?ModelingVideoTra?cinTheWaveletDomainShengMaandChuanyiJiDepartmentofElectrical?Computer?andSystemsEngineeringRensselaerPolytechnicInstitute?Troy?NY?e?mail?shengm?ecse?rpi?edu?chuanyi?ecse?rpi?eduTel?Abstract?Asigni?cantdiscoveryfromthisworkisthatalthoughvideotra?chascomplicatedshort?andlong?rangedependenceinthetimedomain?thecorrespondingwaveletcoe?cientsarenolongerlong?rangedependentinthewaveletdomain?Therefore?a?short?range?dependentprocesscanbeusedtomodelvideotra?cinthewaveletdomain?Inthiswork?wedevelopsuchwaveletmodelsforVBRvideotra?c?Thestrengthofthedevelopedwaveletmodelsincludes?itprovidesauni?edapproachtomodelbothlong?rangeandshort?rangedependenceinvideotra?csimultaneously?ithastheabilitytoreducethetemporaldependencesosigni?cantlythatthewaveletcoe?cientscanbemodeledbyeitherindependentorMarkovmodels?and?themodelresultsinacomputationallye?cientmethodongeneratinghighqualityvideotra?c?Keywords?wavelet?long?rangedependence?short?rangedependence?tra?cmodeling?VBRvideotra?c?Topics?videonetworking?B?ISDNandATM?admissioncontrol?I?IntroductionSinceVBRcompressedvideotra?cisexpectedtobeoneofthemainloadingcomponentsinfutureB?ISDNandwirelessnetworks?accuratemodelingoftheVBRtra?cwillbecrucialtomanyimportantapplicationssuchascontrol?lingtheQualityofService?e?ectivelyallocatingnetworkresourcesanddesigningbu?er?capacityofnetworks?Nu?merousstudieshavebeenconductedontra?cmodelingandperformanceanalysis?seeforexample?andreferencestherein?Oneofthesigni?cantstatisticalpropertiesofVBRvideotra?chasbeenfoundtobetheco?existenceoftheso?calledlong?rangedependence?LRD?andtheshort?rangedependence?SRD?inthevideotrace?Roughlyspeaking?thismeansthattheauto?correlationfunctionofthevideotra?cbehavessimilarlytothatoflong?rangede?pendentprocessessuchasFractionalGaussianNoisepro?cess?atthelargelags?andtothatofshort?rangedepen?dentprocessessuchasDARprocesses?atthesmalllags?Thelong?rangeandtheshort?rangedependenceembeddedinvideotra?cresultsfromscenechanges?andsuggestsacomplexbehaviorinthetimedomain?Thiscomplextemporalbehaviormakesaccuratemodelingofvideotraf?cachallengingtask?Inotherwords?usingeitheralong?rangedependentorashort?rangedependentprocessalonewouldnotdoagoodjobonmodelingthevideotra?c?Ideally?agoodtra?cmodelneedstobe?a?accu?rateenoughtocharacterizepertinentstatisticalproper?tiesinthetra?c?b?computationallye?cient?and?c?feasibletobeusedfortheanalysisneededfornetworkdesign?Theexistingmodelswhichhavebeendevel?opedtomodelboththelong?rangeandtheshort?rangedependenceincludeFARIMAmodels?Transform?Expand?Sample?TES?modeling?scene?basedmod?els?andtheMarkovModulatedProcesses?Acom?monfeatureofallthesemethodsisthattheymodelbothLRDandSRDinthetimedomain?Amongthesemethods?thescene?basedmodeling?andtheMarkovModulatedmodels?provideaphysicallyinterpretablemodeltoin?cludeboththelong?rangeandtheshort?rangedependence?However?duetothedynamicandstochasticnatureofthevideotra?c?itisdi?culttoaccuratelyde?neandsegmentvideotra?cintodi?erentstatesofaMarkovmodel?TESmodelisfastbuttoocomplicatedtobeusedforanalysis?Therestofthemethodsallsu?erthecomputationalcom?plexitytoohightobeusedforgeneratingalargevolumeofsynthesizedvideotra?c?Amorecomputationallye?cientmethodbasedonFastFourierTransformhasbeenproposed?tomodelEthernettra?cintheFrequencydomain?AnothermethodbasedonMarkovmodelshasbeenproposedtomodelthefrequencycomponentsofvideotra?c?Bothmethodssuggestthatinterestingproper?tiesofeitherEthernetorvideotra?ccouldbeinvestigatedintheFrequencydomain?However?noneofthemethodsareyetabletocapturethelong?rangeandtheshort?rangedependencesimultaneously?Thereforethequestionremainsopenonhowtodevelopacomputationallye?cientmodelwhichcancaptureboththelong?rangeandshort?rangedependenceinthevideotra?c?Inthiswork?wewilltacklethisproblembydevelop?inganewmethodbasedonwavelets?Insteadofmodelingthevideotra?cdirectlyinthetime?domain?wemodelthestatisticalpropertiesofwaveletcoe?cientsinthewaveletdomain?Whydowechoosewavelets?Ithasbeenshownin?thatwaveletscanprovidecompactrepresenta?tionsforaspecialclassoflong?rangedependentprocesses?theFractionalGaussianNoise?FGN?processes?Thisisbecausetheself?similar?deterministic?structureofwaveletbasesnaturallymatchesthe?statistical?self?similarstruc?tureofthelongrangedependentprocesses?Thenthewaveletcoe?cientscanbemodeledbysimplestatisticscor?respondingtothe?short?rangedependence?aloneinthewaveletdomain?Inthiswork?wewillshowthatasimplewaveletmodelbasedonindependenceassumptionsiscapa?bleofcapturingboththelong?rangedependenceformoregeneralLRDprocessesandtheshort?rangedependenceas?well?andthusprovidesaparsimoniousanduni?edmodeltocaptureboththelong?rangeandtheshort?rangedepen?denceinvideotra?c?Furthermore?sincecomputationalcomplexityofwavelettransformsandinversetransformsareintheorderofN?ourwaveletmodelscanrapidlygen?eratesynthesizedvideotra?coflengthNwithacom?putationalcomplexityO?N?andtherebyprovideoneofthemoste?cientmethodstosynthesizehighqua