduced
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by Box andJenkins[6] area popularmeansof modellingtime seriesdata. An autoregressive processisdefinedasa serially dependentprocesswherebyelementsin a time seriescanbe describedin termsofpreviouselements:
Xt � φ1Xt � 1 � φ2Xt � 2 � φ3Xt � 3 ������� ε (1)
A moving averageprocessis whereeachelementin a timeseriesis affectedby pasterrors,independentof theautoregressiveprocess:
Xt � µ � εt � θ1εt � 1 � θ2εt � 2 � θ3εt � 3 � ���� (2)
An ARIMA modelincorporatesboth theautoregressive andmoving averageprocesses.Suchmodelsarereferredto asARIMA � p d q� , wherep is theautoregressive parameter, d thenumberof differencingpassesrequiredto make theinput seriesstationary, andq themoving averageparameter. If thetime serieshasa seasonalcomponent,additionalseasonalparametersarerequired,andthemodelis referredto asanARIMA � p d q����� P D Q� s model,whereP, D andQ representthe ARIMA parametersof the seasonalcomponent,ands is theperiodof theseasonality.
For theaggregatesessionmembershipdatafrom Figure4, thereis little to choosebetweena � 1 1 1���� 0 1 1� 48 anda � 2 1 1����� 0 1 1� 48 model(Figure6 shows thediagnosticoutputfor thelatter).Applyingthesetwo modelsto individual servers’ data,however, showed that a � 2 1 1����� 0 1 1� 48 model is themostappropriate.Figure7 shows thediagnosticsfor oneserver; theBox-Piercestatisticindicatesa highgoodnessof fit.
A � 2 1 1����� 0 1 1� 48 modelincorporatesbothnetwork externalities,sincetheautoregressivecompo-nentmeansthat the numberof playersup to an hour prior to a playerjoining hasan effect on a player’sdecisionto join, andalsoincludesthetime-of-dayeffect throughtheseasonal� 0 1 1� 48 component.
Proportionalfairnesshasbecomea popularmetric for allocatingbandwidthbetweenflows on a con-gestedlink [19]. This relieson theassumptionof usershaving logarithmicutility functions.It is unclear,however, whetherthis sameunicastlogarithmicutility functionshouldbeassumedfor a multicastor mul-tipoint transmission.Chiu [8] shows that proportionalfairnessmay producean “unfair” outcomein themulticastcase,andproposesaweightedproportionallyfair solution,wheremulticastflowsreceiveaband-width shareweightedaccordingto the aggregateutility of the downstreamreceivers. Legout et al. [20]suggestthat this bandwidthsharemight relateeither linearly or logarithmicallyto the numberof down-streamreceivers.Thedatapresentedheresupportsthelattersuggestion,sincethey imply that it might bemoreappropriateto assumeindividualutility functionswhich incorporatenetwork externalities.
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Standardized Residuals
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Figure7: ARIMA diagnosticsandcumulativeperiodogramfor � 2 1 1����� 0 1 1� 48 modelfor singleserver
Time-of-daypricing is commonlyusedfor pricing utilities suchaselectricity andtelephoneservice,andhasbeenproposedasasimple,if suboptimal,methodfor pricing Internettraffic [21]. Thetime-of-dayeffectsobserved heremeanthat this might be appropriateon a per-applicationbasis,at leastfor games.Thismightalsohaveimplicationsfor network provisioning,wherebyanetwork designedfor gameswouldwantto beableto dealwith thepeaks.
5 User duration
Gameservers tend to run continuously, with usersjoining and leaving as they wish. As suchit is notmeaningfulto discussthe overall sessionduration,i.e., a whole game. Insteadwe examinethe duration
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Figure8: Durationof user’sgame
of eachindividual session,i.e., a user’s game. Figure8 shows the durationof users’individual sessionsfrom O-II: it canbeseenthat thesedurationsvary quitewidely, andthatmany gamedurationsarelowerthanour polling periodof five minutes. This might be due to droppedconnections,or usersbrowsinggamesby startingasessionto seewhatis goingonanddecidingthataparticulargameis not to their liking.At theotherendof thespectrum,thereareseveral long gamedurationsof over 24 hours.Thesemight be“hardcore”gamers,automatedplayers/botsor userswhohavemistakenly left their connectionsactive.
In Figure 9 we fit the userdurationdatafor two individual servers to a set of randomlygeneratedexponentially-distributeddata. The Quantile-Quantileplots show that this is an appropriatemodel. Thisagreeswith thefindingsfor multicastsessionsin [2]. It is alsoknown thatsomesingle-userapplications,suchasvoicetelephonecalls[4] fit anexponentialdistribution.
Sincewehadalreadyobservednetwork externalityeffectsin thenumberof players,weexpectedto findacorrelationbetweenthedurationof aplayer’ssessionandthenumberof playersin thatgame;agamewithmoreplayersmightbelikely to leadto playersenjoying thegamemore,whichshouldleadto themstayinglonger. Surprisingly, thereappearsto beno evidencefor this. Figure10(a)showsa boxplotof thenumberof playersat thestartof aplayer’ssessionagainstthedurationof theirsession.Theredoesnotseemto beacorrelation,andthemediandurationis relativelyconstantirrespectiveof thenumberof players.Comparingthedurationto theaveragenumberof playersover thefirst hourof asession(Figure10(b))showedaslightcorrelation,but this wasinsignificant.This might indicatethattheabsolutenumberof playersin a sessionis notnecessarilyadeterminantof whenaplayerdecidesto leaveasession;it maybethebehaviour or skillof thespecificplayersthatis moreimportant,or a completelyunrelatedfactor.
6 Interarrival times
Figure 11 shows the interarrival times betweenplayersfor one server. As for duration, there is largevariation. Unlike the durationdata,interarrival timesdo not appearto fit an exponentialdistribution, asshown in Figure12.
Interarrival timesbetweenusersfor single-userapplicationshave beenfoundto fit a Poissondistribu-tion [12, 26]. This is unlikely to be the casefor multiuserapplications,however, wherethe presenceofotherusersmayalteruserbehaviour. Borella[5] findsthat for games,packet interarrival timesarehighlycorrelated.Figure13 showsthatthis is alsotruefor playerinterarrivals;thereis significantautocorrelationatshortlags,whichimpliesthatthearrival of someuserswill leadto othersarriving. Thus,theinterarrivalsdo not fit theindependentarrivalsof thePoissondistribution.
Heavy-taileddistributionshavebeenobservedfor Internetusagebehaviour, for examplein World WideWebusage[9] andaggregateEthernettraffic [30]. Onemethodfor visualisinga heavy-taileddistributionis a log-log complementarydistribution (LLCD) plot, wherethe complementarycumulative distributionis plottedon logarithmicaxes. Linear behaviour in an LLCD plot indicatesa heavy-tailed distribution.Figure 14(a)shows sucha plot for the interarrival times, and linear behaviour canbe observed for the
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largerobservations(Figure14(b)).A morerigoroustestfor heavy-taileddistributionsis theHill estimator[17]. A distribution of variable
X is heavy-tailedifP �X � x��� x� α asx ∞ 0 ! α ! 2 � (3)
TheHill estimatorcanbeusedto calculateα
αn � "1 # k i $ k � 1
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� logX% n � i & � logX% n � k& �(' � 1
(4)
wheren is thenumberof theobservations,andk indicateshow many of thelargestobservationshavebeenusedto calculateαn. Figure15 shows thatα is approximately1.15.
Comparingthe interarrival times to the numberof playersin a sessionshows someevidenceof aninverselyproportionalrelationship(Figure16); asthenumberof playersin a sessionincreases,the inter-arrival timesdecrease.This supportsthe hypothesisthat the numberof playersis a determinantin otherplayers’decisionsto join a session.
Thehigh variationin userdurationandinterarrival timeshave several implicationsfor pricestabilityandprovisioning if the membersof a multicastgroupareto sharethe overall costof a sessionamongstthemselves.Theautocorrelationin thenumberof playersandinterarrival timesmeansthatif theusersaresharingthe costsof a session,this costwill snowball; new usersjoining will be followedby otherusersjoining (anduserswill join fasterasthenumberof usersincreases),leadingto rapiddecreasesin thecostperuser, andvice versafor whenusersleave. This couldberectified,for example,by only changingtheprice for eachuseron a periodicbasisratherthanwith eachjoin or leave. The autocorrelationseemstoexist for large lags,however, which meansthat the periodsof price reevaluationwould alsohave to belarge,andthiscouldimpedetheefficiency of any pricingscheme.
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Costsharingmay alsochangethe behaviour of players,sincewe have observed that the numberofplayersin a sessionis not a largefactorin theutility receivedfrom a game.Oncenetwork pricing or QoSarea featureof networks, thenuserswill needto choosebetweennetwork flows dependingon the valuethat they receive from eachapplication;in otherwords,they will attemptto maximisetheir utility giventheir individualbudgets.Thepriceof asessionthusbecomesa factorin userbehaviour, andif thecostof asessionis sharedamongstsessionmembers,thenthenumberof playersin a sessionwill becomea factor,sinceit will be a determinantin the price of the session.Additionally, the numberof usersin a sessionmight affect theQoS,which would becomea furtherfactorfor users’behaviour.
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Figure13: ACFof interarrival times
7 Conclusions and future work
Therehasbeenlittle study of session-level userbehaviour in large-scalemultiple-sourcescenarios.Inthis paperwe have presentedstatisticalanalysisof severalsession-level tracesof popularmultiplayernet-
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Figure15: Hill estimatorfor interarrival times
workedgames.We have foundthat thenumberof playersexhibits strongtime-of-dayandnetwork exter-nality effects,andwe have fitted anappropriateARIMA model.Players’durationtimesfit anexponentialdistribution, while interarrival times fit a heavy-tailed distribution. The numberof playersin a sessionappearsto have a greatereffect on players’decisionsto join a sessionratherthanleave. In many respectswe have observedsimilar behaviour to that seenfor multicastapplications,despitethe unicastnatureofthesegames.This impliesthatin theabsenceof appropriatemulticastdata,unicastmultipointapplicationsareanappropriatesubstitute.Wehavediscussedhow theseresultscouldimpactpotentialmulticastpricing
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Figure16: Numberof playersversusinterarrival time
policiesandnetwork provisioning.Networking researchinto multiplayergamesis still at an early stage,andthereis muchfuture work
thatneedsto becarriedout. Understandinguserbehaviour is but onestagein creatingappropriatepricingpolicies.It doesnot,for example,helpusexplainwhatusersdesireor require.Futurework will investigatetheQoSrequirementsfor networkedgames,in particular, concentratingon how therequirementschangedependingon thecompositionof asessionandgroup.
We alsointendto look at packet-level traffic statistics.Someof the resultspresentedherehave beensimilar to thoseof previous packet-level gamesstudies,and it will be interestingto conductsimultane-ousanalysisat the packet andsessionlevels, to determinewhetherthereis any relationshipbetweenthebehaviour at bothlevels. This is important,for example,if QoSprovisioningis to take placethroughcon-gestionpricing, i.e., chargingusersfor thenetwork congestionthatthey cause.Unfortunately, mostof thegameserveroperatorsandISPsthatwehavespokento donot log many of theappropriatestatistics.Thus,we arenow runningour own gamesserversin orderto collectpacket-level data.Runningour own serverspresentsmany opportunitiesfor furtherwork. Sincewe canlog theexacttimeswhenplayersconnectandleaveto theserver, wecanbetterestimatetheinaccuracy of thepolling methodthatwehaveusedhere.Wearealsousingthesegamesserversfor experimentalratherthancorrelationalstudy;for examplechangingsuchvariablesasnetwork delayin orderto determinetheeffectson userbehaviour.
Thestudypresentedherehasonly lookedatonetypeof game,theFPS.Althoughweexaminetwo of themostpopulargamesof this genre,it is notnecessarilytruethattheseresultswill hold for otherFPSgamesandthis shouldbefurtherexamined.Moreover, othertypesof games,for instanceMMORPGs(MassivelyMultiplayer OnlineRole-PlayingGames)suchasEverquest,arelikely to exhibit differentuserbehaviour,sincetheMMORPGcanbeslightly slowerpaced,andcaninvolvethousandsof usersconnectingto asingleserver, ratherthanthelargenumberof smallgroupsin FPSgames.
8 Acknowledgements
Thanksto BrendanMurphy at Microsoft ResearchCambridgeUK for allowing us to poll their gamesservers.
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