cubin_TimNeame_Thesis

CHARACTERISATIONANDMODELLINGOFINTERNETTRAFFICSTREAMSTimothyNeameSUBMITTEDINTOTALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYDEPARTMENTOFELECTRICALANDELECTRONICENGINEERINGTHEUNIVERSITYOFMELBOURNEFEBRUARY2003AbstractIncreasingaccesstodatacommunicationsiscreatingsweepingchangesaroundtheglobe.Morepeopleareusingawiderrangeofservices,requiringmoredatatobetransported.Providingcapacityforthislargervarietyofdemandsrequiresimprovedmodelsfornetworktraffic.Duringthe1990s,anumberofstudiesshowedthatmoderntrafficsourcesarefundamentallydifferentinnaturefromtraditionalmodelsforteletraffic,andinparticularthattheyaretypicallyLongRangeDependent(LRD)andburstyinnature.ThisworkpresentsmodelsthatcanbeusedinrepresentingInternettraffic,andalsoshowshowthesemodelscanbeusedinnetworkresourcedimensioning.Inthisthesis,itisdemonstratedthatGaussianmodels,evenLRDGaussianmod-els,areunabletoaccuratelymodelcurrentInternettraffic.Anewmodel,namedthePoissonParetoburstprocess(PPBP)isproposed.ThisnovelmodelisatypeofM/G/∞process,andisalsorelatedtoheavy-tailedon-offmodels.ThePPBPisdemonstratedtosatisfythebasicrequirementsforasimple,butaccurate,modelofInternettraffic.Suchamodelisastochasticprocessthatisamenabletoanalysisandthatisdefinedbyasmallnumberofparameters.Theseparametersshouldbeabletobefittedusingmeasurablestatisticsofanactualtrafficstream.Whentheparametersoftheprocessarefittedtotherelevantstatisticsofanactualstream,thefirstandsecondorderstatisticsoftheprocessshouldmatchthoseoftheactualtrafficstream.Whenfedthroughasingleserverqueue(SSQ),thefittedmodelshouldproduceperformanceresultsthataccuratelypredictthoseoftherealtrafficstreamfedintoanidenticalSSQ.Thismatchingofperformanceresultsshouldbetrueforawiderangeofbuffersizesandforawiderangeofservicerates.iiiiiRelationshipsalsoexistbetweenthePPBPandLRDGaussianprocesses.Theserelationshipsareexplored,anditisshownthat,assumingcurrentgrowthtrendscon-tinue,GaussianmodelswillbecomemoreaccurateasmodelsofcoreInternettrafficinthefuture.UsingthePPBPandGaussianmodels,simplemethodsforlinkdimensioningareexamined.Adimensioningrulebasedoneffectivebandwidthsisproposed,andshowntoallowutilizationofcapacitythatismoreefficientwhencomparedwiththeutilizationachievableusingtraditionaleffectivebandwidthsmethods.Finally,capacityassignmentsbasedonconservativeestimatesofdemandareexamined,andmeasuresaremadeoftheamountofcapacitywastedasaresultoftheseconservativeestimates.DeclarationThisistocertifythat(i)thethesiscomprisesonlymyoriginalworktowardsthePhD(ii)dueacknowledgementhasbeenmadeinthetexttoallothermaterialused(iii)thethesisislessthan100,000wordsinlength,exclusiveoftables,maps,bibliographiesandappendices.TimothyNeameivAcknowledgementsIwouldliketothankmysupervisors,ProfessorMosheZukermanandDrRonAddie,fortheirmanysuggestionsandconstantsupportduringthisresearch.IamgratefulforthesupportIhavereceivedfromtheAustraliangovernment,throughanAPAscholarship,andalsoindirectlythroughtheARCSpecialResearchCentreforUltra-BroadbandNetworks(CUBIN).IhavebeenextremelyfortunateinthatIhavebeenabletopursuemystudieswiththesupportofmyemployer,Telstra.IappreciatethesupportIhavereceivedfromtheorganisation,andparticularlyfromspecificindividualsattheTelstraResearchLaboratories.IamparticularlygratefultoPeterHicks,RobertAyreandPaulKirtonforsmoothingmywayatTelstra.Withoutthesacrificesmadebymyparents,Icouldneverhavehadtheopportu-nitytoundertakethisstudy.Iowethemadebtofgratitudeforallmysuccesses;myfailuresareentirelyofmyownmaking.IamalsoextremelygratefultoCarolineforhersupportandbeliefinme.Finally,IwishtothankBrendan,Michael,Teck,David,Allen,Ravi,Azzam,Fraser,Robert,Lucia,Dusshy,Lachlan,TedandRamiformakinguniafunplacetobeandalsofortheirwillingnesstohelp.Melbourne,VictoriaTimNeameFebruary,2003vTableofContentsAbstractiiDeclarationivAcknowledgementsvTableofContentsxListofTablesxiListofFiguresxii1Introduction11.1BackgroundtotheProblem......................11.2ModellingLongRangeDependentTraffic..............51.3ContentsofthisThesisbyChapter..................71.4ContributionsofthisThesis......................81.5PublicationsbytheAuthor......................101.5.1PublicationsbytheAuthorRelatedtothisThesis......101.5.2OtherPublications......................122TrafficModelsforVBRTrafficSources132.1Introduction..............................132.2MeasuringPerformanceinaPacketNetwork............152.3TrafficModels.............................172.4TypifyingTrafficStreams.......................212.4.1MeasuresofCorrelationinSRDProcesses.........222.4.2Self-similarityandLongRangeDependence........222.4.3EstimatingtheHurstParameter...............252.5ShortRangeDependentTrafficModels...............272.5.1On-OffModels........................272.5.2MarkovModulatedModels..................282.5.3AutoregressiveModels....................29viCONTENTSvii2.5.4AutoregressiveMovingAverageModels...........302.5.5AutoregressiveIntegratedMovingAverageModels.....312.5.6GeneralGaussianModels..................312.6ImpactofLRDonQueueingPerformance..............332.7HeavyTails......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