L NarasimhaReddy EliUpfal Texas AMUniversity IBMAlmadenResearchCenter 214 Zachry 650 HarryRoad CollegeStationTX778433128 San JoseCA95120 reddyeetamuedu elyalmadenibmcom Phone 4098457598 FAX4098452630 Abstract In this pap er we will address the proble ID: 25843
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communicationschedulingmulticomputerserverA.L.NarasimhaReddyEliUpfalTexasA&MUniversityIBMAlmadenResearchCenterZachryHarryRoadCollegeStation,TX77843-3128Jose,CA95120.reddy@ee.tamu.eduely@almaden.ibm.com409-845-7598FAX:409-845-2630paper,weschedulingcommunicationoverinter-networkofadistributed-memorymulticomputervideoserver.Wewillshowmovieschedulingsuchasystem.Asolutionisproposedinthispaperthataddressesatonce.moviesevenlyovernodesmulticomputer.proposedsolutionminimizesthecontentionforlinksovertheswitch.Theproposedsolutionmakesmovieschedulingverysimple-blockmovieisscheduled,movieisautomaticallyscheduled.Moreover,ifthe rstblockofthemoviestreamisscheduledwithoutnetworkcontention,theproposedsolutionguaranteesthattherewillbenonetworkcontentionduringtheentiredurationofplaybackofthatmovie.Wewillshowthattheproposedapproachtocommunicationschedulingisoptimalinutilizingthenetworkresources.Extensivesimulationresultsarepresentedtoshowthee ectivenessoftheproposedapproach. IntroductionSeveraloperatorsserverswouldservevideostreamstocustomersovertelephonelinesorcablelines.Theseprojectsenvisionsupportingseveralthousandsofcustomerswiththehelpofoneorseverallargevideoservers.projectsmoviesmoviebedisplayed.projectsaimtocompetelocalrentalbetterabilitywatchanymovieany(avoidingmovierentedmovies.ProvidingmoviesnumbermoviesbeavailableCurrently,MPEG-1compression,amovieofroughlyminutedurationtakesabout1GBworthofstorage.Avideoserverstoringabout1000movies(atypicalvideorentalstorecarriesmore)wouldthenhavetospendabout$250,000justforstoringmovies$0.25/MB.Thisrequirementamountsthattheserviceprovidersneedtocentralizetheresourcesandprovideservicetoalargenumberofcustomerstoamortizecosts.Hence,therequirementtobuildlargevideoserversthatwouldstorealargenumberofmoviesinasinglesystemandbeabletoservicealargenumberofcustomers.Multicomputersystemsmaybesuitableforsupportingsuchlargeamountsofreal-I/Obandwidththeselargevideoservers.Severalproblemstobeaddressedprovidingsuchmulticomputerpaper,weserveronmulticomputers.Inthispaper,wewillusethetermmulticomputersystemtodescribeasystemmaybevariouslyknownmulticomputerWewillassumethatthemulticomputervideoserverisorganizedasshowninFig.AnumberofnodesactasstoragenodesStoragenodesareresponsibleforstoringvideodataeitherinmemory,tapedeliveringnodesnetworknodesresponsibledatablocksfromstoragenodesandroutingthemtothecustomers.Boththesefunctionscanresidemulticomputernode,nodebestoragenode,networknodebothatthesametime.Eachrequeststreamwouldoriginateatoneoftheseveralnetworknodesinthe systemandthisnetworknodewouldberesponsibleforobtainingtherequireddataforthisstreamfromthevariousstoragenodesinthesystem.ToobtainhighI/Obandwidth,datahastobestripedacrossanumberofnodes.Ifamovieiscompletelystoredonasingledisk,thenumberofstreamsrequestingthatmoviewillbelimitedbythediskbandwidth.Asshownearlierby[1],a3.5"2-GBIBMdiskcansupportupto20streams.popularmoviemayreceivethan20requestsoverthelengthoftheplaybacktimemovie.Tonumbermovie,eachmoviebestripedacrossanumberofnodes.Asweincreasethenumberofnodesforstriping,weincreasethemovie.moviesstripednodes,weimprovetheloadbalancingacrossthesystemsinceeverynodeinthesystemhastoparticipateinprovidingaccesstoeachmovie.Hence,weassumethatallthemoviesarestripedacrossallthenodesintheEvenwhenthemoviesarestoredinmemory,therequiredcommunicationmaymoviebestripeddi erentnodesofthesystem.Fortherestofthepaper,wewillthatthemoviesarestripedallthestoragenodes.Theunitofstripingacrossthestoragenodesiscalledablock.Inourearlierstudiesondiskscheduling[1],wefoundthat64-256Kbytesisasuitablediskblocksizefordeliveringhighreal-timebandwidthfromthedisksubsystem.Asaresultofthis,anetworknodethatisresponsiblefordeliveringamoviestreamtotheusermayhavecommunicatenodesplaybackmovie.pointtopointcommunicationfromallstoragenodestothenetworknode(possiblymultipledependingblocknumbernodessystemandthelengthofthemovie)duringtheplaybackofthemovie.Eachnetworknodewillberesponsibleforanumberofmoviestreams.Hencetheresultingcommunicationpatternisrandompoint-to-pointcommunicationamongthenodesofthesystem.Itispossibletoachievesomelocalitybymoviesnodesnetworknodesmoviebeamongthissmallersetofstoragenodes.Weobservethatthedeliveryofvideodatatotheconsumerrequiresthreecomponentsofservice:(1)readingoftherequestblockfromthedisktoabu eratthestoragenode,(2)transmissionofblocknodenetworknodeovermulticomputernetworkblocknetworknodecomponentofservicewoulddependdeliveryorLAN),wenotaddressthatissuehereandwillourattentiontotheservicethathastobeprovidedbythevideoserversystem,components(1)and(2).serverblocksmovieatregularperiods 4 StorageStorageComboNetworkStorageNetworkMultiprocessorCommunication Systemmodelofamulticomputervideoserver. dataisnottransferedatregularintervals,theconsumermayexperienceglitchesinthedeliveryofmovie.Toglitch-freeserverguaranteecomponentsamountGuaranteeingdelayboundscomponentbyscheduling[2,3,4].delayboundsinservicecomponent(2)isaddressedinthispaper.Whenmultipletransmissionstakeplacesimultaneouslyoverthenetwork,thedelaysexperiencedbydependcontentionexperieincednetwork.Worstassumptionsofcontentionaretypicallymadetoobtainguaranteeabledelayboundsanetwork.Ourapproachtothisproblemistocarefullyscheduletranmissionsoverthenetworksoastominimize(oreliminate)thecontentioninthenetwork.Thisapproachenablesustoguaranteetighterdelayboundsontransmissionsoverthemulticomputernetworkofthevideoserver.Fortherestofthepaper,wewillassumethateverynodeinthesystemisbothastoragenodenetworknodecombinationnode.WemulticomputersystemwithanOmegainterconnectionnetworkasanexamplemulticomputersystem.Moviedistribution(ordatadistribution/organization)istheproblemofdistributingtheblocksofmoviesacrossthestoragenodes.Thisinvolvestheorderinwhichtheblocksarestripedthestoragenodes.Dataorganizationdeterminesthebandwidthavailabletoamovie,loadbalanceacrossthestoragenodesandthecommunicationpatternsobservedinthenetwork.MovieschedulingschedulingastoragenodenetworknodesuchblocksmoviearrivenetworknodeAtanygivenpointnodebeinvolvedinsendingoneblockofdataandreceivingoneblockofdata.MovieschedulingisconcernedwithschedulingthetransferofblocksofamoviebetweenstoragenodesandthenetworknodeformovieCommunicationschedulingmovieschedulingWhentwotransfersarescheduledtotakeplacebetweentwodi erentsetsofsourceanddestinationpairs,thecommunicationmaynothappensimultaneouslybetweenthesepairsbecauseofcontentioninthenetwork.shows16-nodenetwork[5]switches.righteachnodeportportWeeachnodeportportnoderecieveoperationsimultaneously.Communicationtakesimultaneouslybetweennodesnodesmoviesbescheduledsuchcontentionnetwork?Communicationschedulingschedulingnetworkcommunicationdelays. 6 (0000)00 (1100)12(1011)11(1010)10(1001)09(1000)08(0111)07(0110)06(0101)05(0100)04(0011)03(0010)02(0001)01(0000)00 A16-nodeOmeganetwork. problemofschedulingcommunicationoverthemulticomputerinterconnectionnetworkisthefocusofthispaper.Ifthenodesinthemulticomputersystemareinterconnectedbyacompletecrossbarnetwork,thereisnocommunicationschedulingsinceanypairofnodesinthesystemcancommunicatenetwork.schedulingeachnodeseparatelyandwewillassumethatthesystemloadissuchthatdiskbandwidthisnotaproblem.scheduling[6]knownbeschedulingknownadvance.schedulingshowntobeevenarenotnotBut,bothassumethatthetaskcompletionareknownadvance.blocktransfertimethenetworkisdependentonwhetherthereisanycontentionfortheswitchlinksandthiscontentionvariesbasedonthenetworkload.Also,anetworktransferrequiresmultipleresources(links,inputports)unliketheseresultscannotbedirectlyappliedtoourproblem.Recentwork[2,1,3,4,8]haslookedatdiskschedulinginavideoserver.Filesystemsforhan-continuousmediahavebeenproposed[9,10,11,12,13].basedvideoserversarestudied[14,15,16].workinmulticomputercommunicationdelaysthenetwork[17,18,19],studiesonnetworkhotspots[20]andmanyapplicationspeci cnetworktopology,[21].approachessupportingmultimedianetworktracincludebest-e ortapproaches[22,23].SchedulingprocessApproachWewillassumethattimeisdividedintoanumberofThelengthofaslotisroughlyequaltotakentotransferablockmovieoverthemulticomputernetworkfromastoragenodetoanetworknode(wewillsaymorelateronhowtochoosethesizeofaslot).Eachstoragenodestartstransferringablocktoanetworknodeatthebeginningofaslotandthistransferisexpectedto nishbytheendoftheslot.Itisnotnecessaryforthetransferto nishstrictlywithintheslotbutforeaseofpresentation,wewillassumethatablocktransfercompleteswithinaslot.ThetimetakenfortheplaybackofablockiscalledframeThelengthoftheframedependsblockForblockKbytes Kbytes/sec,paper,weConstantconstantblocktakestransferfromstoragenodetonetworknodeandtakesaframeforplaybackattheclient.Hence,astreamrequiresdatatransferservicemulticomputernetworkforasloteveryIfwecanprovideguaranteesthatablockofdatacanbeprovidedtotheclienteveryframe,withdoublebu eringattheclient,theclientcanplaybackthemoviecontinuously.Wewillassumethatintegralmultiplebemakethispossible.Nowconsiderschedulingthecommunicationrequiredbyasinglerequeststream.Wewillassumethatasinglenetworknodecoordinatedeliveryofthisstreamtotheclient.bynodebyberepresentedby;s;seachrepresentsinvolvedcommunicationeachnetworknodeinvolveddeliveryForasinglestream,theresultingtracpatternismany(storagenodes)toone(networknode).Eachstreamrequiresnetworkservicefromthesystem.thenetworkserviceforallthestreamshasamanytomanytracpattern.Datadistributionamongthestoragenodesdeterminestheexacttracpattern.Wewillassumeinthispaperthatanodecansimultaneouslyparticipateinasendandareceiveoperation.ThescheduleinthesystemcanthenberepresentedbyatableasshowninFig.Eachrowinthetablerepresentsanetworknode,eachcolumnrepresentsatimeslotandeachentryinthetablerepresentsnodeblocknetworknodeEachentriesbyentrynodenetworknodethenthatstreamwillhaveanentryintimeslotrequiringservicefromstoragenodenetworknode,whereisthestoragenodestoringthenextblockofdataforthisstream.orderofstoragenodesisdeterminedbythedatadistribution.Toavoidschedulingcon\rictsatthenodes,astoragenodecannotbescheduledtwiceinthesamecolumnofthistablesincethatrepresentstwotransmissionsinthesametimeslot.Con\rictsinthenetworkcanbeavoidedifthenodesinvolvedcommunicationentriesbeconnectedbyedgedisjointpathsinthenetwork.Now,theproblemcanbebrokenupintotwopieces:(a)Canwe ndadatadistributiongivenassignment;sproduceschedulewegivenassignment;s 9 0312FrameStorage node l can't serve Characteristicsofaschedule networkcon\rict-free,produceasource,networkcon\rict-freescheduledependsnetworkmulticomputerthatistheonlyreasonforaddressingtheproblemintwostages.Wewillproposeageneralsolutionthataddresses(a).Wethentailorthissolutiontosuitthemulticomputernetworktoaddresstheproblem(b).MovieSchedulingAssumeallthemoviesarestripedamongthestoragenodesstartingatnode0inthesamepatternblockofeachmoviestoredonastoragenodegivenbyimodbeingnumbernodesinthesystem.Then,amoviestreamaccessesstoragenodesinasequenceonceitisstartedatnode0.Ifwecanstartthemoviestream,itimpliesthatthesourceandthedestinationdonotthattimestreamsfollowsamesequenceofsourcenodes,istimetoschedulethenextblockofastream,allthestreamsscheduledinthecurrentslotwouldrequestablockfromthenextstoragenodeinthesequenceandhencewouldnothaveanycon\ricts.Inournotation,aset;sinslotjisfollowedbyaset+1)modNinslotinthenextframe.Itisclearthatif;sissourceanddestinationcon\rict-free,+1)modNisalsosourceanddestinationcon\rict-free.Variantsofsuchdatadistributionshavebeenproposedandanalyzed[11,8].approachmakesmovieschedulingstright-forward.However,doesnotaddressthecommunicationschedulingAlso,ithasthefollowingdrawbacks:notmorethanonemoviecanbestartedinanygiveneverymoviestreamhastostartstoragenodenodebecomesbottleneckmovies.movieareplayedalongwithlongmovies,shortclipstheloadonthe rstfewnodesinstoragenodesequenceresultinginnon-uniformloadsonthestoragenodes.(iii)asaresultsof(i),moviemaybearrivesnodebeforesequenceofscheduledbusyslots.proposednodesmovies.doesnotstipulatethateverymoviestartatnode0.Weallowmoviestobedistributedacrossthestoragenodesdi erentpoints.Forexamplemoviebedistributedinthesequenceof0,1,2,...,N-1,movie1canbedistributedinthesequenceof1,2,3,...,N-1,0andmoviek(modN)canbedistributedinthesequenceofk,k+1,...,N-1,0,...,k-1.Wecanchooseanysuchsequenceofstoragenodes,withdi erentmovieshavingdi erentstartingpointsinthissequence. Whenmoviesaredistributedthisway,weachievethefollowingbene ts:(i)multiplemoviescanbestartedinagivendi erentmovieshavedi erentstartingnodes,twomoviestreamscanbescheduledtostartattheirstartingnodesinthesameslot.(ii)Sincedi erentmovieshavedi erentstartingnodes,evenwhenthesystemhasshortmovieclips,allthenodesarelikelytoseeworkloadandhencethesystemislikelytobebetterDi erentshortmovieclipsplacetheloadondi erentnodesandthisislikelytoevenout.(iii)Sincedi erentmovieshavedi erentstartingnodes,thelatencyforstartingamovieislikelytobelowersincetherequestsarelikelytospreadoutmoreevenly.Thebene tsoftheaboveapproachcanberealizedonanynetwork.Again,iftheset;ssourceanddestinationcon\rict-freeinslotofaframe,thentheset+1)modNisgiventobesourceanddestinationcon\rict-freeinslot,whetherornotallthemoviesstartatnodeAsmentionedearlier,itispossibleto ndmanysuchdistributions.approachestoloadhavebeenadoptedin[24,11].nextsection,itwillbeshownthatwecanpickdatadistributionthatcanalsoguaranteecon\rict-freetransfersinthenetwork.CommunicationSchedulingTheissuesaddressedinthissectionarespeci ctothenetworkofthesystem.Asmentionedearlier,wewillOmeganetworkasanexamplemulticomputerinterconnectionnetwork.ThisproblemaroseoutofaneedtobuildaVODserveronanIBMSP2machinethatemploysanOmeganetworkasaninterconnectionfabric.Thesolutiondescribedisdirectlyapplicabletohypercubenetworksaswell.Thesametechniquecanbeemployedto ndasuitableforothernetworks.Wewillshowthatthemoviedistributionsequencecanbecarefullychosentoavoidcommunicationcon\rictsinthemulticomputernetwork.Theapproachistochooseanappropriatesequenceofstoragenodessuchthatifmoviestreamscanbescheduledinslotofaframewithoutcommunicationthentheconsecutiveblocksofthosestreamscanbescheduledinslotwithoutcommunicationnodes;s;:::;ssuchthatgivenasetofnodes;sthataresource,destinationandnetworkcon\rict-free,itisautomaticallyguaranteedthatthesetofnodes;sarealsoautomaticallysource,destinationandnetworkcon\rict-free.First,letusreviewtheOmeganetwork.showsamulticomputersystemwith16nodeswhichinterconnectedbyswitchbetweenanynodes. isanOmeganetworkconstructedoutof4x4switches.Torouteamessagefromasourcenodewhoseaddressgivenbytoanodewhoseaddressgivenby,thefollowingprocedureemployed:(a)shiftbytwobitsproduce(b)useswitchthatstagetoreplace(c)repeatabovetwostepsforthenexttwobitsoftheaddress.Ingeneral,steps(a)and(b)arerepeatedasmanytimesasthenumberofstagesinthenetwork.Networkcon\rictsariseinstep(b)oftheaboveprocedurewhenmessagesfromtwosourcesneedtobeswitchedtothesameoutputofaswitch.Now,guaranteeingnetwork;sgiventhattheset;siscon\rict-free.OurresultisbasedonthefollowingtheoremofOmeganetworks.Theorem1nodes;scon\rict-free,nodesisnetworkcon\rict-free,foranyProofReferto[5].Theabovetheoremstatesthatgivenanetworkcon\rict-freescheduleofcommunication,thenauniformshiftofthesourcenodesyieldsanetworkcon\rict-freeschedule.Thereareseveralpossibilitiesforchoosingastoragesequencethatguaranteestheaboveprop-erty.Asequenceof0,1,2,....,N-1isoneofthevalid-asimplelookatanexample.Theset(0,0),(1,1),(2,2),...,(14,14),(15,15)ofnetwork-storagenodesiscon\rictfreeoverthenetwork(identitymapping).Fromtheabovetheorem,theset(1,2),(2,3),...,(14,15),(15,0)isalsocon\rict-freeandcanbesoveri ed.isthecon\rict-freescheduleinaslotbetheschedulein,whichisalsocon\rict-free.Wehaveshownmovieblockse ectivedi erentpointsdi erentmoviessolvesmovieschedulingmovie,communicationschedulingNow,theonlyquestionthatremainstobeaddressedishowdoesoneschedulethemoviestreamwhichmoviebearrivesnode,we rstdetermineitsstartingnodebasedonthemoviedistribution.Welookateach availablescheduledmoviesnotcon\rictforcommunicationwiththispair.Wesearchuntilwe ndsuchaslotandschedulethemovieinthatslot.Then,thecompletelengthofthatmovieisscheduledwithoutanycon\ricts.AnexamplescheduleisshowninFig.Thesystemhas4nodesinterconnectedbyanOmeganetworkshownnodes,containsmoviesA,B,C,D,andE.ThedistributionofmoviesA,B,C,D,Eacrossthenodes0,1,2,and3isshownin4(b).Forexample,movieCisdistributedacrossnodesintheorderof2,3,1,and0.Forthisexample,wewillassumethattheframelengthF=3.ConsiderschedulingfollowingMovieCbynetworknode0(ii)movieArequestedbynode1inslot1(iii)movieErequestedbynode3inslot1(iv)movieBrequestedbynode3inslot2(v)movieArequestedbynode1inslot3.Since(i)isthe rsttherequest,itcanbescheduledwithoutanycon\ricts.Weschedulethe rstblockofthemovieCfromstoragenode2tonetworknodeslot0.SubsequentblocksmoviescheduledshownEachrowscheduleshowsblocksreceivedbynodedi erententriesmovieandtheidofthesendingnode.Therequest(ii)formovieAcanbescheduledinslot1sincenodesinvolved0andslot1.moviecannotbescheduled1sincecontendsforthestoragenodeas(ii).Wescheduletimeslot2.Request(iv)formovieBrequiresservicebetweennodes1and3inslot2.Thiscausesacon\rictatthenetworknodewithrequest(iii)inslot2.Wecanschedulerequest(iv)intimeslot3sincethereisnocontentionbetweenalreadyscheduledmoviestream(i)inthatslot.Request(v)formovieAintimeslot3contendswiththealreadyscheduledrequest(iv)inthenetworkintimeslot3.Lookingforward,we ndthatrequest(v)canbescheduledtimeslot8(networknode1busyintimeslot4,networkcon\rictwith(3,1)intimeslot5,storagenodecon\rictintimeslot6,networknodehowschedulingtakesavoidingnodesnetwork.beschedulestreams,weonlytheproblemofschedulingthe rstblockwithoutanycon\ricts.Onceacon\rict-freeslotisfoundforthe rstblock,therestofthemoviedidn'thaveanycon\rictswiththealreadyscheduledSchedulingProcessWehaveproposedtousethepacket-switchednetworkofIBM'sSP2inatime-divisionmultiplexingmodetoguaranteedelayboundsonindividualtransmissions.Doesthisapproachutilizethenetwork 14 00 Example4-nodeVODsystem.Movie/BlocksMoviedistribution. Req/Movie.Sender Slot0 1 2 3 4 5 6 7 8 9 10 11 0 2i 3i 0i 1i 1 0ii 1ii 2ii 0v 3ii 1v 2 3 0iii 1iv 1iii 2iv 2iii 3iv 3iii Completeexampleschedule. resourcesoptimally?Isitpossiblethattheproposedapproachfailsincaseswherepacketswitchedoperationmaye ectivelyguaranteetherequireddelaybounds?Inthissection,wewillshowthattheproposedapproachisoptimalinutilizingnetworkresources.Assumethattherearestoragenodes,andnetworknodes(ornodesthatarebothstoragenodes)bynetwork.Nodesnumbered;::;NMoviesintoblocksbetweennodes.blockmoviemaynodedi erentmoviesdi erentnodes).However,whichblocksbetweennodesweassume,withoutlossofgenerality,thatifagivenblockofamovieisatnode,thenextblockisatdatanode+1(modNAframehasslotsandeachmoviestreamneedstobeservedonceineachframe.Astreamissaidtobeschedulableifthestreamcanbescheduledwithnocon\rictsatthestoragenode,networknodeandinthenetwork.schedulelegaleverymovieservedeach(data-node,network-node)havecommunicateeachbebyedge-disjointpathsonthenetwork.Alegalscheduleguaranteesthateachscheduledmoviestreamreceivessucientscheduledtakewithoutanycon\rictinthenetwork.proposedschedulingprocess:scheduledpossiblewhichnetworknodebebydisjointnodeblockmovie,changinganyscheduledcommunication).Oncecommunicationforthe rstblockhasbeenscheduled,subsequentcommunicationstepsarescheduledatintervalsofexactlyverifyscheduleschedulingprocess,moviescheduled.moviestreamneedscommunicationpairs()wouldhaveshiftedto(+1Fromtheorem1,ifthesetiscon\rict-free,thentheset+1isalsocon\rict-freeandhencethescheduleislegal.Weproveschedulingproceduregivesnetworkbandwidth. Sinceeachmovieneedstobeservicedatleastonceineachframe,andadatanodecanserveonlyonerequestperstep,itisclearthatnocommunicationprocess(packetroutingorcircuitswitching)pernetworknodeeachfollowingprovesaboveschedulingprocessanypernetworknode,thusprovingthattheproposedpolicyprovidesasmuchbandwidthasanyotherschedulingprocedureforthisproblem.Claim1Letbedirectedin-degreeout-degreeeachinternalnodeinareequal.Assumethatasetofinputsinareconnectedbyedgedisjointpathnodedoesparticipateinanypath.Therepath,edgedisjointfromalltheexistingpaths,connectingsomeoutputnode.Proof:Nodetosomeinternalnode.theindegreeofthatnodeoutdegreeithasafreeoutgoingedge.Eitherthisout-goingedgeisconnectedtoanoutputnode,oritisconnectedtoanotherswitch.Repeatingthisargumentweeventuallyobtainapathfromtoanoutputnode,thatisdisjointoftheotherexistingpaths.networkbeportsnodesbeingbyunidirectionaltotheinputportsofthenodesasshowninHencegivenanysetofexistingedge-disjointtransfersthroughthenetwork,wecanconnectanidlestoragenode(outputport)toanidlenetworknode(inputport)withoutanycon\rictswithinthenetwork.Theorem2streamsalreadybeenscheduled,nodeprocessingrequests.nodemorerequests,requestcanbesatis edNkfromtransmittingthe rstblockofanymovieisNkProof:arrivednoderequests,thereisaslot,intheintervalt;t+1;:::;t1inwhichnodeisnotactive.theOmeganetworksatis estheconditionsoftheabovefact,canbeconnectedatslottosomeoutputnodeAttimecanbeconnectedtooutputnode+1(modN)andsoon.Thus,thereisaslotintheintervalt;:::;tNk1inwhichnetworknodecanbeconnectedtothedatanodethatcontainsthe rstblockoftherequestedmovie,andtherestofthemovieisscheduledinintervalsof aboveweschedulenetworknodeslotsinaframeisnotbusyatthatnetworknode.Sinceeverytransmissionrequiresthedatabesentfromanode,networkresourcesbeWepresentsimulationsgivedelaysmaybeexperiencedemptyi.e.,latencyforschedulingthe rstblockofthemoviestream.SimulationOuranalysisoftheschedulingalgorithmhasshownthattheproposedpolicyisoptimalinutilizingnetworkresources.Thissectionpresentssimulationresultstoshowthatsatisfactorylatenciesbeachievedforstartingamoviestreamusingsuchanapproach.Wesimulateda16-nodeOmeganetworkswitches.containmovies.moviesaredistributeduniformlyacrossallthenodesinthesystemwiththestartingblocksofthemoviesnodes.arrive(network)nodes.Severaldi erentmoviesareconsideredasdescribedbelow.WeblockKbytes.Atto256KB/200KB/s=1.28seconds.Aslotof6.4ms(with40MB/secsustainednetworkthroughputofIBMSP2,256KB/40MB/s=6.4ms)waschosen.Sincethesizeoftheframeintegermultipleofslot(1.28sec/6.4ms=200),noadjustmentsofslotwerenecessary.16nodessystem'scapacity16*200=3200moviewassimulatedsuch80%ofweredeliveringmovieWewillshowlaterthatathigheroperatingpoints,movieschedulabilitydecreasesrapidly.At80%capacity,2560moviestreamsarescheduled.Wesimulatedscheduling2560randommoviereachoperatingcapacity.operatingpointreached,scheduledmovieprobability)schedulemovienetworknodes.movies,wouldblockmovie.scheduledsoonaspossiblewithoutalteringthescheduleofthestreamsscheduledmovieschedulingfollowedtheproceduredescribedlooksatalltheslotswherethestoragenodeblockmovienetworknodeblockbescheduledscheduledstreamsinnetwork(bothswitcheswemaintainoperatingcapacityat80%.Thelatencyrequiredtoschedulethe rstblockofthenewlygeneratedrequestisnoted.Wegenerated100,000suchnewrequests(alongwithdeletionsofoldrequests). 18 |||||||||||||||||||||||||||| Latency frequency Startuplatencydistributionat80%operatingcapacity.scheduleblockperformanesimulations.arrives rstblockofthestreamisscheduled,thenstartuplatencyThelatencysuchshownbeobserveverypercentageexperiencingWeaveragepercentileshownTableobservedaverageobservedbythenewrequestsislow,than171ms.Veryfewrequests,lessobserveabove0.960seconds.forstartingblockofamovieinavideoserver.Sinceourgoalinthispaperisavideo-on-demandservice,eventhemaximumlatencyof2.61secondsisquitetolerableforstartingamovie.Itispossibletoreducethislatencyfurtherbyshiftingalreadyscheduledstreamsaround(withoutviolatingtheirdeadlinerequirements)makeroomforbeenshownthatsuchtechniquesquitee ectiveinreducingthestartuplatenciestoafewslots[25]. Table1.Startuplatencydistributionwithuniformmoviedistribution. Performancemeasure slots seconds Averagelatency 26.757 0.171 90-percentile 65 0.416 95-percentile 89 0.570 99-percentile 150 0.960 Maximumlatency 408 2.611 Table2.Startuplatencydistributionwith95-5moviedistribution. Performancemeasure slots seconds Averagelatency 26.963 0.173 90-percentile 65 0.416 95-percentile 90 0.576 99-percentile 151 0.966 Maximumlatency 436 2.791 Tostudytheimpactofdi erentdistributionsofrequeststomoviestreams,weconsideredfollowingcases:(1)80%oftherequestsgoto20%ofthemovies(2)90%oftherequestsgoto10%ofthemoviesand(3)95%oftherequestsgoto5%ofthemovies.Theresultsforthesethreecases,fromastatisticalpointofview,wereidenticalasshowninTableInTables1and2,x%oftherequestsexperienceastartuplatencydelaybelowthex-pecentilelatencyshown.Eventhoughtherequeststomoviesarenonuniformlydistributed,theblockrequestswereuniformlydistributedamongthenodessincethemovieswererandomlydistributedamongthenodes.Themovieswererankedblockmovieswereamongthenodesoftheirevenlynodesbyfrequentlymoviesnodes.Forexample,the95-5distribution,320moviessystem,mostfrequentlywatchedmoviesmoviesmovies.weblocksmoviesacross16nodesandthestartingblocksofother95%ofthemoviesuniformlyacross16nodes,itispossibletomaintainauniformloadacrossallthenodes.Fromtheresults,itisobservedthattheaverageswereslightlyhighercomparedtoresultsinTable1,butnotsigni cantlydi erent. 20 |40|50|60|70|80|90|100|1|2|3|4|5|6|7|8|9|10|20|30|40|50|60|70|80|90|100|200|300|400|500|600|700|800|900|1000 Operating capacity Average/99-percentile latency____ average latency Impactofloadonstartuplatency.Sofar,wehaveconsideredasystemthatisoperatingat80%capacity.Wevariedtheoperatingcapacityfrom50%to90%tostudytheimpactofloadontheresults.showstheimpactonaveragelatencies(solidlines)and99-percentilelatencies(dashedlines)astheoperatingcapacityisvariedfrom50%to90%withdi erentloadimbalances.Atlowoperatingcapacitiesofupto70%,lowvarysigni cantly.beyond,growconsiderably.possiblelowerbytoaextent.overdesigningovercon guringthesystem.Toseetheonschedulability,wecreatedloadimbalanceacrossthenodesevenlynodesmoviesstripednodesmovieeverynodeplayback.Tocreateimbalancedload,weconsideredasystemwheredataisstripedacrosstwosetsofN/2nodes6.3forhowbeexperiments, 21 50-50 \r 55-45 60-40 65-35 |40|50|60|70|80|90|100|0.0|0.5|1.0|1.5|2.0|2.5|3.0|3.5|4.0|4.5|5.0 Operating capacity % Unschedulable requests \r\r\r\r Impactofloadonstreamschedulability.nodesreceivedx%oftherequestsandtheotherhalfofthenodesreceived(100-x)%oftherequests.Whenx=50%,thesystemisloadbalanced.Whenx=60%,halfthenodesreceived60%oftherequests,andtheotherhalfofthenodesreceived40%oftherequests,resultinganimbalancedWevaluesnodesnearlytwiceasmanyrequestsastheotherhalfofthenodes.showsthenumberofrequeststhatcouldnotbescheduled(outof100,000attempted)Atbescheduled,speciallythesystemisnotloadbalanced.Evenat90%ofoperatingcapacity,thenumberofunschedulablebelowoperatingcapacitybescheduledevenimbalancedpointimportancekeepingbesupportnumberstreams(operatecapacity)o erbetterimbalanced ClockSynchronizationpaper,thattheclocksnodessomehowsynchronizedandthattheblocktransferscanbestartedattheslotboundaries.Ifthelinkspeedsare40MB/sec,ablocktransferof256Kbytesrequires6.4ms,quitealargeperiodoftimecomparedtotheprecisionofthenodeclockswhichtickeveryfewnanoseconds.Iftheclocksaresynchronizedsaynodesobserveboundariespossiblethattheblocktransfersobservecollisionsthenetwork.Butduringtherestblocktakeanycontentionovernetwork.showsclocksynchronizationrequirementsverypossiblesynchronizeclockssuchlevelbypacketintervalsnodesswitchnetwork.nodesmachinecanbesynchronizedtowithinafewmicrosecondsofeachother[26].Di erentWehaveassumedthatalltherequeststeamsrequirethesamedataratefromthesystem.However,duetodi erentcompressionstandardsorduetodi erentqualitiesofcompression,di erentstreamscanhavedi erentdataraterequirements.Givenastreamrateandthedesignparameterofframesize,wecancalculatetheamountofdatathathastoberetrievedbythesystemtokeeptheclientbeaccommodateamountForforrealizing3Mbits/secstreamrate,2slotsareassignedtothesamestreamwithinframeifaslotcanfetchenoughdatafora1.5Mbit/secstream(asinourearliertwoslotsarescheduledasiftheyaretwoindependentstreamsmakingsurethattheassignedsecondslotisnotmorethanhalfaframebehindthe rstslot(otherwise,streamstarvationresults).networknodenumberblockdi erentlythanwithastreamatbasicrate.Whentherequiredstreamrateisnotamultipleofthebasicstreamrate,asimilarmethodcanbeutilizedwiththelastslotofthatstreamnotnecessarilytransferringacompleteblock.Thecomplexityofbu ermanagementincreasesatthenetworknode. Di erentnetworknodesnodesWehavenodesnetworkcombinationnodes.Evenpossiblenetworknodesnodesmulticomputernodesguaranteenetworkcon\ricts.Fornetworknodesevennodesoddnetwork,themoviesinround-robinfashionamongthestoragenodesyieldsguarantees.Forstoragenodestoaddressesof(0,networknodes8-nodenetworkprovidesguarantees.communicationmovienodefollow...(1,0),(1,2),(1,4),(1,6),communicatingfollowedby+2)modNinthenextframeandhencebytheorem1(withshifta=2)areguaranteedtobecon\rictfreeiftheoriginalsetwascon\rict-free.itcanbeshownthatitispossibletoprovidecon\rict-freedeliverywhendataisstripedacrosshalfofthestoragenodes.ChoosingIdeally,wewouldlikeblockHowever,variationsdeliveryblockmayTransferdelayvariationsareminimizedbytheproposedapproachthroughcarefulschedulingandminimizationofnetworknetworkadaptersvariationsdeliverytimeduetomemorybandwidthcon\ricts.Whenthetransfertimeexceedsaslot,di erenttransfersmaycontendforthesamelinkinthenetwork.Toavoidsuchproblems,itwillbenecessarytooverestimatetheslotsize.Itisalsopointedoutearlierthattomaketheframeanintegralmultipleoftheslotsize,wemayhavetooverestimatetheslotsize(sinceexactvaluesmaynotbemultiples).Thislargerslotsizewouldalsomitigatethepossiblee ectsofthedriftamongclocksatthenodesinthenetwork.CommunicationOverheadnodescommunicationpatterns.Forexample,anetworknodeservingamoviestreamcommunicateswithnodespossiblelocalizecommunicationtoasmallsetofnodes.Forexample,ifthemovieisstripedacross4nodesofthe system,thenetworknodewouldonlyhavetocommunicatewiththose4storagenodes.However,localizationachievedmoviesnodes.Thenumberofstreamstomoviesonthese4storagenodeswillbelimited.Thislocalizationimbalancenodeimbalancecommunicationacrossthenetwork,storagenodeswithpopularmoviesreceivingmoredemandthanothers.above,makestheatthenetworkmakingiteasiertoschedulestreamsforguaranteedservice.ItisalsotobepointedoutthatinmultistageinterconnectionnetworkssuchasanOmeganet-work,communicationbetweenanypairofnodestakesthesamenumberofhops(linksandswitches)network.Localizationbene tsuchnetworks.However,networkssuchhypercubes,bene tlocalizationcommunicationInterconnectionNetworksproposedmaybeemployedevenmulticomputerinterconnectedbyanetworkotherthananomeganetwork.Toguaranteecon\rict-freetransfersoverthenetwork,networkshavebeForhypercubetypenetworksthatcanemulateanomeganetwork,samedatadistributionprovidesguaranteesnetwork.beshownmovieblocksovernodesahypercube;:::;ndi erentnodes),scheduleslotguaranteesthattheoftransfersrequiredaframelaterwouldalsobecon\rictfree.Oracle'smediaserverusesNCube'shypercubemachine[14].SummaryschedulingForeachnetworknodenodethatblock.EachstoragenodeservestherequestwiththeearliestThenetworkalsoneedstoimplementdeadlineschedulingforswitchingpacketsthroughthenetwork.Also,evenifallthecomponentsofthesystemcouldimplementscheduling,thefollowingissueswillremaintobeaddressed:(a)itispossiblefortwostoragenodestoinitiatetwotransfersthatcollidenetwork.delayedschedulingemployed thusidlingthatstoragenode)orboththetransferstaketwiceaslongifround-robinschedulingemployed.thisscenario,schedulingarebeingindependentlyatthestoragenodesswitchesnetwork.Howdoesavoidsuchhowdoescentralizeddeadlinescheduling(withouttheknowledgeofthecurrentpacketsinthenetwork)?whenshouldamoviebestarted?Ourapproach/solutionaddressedalargenumberoftheseissueswhichremaintobeaddressedapproaches.paper,wepresentedmovieschedulingandcommunicationschedulinginamulticomputervideoserver.Thesolutionisproposedintwostages.The rststeparguedthatasimpleregularpatternforstoringmoviesacrossstoragenodeswithdi erentstartingnodescanreducethemovieschedulingproblemtoasimplerproblemofschedulingthe rstblockofthemoviewithoutanyadversea ectsoftheearlierproposals.secondstepconsistsofderivingsuchasequencesuchthatcommunicationcon\rictsareminimizedinthenetwork.Weexploitedthenetworktopologyofthemulticomputertoderivesuchasequencethatguaranteesfreedomfromcommunicationcon\rictsifthe rstblockofthemovieisscheduledwithoutanycommunicationWepresentedextensivesimulationtoshowthee ectivenessproposedapproach.Weworldsuchclocksynchronization.Wehaveshownbemaybepresent,proposedbepointforreducing(ratherthanguaranteeingfreedomfromcollisions)thecommunicationschedulingproblemsinavideoserver.AcknowledgmentshavecontributedReviewerscommentshavehelpedtoimprovethepresentationofthepaper. 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