Communication Architectures and Algorithms for Media Mixing in Multimedia Conferences

MediaMixinginMultimediaConferences

P.VenkatRangan,HarrickM.VinandSrinivasRamanathan

MultimediaLaboratory

DepartmentofComputerScienceandEngineering

UniversityofCaliforniaatSanDiego

LaJolla,CA92093-0114

E-mail:venkat,vin,sramanat@cs.ucsd.edu,Phone:(619)534-5419,Fax:(619)534-7029

Abstract

Advancesincomputerandcommunicationtechnologieshavestimulatedtheintegrationofdigitalvideoandaudiowithcomputing,leadingtothedevelopmentofcomputer-assistedmultimediaconferencing.Weaddresstheproblemofmediamixingwhicharisesintele-conferencingapplicationssuchastele-orchestra.Wepresentamixingalgorithmwhichminimizesthedifferencebetweengenerationtimesofthemediapacketsthatarebeingmixedtogetherintheabsenceofgloballysynchronizedclocks,butinthepresenceofjitterincommunicationdelaysonpacketswitchednetworks.Thealgorithmisshowntobecomplete:giventhattherearenoothermessageexchangesexceptmediadatabetweenmixersandmediasources,therecannotbeanyotheralgorithmthatsucceedswhenouralgorithmfails.Mixingcanbeaccomplishedbyseveraldifferentcommunicationarchitectures.Inordertosupportapplicationssuchastele-orchestra,whichinvolvealargenumberofparticipants,weproposehierarchicalmixingarchitectures,andshowthattheyareanorderofmagnitudemorescalablecomparedtopurelycentralizedordistributedarchitectures.Furthermore,wepresentmechanismsforminimizingthedelaysincurredbymixinginvariouscommunicationarchitectures.WehaveimplementedthemixingalgorithmsonanetworkofworkstationsconnectedbyEthernets,andhaveexperimentallyevaluatedtheperformanceofvariousmixingarchitectures.Theseexperimentsrevealedinterestingresultssuchasthemaximumnumberofparticipantsthatcanbesupportedinaconference.

1

1Introduction

1.1Motivation

Untilrecently,voice,video,anddatacommunicationshavebeenhandledbydifferentcommunicationnetworks.Theprimarycarrierofvoicehasbeenthepublicswitchedtelephonenetwork,videohasbeentransmittedbycableTV,anddatahasbeenhandledbyspecializedcomputernetworks(LANsandWANs).Thishistoricalseparationcanbeattributedtofundamentaldifferencesincharacteristicsofvoice,videoanddatatraffic.Voiceandvideocharacteristicssuchassensitivitytodelay,highbandwidthrequirement,andtheabilitytotoleraterelativelyhigherrorratesareincompletecontrastwithrequirementsofdata.Hence,voiceandvideotransmissionusecircuitswitchingofanalogsignals,whereasdatatransmissiontypicallyusesdigitalpacket-switchednetworks.

Interestin‘integrating’thesedifferentmediahasbeenstimulatedbyadvancesincommunicationandcomputertechnologies.Advancesincommunicationtechnologyhavemadeavailablelargebandwidthatmodestcost,whereasadvancesincomputertechnologyhaveresultedinthedevelopmentofhigh-performanceworkstationswithaudioandvideocapabilities.Theseadvanceshaveledtothefeasibilityofsupportingmanymultimediaapplicationsoncomputersystems.

Onesuchclassofapplicationsismultimediaconferencing,whichpermitsindividualstocarryoutcollaborativeactivitiesbyexchangingaudio,video,andtextinformationthroughmultimediaworkstations.Therearevariouskindsofconferences,amongwhichthemostdemandingones(intermsofperformance)arethoseinwhichvideoandvoicestreamsarebeingcontinuouslytransmittedbyindividualsintheconference,andtheindividualvideoimagesandvoicestreamshavetobemixedtogethertoobtainacompositeimageandaudiostream.Anexampleofsuchanapplicationisatele-orchestra,inwhichalargenumberofperformersarecontinuouslyplayingtheirrespectivemusicalinstruments,eachathisorherownmultimediaworkstation.Theaudiostreamsbeingreceivedfromalltheperformersneedtobecontinuouslymixedsoastoyieldacoherentmusicalcomposition,andthenbroadcasttotheentireaudience(whichmayalsoconsistofindividualsreceivingaudioattheirrespectiveworkstations).

Thetechniquesformixingdependuponthetypeofthemediaaswellastheapplication.Inthecaseofaudio,mixingmultiplestreamsinvolvesdigitallysummingtheaudiosamplesandthennormalizingtheresult.Inordertoeliminateone’sownfeedback,eachparticipant,onreceivingamixedaudiopacket,removeshisowncontributionbeforeplayingitback.Inthecaseofvideo,whereasitispossibletosimplyjuxtaposethedisplayofmultiplevideostreamswithouthavingtomixthem,applicationssuchastele-virtualconferencingmaybenefitfromthemixingofindividualvideostreamstosynthesizetheimageofavirtualmeetingroom.

Theneedtocontinuouslymixmediastreamsfromseveralsources,coupledwiththereal-timenatureofthemediaposesspecialrequirementsformediatransmissionprotocols.Thedesignofalgorithms,protocols,andcommunicationarchitecturesforsupportingmediamixinginmultimediaconferencesisthesubjectmatterofthispaper.

2

1.2RelatedWork

Inrecentyears,therehavebeenmanyeffortstowardsintegratingmultimediaconferencingintocomputersystems.Lantz[3]proposesatext/graphicsconferencingarchitecturewherethebasicgoalistofitintoexistingsystemswithminimalimpactontherestofthesystem.SarinandGreif[6]havestudiedconferencingarchitecturesfortextandgraphics,buttheirsystemdoesnotincludeaudio.Aguilaretal.atSRI[1]haveproposedarchitecturesforperson-to-personvoiceconferencing.Ziegleretal.[8]presentananalyticalperformanceevaluationofvoiceconferencingonbroadcastandringnetworks.AhujaetalatBellLaboratories[2],andSwinehartetal.atXeroxPARC[4]haveproposedarchitecturesforvideoconferencing.However,theemphasisofallofmostoftheseeffortshasbeenperson-to-persontelephony-typeconferences,andhighperformanceapplicationssuchastele-orchestrawhichrequirecontinuoustime-criticalmixingofmediastreamsfromseveralsourcesarenotsupported.Algorithms,protocols,andcommunicationarchitecturesforsupportingmediamixinghavenotreceivedmuchattention.

1.3ResearchContributionsofThisPaper

Inthispaper,weaddresstheproblemofmixingmediastreamstransmittedbymultiplesourcesinamultimediaconferenceonapacket-switchednetwork.Owingtothereal-timenatureofthemediabeingmixed,packetsfromdifferentsourcesgeneratedataboutthesametimearerequiredtobemixedtogether.Moreprecisely,forcoherentreproductionofaudioandvideoinapplicationssuchastele-orchestra,orformaintainingconsistentorderingofuser-triggeredeventsindistributedreal-timegames,thedifferencebetweenthegenerationtimesofpacketsbeingmixedmustbeminimized.Reductioningenerationtimedifferencesalsoreducesthewaitingtimeofpacketsduringmixing,leadingtolowerbufferingrequirements.Wepresentamixingalgorithmwhichminimizesthedifferencebetweengenerationtimesofthemediapacketsthatarebeingmixedtogetherintheabsenceofgloballysynchronizedclocks1,butinthepresenceofjitterintransmissiondelays.Thealgorithmisshowntobecomplete:giventhattherearenoothermessageexchangesexceptmediadatabetweenamixerandthemediasources,therecannotbeanyotheralgorithmthatsucceedswhenouralgorithmfails.

Mixingcanbeaccomplishedbyseveraldifferentcommunicationarchitectures.Inordertosupportappli-cationssuchastele-orchestra,whichinvolvealargenumberofparticipants,weproposehierarchicalmixingarchitectures,andshowthattheyareanorderofmagnitudemorescalablecomparedtopurelycentralizedordistributedarchitectures.Furthermore,liveperformancessuchastele-orchestrarequirethateachperformerre-ceivestheaudioplayedbyotherperformersalmostinstantaneously.Towardsthisend,wepresentmechanismstominimizethereal-timedelaysincurredbymixinginvariouscommunicationarchitectures.

WehaveimplementedthemixingalgorithmsonanetworkofworkstationsconnectedbyEthernets,andhaveexperimentallyevaluatedtheperformanceofvariousmixingarchitectures.Theseexperimentsrevealedinterestingresultssuchasthemaximumnumberofparticipantsthatcanbesupportedinaconference.

3

Therestofthepaperisorganizedasfollows:InSection2,weformulatetheproblemofmixing.InSection3,wepresentalgorithmsformixingtwomediasources,andinSection4,weextendthemtomorethantwosources.InSection5,weanalyzevariouscommunicationarchitecturesformixing,andinSection6,wepresentmechanismsforminimizingreal-timedelaysduetomixing.Section7presentsourexperiencewithimplementingthemixingalgorithms,andfinally,Section8concludesthepaper.

2ProblemofMediaMixinginConferencing

Initssimplestform,amultimediaconferenceisestablishedbysettinguplogicalmediacommunicationchannelsamongagroupofparticipants.Onceaconferenceisestablished,mediainformationcanbeexchangedamongitsparticipants.Inamulti-partyconference,eachparticipantmustreceivethecompositemediastreamobtainedbymixingthemediastreamstransmittedbyalltheotherparticipants.

Inapacketswitchednetworkenvironment,animportantproblemistodeterminethesetofpacketsfromdifferentsourcesthataretobemixedtoformacompositemediapacket.WecallsuchasetofpacketsastheFusionSet.Ifeachsourcegeneratesmediapacketsataconstantratewithaperiodof,thenthesmallesttime

windowduringwhichtwoindependentsourcesareguaranteedtogeneratepacketsis

.(Theproofisbyasimpleinductiononthenumberofsources).If

2

1

isunbounded,thesmallest

windowduringwhichweareguaranteedtohavepacketsfromeachofthesourcesis.Thisisformalizedbythefollowingmixingruleforamulti-partyconference:MixingRule:Packets

1

and

2

canbelongtoaFusionSet(i.e.,canbemixedtogether)ifandonlyif

1

2

1

where

istheperiodofgenerationofmediapacketsatasource,and

1

and

2

arethegeneration

timesofpackets

1

and

2

attheirrespectivesources.

Thefusionsetcanbedeterminedinastraight-forwardmannerwhentheclocksofthegeneratingsourcesaregloballysynchronized.However,clocksynchronizationrequiressophisticatedprotocolsfornegotiationandagreementamongmediasources.Weassumethatthemediasourcescandigitize,packetize,andtransmitdataonthenetwork,butmaynothavethesophisticationtoexchangecontrolmessagesandruncomplexprotocols.Hence,anyprotocolthatrequirestheexchangeofmessagesotherthanmediadataisoutofquestion.Furthermore,theoverheadofclocksynchronizationprotocolsmaybeexcessivecomparedtosimplerprotocolsthataresufficientfordeterminingafusionset.Hence,determinationofafusionsetintheabsenceofgloballysynchronizedclocksisanimportantproblemthatneedstobesolvedinmultimediaconferencing.

4

3AlgorithmsforMediaMixing

Consideramultimediaconferenceinwhichthereare

sources

1,

2,...,

(seeFigure1).Eachsourcegenerates

mediapacketsataconstantratewithperiod,andtransmitsthemtoamixernodes,beboundedbetween∆generatedbyasource

.Letthecommunicationdelay

fromasourcetoamixer,whichincludestransmissiontimesonthenetworkandqueuingdelaysatintermediate

and∆

.If

isthearrivaltimeatthemixerofapacketnumbered

,thentheearliestandthelatestpossiblegenerationtimes(denotedby

and

,

respectively)ofpacket

canbederivedas:

∆

23

∆

Measuredonthemixer’sclock,thegenerationtimeinterval

ofamediapacket

atsource.

belongstothe

,whichisreferredtoasthegenerationintervalofpacket

Arrival timesτ1Packet numbersn1n2S1S2SsMτsnsτmτ2nmSmFigure1:Mixinginamultimediaconference.MixerAstraightforwardmechanismforthemixerfromsources

mixespacketsfromsources

1

tocarryoutmixingistobufferthemediapacketsitreceives

1,

2,...,

,untilatleastonepacketisreceivedfromeachofthem,atwhichtime,cancombine

allthepacketsandtransmitthemixedpacket.BytheMixingRule,theseparationinthegenerationtimesofpackets(ofdifferentsources)beingmixedtogethercanbeatmost.Inthepresenceofcommunicationdelay

jitter,twopacketsgeneratedandarriveatthemixer

apart(attwodifferentsources)maysufferdelaysof∆

and∆

,respectively,

∆

∆

apart,whichthenisthemaximumwaitingtimeofapacketinthe

2

∆

∆

mayalsoarriveat

mixer’sbuffersbeforebeingmixed.However,sucha“bufferandmix”schemehasseveraldisadvantages:Duetoaquirkoftheeffectofjitter,twopacketsgeneratedasfarapartasthemixerwithinawindowof

∆

∆

,therebymisleadingthemixertocombinethosetwopackets

inviolationofthemixingrule.Higherthejitter(asinwideareanetworks),greateristheextentoftheviolation.Thisproblemgetsfurthercompoundedinthepresenceofpacketlosses.Forinstance,whilemixingpacketsfromthreesources

1,

2,and

3,packetlossmaycausethemixertoderivefusionsetsinapairwisemannerfor

5

1

2

and

2

3

,eachofwhichmaycontainpacketsmaximallyseparatedintheirgenerationtimes(i.e.,

by

2∆

∆.Inordertomixpacketsfromallthreetogether,ifthemixertakesaunionofthese

pairwisefusionsets,packetsseparatedasfarapartas22

∆

∆

maygetmixedtogether,and

thisseparationmayincreaselinearlywiththenumberofsources.Ontheotherhand,ifthemixerdecidestoderiveanewfusionsetcontainingmorecloselygeneratedpacketsfromallthethreesources,itmaybefloutingtherequirementofmaintainingconsistentrelativeorderingofpacketsinsuccessivefusionsets.

WenowproposeamixingalgorithmwhichguaranteesthatthepacketsbeingmixedtogetheralwayssatisfytheMixingRule,firstforthecasewhenthereareonlytwomediasources(i.e.,abinarymixing),andthenextendittoacasewhentherearemultiplemediasources(i.e.,aM-arymixing).Thealgorithmisrobusttowardspacketlossesonthenetwork.Hence,evenintheabsenceofarrivalofacurrentpacketfromasource,themixercanstillderiveafusionsetwiththehelpofanyearlierpacketreceivedfromthatsource.Thus,thealgorithmeffectivelydecouplesthedeterminationoffusionsetsfromlivemixingofpackets.Anextremevariationofthissituationisthedeterminationoffusionsetsfrompacketstransmittedserially(ratherthan,concurrently)bythevarioussources,whichfindsanimportantapplicationinliveperformances.Inparticular,aliveperformancegenerallyhasaninitialsound-checkperiodprecedingitscommencement,duringwhichamixercansequencethroughthevariousperformers/performinginstrumentspromptingeachofthemtotransmitaaudiopacket,oneatatime.Attheendofthesound-check,themixercomputesthefusionset(inadditionto,ofcourse,carryingoutroutineadjustmentssuchasvolumelevel,tonefrequency,etc.),andkeepsitforlateruseduringtheactualperformance.

3.1BinaryMixingAlgorithm

Letthearrivaltimesatamixerofpackets

1

and

2

fromtwosources

1

and

2

be

1

and

2.Theearliestand

thelatestpossiblegenerationtimesofpackets

1

and

1

2

are:

1

1

∆

1

1

1

∆∆

2

22

22

2

∆

Sincethegenerationtimesofsuccessivepacketsfromthesamesourcearedisplacedby,thegenerationinterval

ofpacket

fromsource

canbeestimatedas:

45

Sincetheexactgenerationtimesofpacketsareunknownatamixer,determinationofabinaryfusionsetwillhavetobebasedontheaboveestimatesoftheearliestandthelatestpacketgenerationtimes.If

6

max

1

1

2

2

and

min

1

1

2

2

,then

1

1

2

2

and

2

2

1

1

.Consequently,if

6

then,thegenerationtimesofpackets

1

and

2

areguaranteedtosatisfytheMixingRule,andhence,packets

1

and

2

belongtoabinaryfusionset.Equation(6)definesastrongerconditionthantheMixingRulefor

determiningafusionset.Nevertheless,sincetheexactgenerationtimesofpacketsareunknownatamixer,determinationofafusionsetwillhavetobebasedonEquation(6)ratherthanontheMixingRule.Hence,intheremainderofthispaper,weuseEquation(6),referredtoastheStrongMixingRule,astheconditionfordeterminingafusionset.

Themaximumuncertainty,intervalsof

inestimatedgenerationtimesisatleastaslargeasthegeneration

1

and

2,eachofwhichequals∆

∆

induration.Hence,

∆∆

Clearly,ifthejitterincommunicationlatency,∆thegenerationintervalsoffrom

and

∆

exceeds,

willalsoexceed,and

1

and

2

cannotsatisfytheStrongMixingRule(Equation(6)).Infact,sincethe

generationintervalofeverypacketequalsthetransmissionjitterinduration,ifthisjitterexceeds,notwopackets

1

2

cansatisfytheStrongMixingRule.Hence,∆

∆

isanecessaryconditionfor

determiningabinaryfusionset.Thisisthefirstresultofimportance,andisformallystatedasProposition1inTable1.

Ontheotherhand,supposethatthejitter∆packets

∆

.Ifitisalsothecasethat

,then

,

1

and

2

formabinaryfusionset.However,if∆

∆,but

,thenitmayseem

likelythatabinaryfusionsetcannotbedetermined.Surprisingly,thisisnottrue;evenwhenintervalsof

and

donotsatisfytheStrongMixingRule,thoseoftwootherpackets

therearesituationsinwhichamixercandetermineabinaryfusionset.Thisisbecause,eventhoughthegeneration

1

2

1

and

2

maydoso.

However,noticethatifpackets

1

and

2

satisfytheStrongMixingRule,sowillpackets

1

and

2

1

1

(because,thegenerationintervalsofsuccessivepacketsfromthesamesourcearedisplacedby).Hence,in

ordertodetermineabinaryfusionset,itsufficestosearchforapacketfromwith

2

thatcanformabinaryfusionset

1.Weshallnowderiveexactlythosecasesinwhichamixercandetermineabinaryfusionsetevenwhen

.

Withoutlossofgenerality,letusassumethatrelativepositionsofthegenerationintervalsof

1

1

2

2

and

1

1

2

2

.Dependingonthe

1

and

2,twopossiblescenariosarise:

Thegenerationintervalsofgenerationintervalsofitcanbeshownthat

1

and

2

overlap(seeFigure2):

Insuchacase,nomatterwhichpacket

2

from

2

isconsidered,bycomparingtheinEquations(4)and(5))and

2

(derivedbysubstituting

2and

1,

2

and

1

donotsatisfytheStrongMixingRule.Thisisthesecondresultof

importance,andisformalizedasProposition2inTable1.

7

eg (n )11lg (n )11Timeeg (n )22lg (n )22Figure2:Packetswithoverlappedgenerationintervals

ge(n )22< p< k * pgl(n )22ge (n )11< pgl(n )11Time< (k + 2) * pFigure3:Mixingofpacketswithdisjointgenerationintervals

Thegenerationintervalsofpositiveintegersuchthathand,isgivenby:

1

and

2

aredisjoint(seeFigure3):

Inthiscase,theirminimumseparation,

1

1

2

2

isboundtobepositive,andlet

1bethesmallest

1

1

1

2

2

.Theirmaximumseparation,ontheother

1

1

2

2

1

1

1

1

1

1

2

2

2

2

2

2

Since

1

1

1

1

2

2

2

2

∆

∆

,weobtain,

1

1

2

2

2

∆

∆

1

1

2

2

Since∆

∆

,weget:

1

1

1

2

2

2

7

ElaborationofEquation(7)yieldsthreesub-scenarios:1.

1

1

1

2

2

:Inthiscase,bycomparingthegenerationintervalsof

2

1

andand2.

2

(derivedusingEquations(4)and(5))withthatof

1,itcanbeshownthatboth

2

1

2

formfusionsetswith

1

1.Wewouldbeutilizingthisresultinderivingacomprehensive:Inthiscase,bycomparingthegenerationintervalof

binarymixingalgorithm,andisformallystatedasProposition3inTable1.

1

1

2

2

2

(derivedagainbyusingEquations(4)and(5))withthatofafusionsetwith3.

1

1,itcanbeshownthat

2

forms

1.Thiswillalsobeutilizedinthebinarymixingalgorithm,andisformalizedas

2

:Inthiscase,nomatterwhichpacket

Proposition4inTable1.

1

1

2

2

2

from

2

isconsidered,acomparisonofthegenerationintervalsof

2

and

1

showsthattheydo

notsatisfytheStrongMixingRule.ThisimpossibilityresultisformallystatedasProposition5inTable1.

8

Proposition1Ifthejitterincommunicationlatency,∆deriveabinaryfusionset.

∆

,thenitisnotpossibleforamixerto

Proposition3Ifthegenerationintervalsofpacketsinteger,

1

and

2

asestimatedbyamixeraresuchthat,forsome

1,

1

1

1

2

2

and

1

1

1

2

2

1

canformabinaryfusionsetwitheitherpacket

2

1orpacket

2

.Wereferto

1

2

1

asthelowerbinaryfusionsetand

1

2

astheupperbinaryfusionset.

Proposition5Ifthegenerationintervalsofpacketsinteger

1

and

2

asestimatedbyamixeraresuchthat,forsome

1,

1

1

1

2

2

and

1

1

1

2

2

2

andthen,itisimpossibleforthemixertodetermineabinaryfusionsetofpacketsfromthetwomediastreams.

Table1:Binarymixingpropositions;rigorousmathematicalproofsofthesepropositionshavebeenomittedforthesakeofbrevity,andcanbefoundin[5].

9

Propositions1-5(seeTable1)yieldpowerfultechniqueswhichcanbecombinedtogetherintothefollowingalgorithmthatamixercanexecutetodetermineabinaryfusionsetwhenitreceivespacketsfromtwomediasources.

BinaryMixingAlgorithm:

Supposethatpacketsthemixer.1.If∆

1

and

2

arriveatthemixerattimes

1

and

2,respectively.Let∆

and∆

be

themaximumandminimumpossibletransmissiondelaysofpacketsonthenetworkbetweenamediasourceand

∆

,thenabinaryfusionsetcannotbedetermined(Proposition1).,computethegenerationintervalsofpackets

2.If∆

∆

1

and

2

tobe

1

1

1

1

and

1

2

2

2

2

,respectively,where,

∆

,

∆

,and

1

12.Without

lossofgenerality,let(a)If

min

1

1

2

2

2

2

and

1

max

1

2

2

1

.

1

1

2

2

,thenthebinaryfusionsetis

2

(byEquation(6).

(b)Ifthegenerationintervalsofpackets(c)Ifthegenerationintervalsofpackets

1

andand

2

overlap,and

1

1

2

2

,thenitisimpossible

1suchthat

1,

forthemixertodetermineabinaryfusionset(byProposition2).

1

2

aredisjoint,andthereexistsaninteger

1

1

1

2

2

,then:

i.If

1

1

1

2

2

,thentwobinaryfusionsetsarepossible:

1

2

whichisthelowerbinaryfusionset,andProposition3).ii.Ifiii.If

1

2

,whichistheupperbinaryfusionset(by

(byProposition

1

1

2

2

1

,thenthebinaryfusionsetis2

1

2

4).

1

1

1

2

2

,thenitisimpossibletodetermineabinaryfusion

set(byProposition5).

3.2CompletenessofBinaryMixingAlgorithm

Theeffectiveness(i.e.,thesuccess)oftheabovealgorithmindeterminingabinaryfusionsetcriticallydependsontherelativevaluesofthetransmissionjitter(i.e.,∆inthefollowingTheorem.

Theorem1Whenamixerexecutesthebinarymixingalgorithmontwopacketsand

∆

),andthepacketduration.Thisisquantified

1

and

2

receivedattimes

1

2,respectively,

(1)if∆(2)If

∆

2,thealgorithmalwaysproducesabinaryfusionset.

2

∆

∆

,thealgorithmmaysucceedorfailindeterminingabinaryfusionset.

(3)If∆

∆

,thealgorithmfailstodetermineabinaryfusionset.

(4)Thealgorithmiscomplete:giventhattherearenoothermessageexchangesexceptmediadatabetweenamixerandthemediasources,therecannotbeanyotheralgorithmthatsucceedswhenouralgorithmfails.

10

Proof:Lettheearliestandlatestgenerationtimesofpackets

1

and

2

becomputedas:

∆

,and

2

∆

,where

12.Again,withoutlossofgenerality,let

2

2

1

1

,and

2

2

1

1

.Hence,ifthegenerationintervalsof

1

and

2

2

overlap,then

2

2

1

1

2

1

1

.

Similarly,iftheintervalsaredisjoint,thenabovetheoremcanbeprovedasfollows:1.∆

2

2

2

1

1

1

1

.Thefourassertionsofthe

∆

2:

Itmaybeobservedthatthelengthsofthegenerationintervals(ofpacketsand

1

and

2),

1

1

1

1

2

2

2

2

areeachequalto∆

∆

,andhenceneitherofthemexceeds

2.Therefore,

1

1

1

1

2

2

2

2

8

Thegenerationintervalscanbeeitheroverlappedordisjoint.Ifthegenerationintervalsoverlap,weobtainthat,

1

1

1

1

2

2

2

2

9

Thus,abinaryfusionsetmixingcanbederivedusingEquation(6).Supposethat,ontheotherhand,thegenerationintervalsofpackets

1

and

2

aredisjoint;thatis,

2

1

1

2

2

1

1

1

1

1

1

2

2

2

2

2

10

Let

beanintegersuchthat:

1

1

1

2

2

11

UsingEquations(8),(10),and(11)weobtainthat,

1

1

1

2

2

1

12

HenceconditionsofeitherProposition3orProposition4aresatisfied,leadingtothedeterminationofabinaryfusionset.2.

2

∆

∆

:

Thelengthsofthegenerationintervalsofpacketsexceed2,butcanlieeitherbetween0and

1

and

2

willeachliebetween

2and,andthe

generationintervalscanbeoverlappedordisjoint.Iftheyareoverlapped,

1

1

2

2

willnot

inwhichcaseEquation(6)yieldsthebinaryfusionset,

orbetweenfusionset.

and2inwhichcaseProposition2showsthatitisimpossibletodetermineabinary

Supposethat,ontheotherhand,thegenerationintervalsofpackets

1

and

2

aredisjoint,thatis,

2

1

1

2

2

1

1

1

1

1

1

2

2

2

2

2

13

11

Let

1beanintegersuchthat,

1

1

1

2

2

14

GiventhatthelengthsofgenerationintervalsarenolessthanEquation(13)and(14)yield:

2butaredefinitelylessthan,

1

1

2

2

2

Hence,eitherProposition4issatisfiedinwhichcaseabinaryfusionsetcanbedetermined,orProposition5issatisfiedinwhichcaseitisimpossibletodetermineabinaryfusionset.Thus,thealgorithmmaysucceedorfailindeterminingabinaryfusionset.3.∆

∆

:

ByProposition1,itisimpossibletoderiveabinaryfusionset.4.Completeness:

Thealgorithmfailstodetermineabinaryfusionsetonlywhen(a)∆(b)

∆

,or

2

∆

∆

and,eitherthegenerationintervalsareoverlappedand

,

ortheyaredisjointbutsuchthat,

1

1

1

2

2

2

,where

1isaninteger

1

1

1

2

2

.

Incase(a),Proposition1showsthatitisimpossibletodetermineabinaryfusionset,andincase(b),Propositions2and5showtheimpossibility.Hence,therecannotbeanyotheralgorithmthatsucceedsinsuchcases,whichgoestoshowthatourbinarymixingalgorithmiscompleteunderthenetworkingassumptionsstatedinSection2.

Intheabovetheorem,thelimitationtotheeffectivenessofthebinarymixingalgorithmarisesduetotheuncertaintyingenerationintervals,whichisatmostthejitterincommunicationdelay.Inpractice,however,amixermaybeabletoreducetheuncertainty(soastobemuchbelowthejitter)byiterativelyrefiningitsestimatesofthegenerationintervals,everytimeanewpacketarrives.Toseehow,supposethat

denotethegenerationintervalsofpackets

fromthatof

fromsource

,predictedfromthatof,

using

Equations(4)and(5).Arrivalofasubsequentmediapacketgenerationintervalsofhence,in

from

enablesthemixertorecomputethe

tobe:

,againusingand

Equations(4)and(5).Theactualgenerationinstantofpacket

isguaranteedtobeinboth

,and

.Therefore,

representsarevisedandpossiblymorepreciseestimateofthegeneration

intervalforpacket

.Surprisingly,theintersectionissmallwhenmediapackets(onwhichestimatesare

based)undergowidelydifferentcommunicationdelays.Inthelimit,theexactgenerationtimecanbedeterminediftheintersectionreducestoasinglepoint,whichcanoccurwhentwomediapacketstransmittedbyasourcesuffernetworkdelaysof∆

and∆

,respectively.

12

4M-aryMixing

Inmultimediaapplicationssuchasatele-orchestra,theremay,ingeneral,bemorethantwomediasources.Inthissection,weextendthebinaryalgorithmtohandlemixingofmediapacketsreceivedfrommorethantwosources.TheresultingM-arymixingalgorithmyieldsfusionsetssuchthattheentirerangeofgenerationtimesofallthepacketsinafusionsetareboundedwithinawindowofSection2).

Letussupposethatamixerhastodetermineafusionsetofpacketssources

(whichistheshortestwindowpossible,asshownin

1,

2,

...,

beingreceivedfrom

1)binaryfusion

1,

2,...,

.Inastraightforwardextensionofthebinaryalgorithm,themixercandeterminethefusion

setforeachofthepairs(1,

2),(

1,

3),...,(

1,

),andtaketheunionofallofthose(

sets.Ifthemaximumofthelatestgenerationtimes,andtheminimumoftheearliestgenerationtimesofallthepacketsintheunionarewithinawindowof,thentheunionconstitutesaM-aryfusionset.

However,recallthatinthebinaryalgorithm,therearescenarioswhentwobinaryfusionsets(lowerandupper)arepossible.Itislikelythat,choosingoneofthetwobinaryfusionsetscanleadtotheformationofaM-aryfusionset,whereaschoosingtheotherbinaryfusionsetdoesnot.Intheworstcase,giventhattherearetwoalternativesforeachbinaryfusionset,thereare2

1

alternativesfortheunionsof

1binaryfusionsets

thatmayneedtobecomputedinthedeterminationofaM-aryfusionset,yieldingexponentialexecutiontimes.

WewillnowpresentanalgorithmthatusesawindowslidingtechniquetoobtainaM-aryfusionsetinalinearnumberofexecutionsofthebinaryalgorithm.

4.1AlgorithmforM-aryMixing

Let

1

1

,

2

2

,...,

bethegenerationintervalsofpackets

min

1,

2,...,

generatedby

sources,

respectively.Let

1

max

1

Withoutlossofgenerality,letthegenerationintervalofpacket(wecanalwaysreplacepacketgenerationtimeofpacket(

1,

1

bedisjointfromthoseofalltheotherpackets

2,

3,

1

by

1,

where

1

1

isanintegersufficientlylargesuchthattheearliest

1

exceedsthemaximumlatestgenerationtimeofpackets...,

1,

).Usingthe(

binarymixingalgorithm,computethebinaryfusionsetsofpacketsfrompairsofsources(

2),1,

3),...,

).Clearly,theremustexistbinaryfusionsetsforeachoftheabovepairsofsources,ifthereexistsaM-ary

fusionsetforthe

Let

mediastreams.Sincethegenerationintervalof

1

isdisjointfromthoseofallothers,the

determinationofeachofthebinaryfusionsetswouldrequiretheuseofPropositions3or4.

1

2

3

bethesetobtainedastheunionofbinaryfusionsetscorrespondingtopacket

1

fromsource

1

usingthepropositionsofSection3,withthelowerbinaryfusionsetalwaysbeingchosenin

caseofchoice.IfsetdoesnotturnouttobeaM-aryfusionset,itisonlybecausethechoiceoflowerbinary

fusionsetforsomepacketin

isincorrect;itmustbesetrightbyreplacingpacket

with

1.We

13

refertothiscorrectiontechniqueaswindowsliding.Therecanbeatmost

1incorrectchoicesintheset

.

Thewindowslidingoperationstartsbyconsideringthepacketwiththelowestgenerationinterval,andterminateswheneither(1)aM-aryfusionsetisformed,or(2)apacketforwhichthereisnochoiceofbinaryfusionsetsisencountered,or(3)allthe

1choiceshavebeencorrected.Theexactalgorithmisasfollows:

M-aryMixingAlgorithm:1.Letamixerreceivepackets

1

2

from

mediasources.Let:

˜

max

2

Let

1

bethesmallestpositiveintegersuchthat

1

1

1

˜

Replacepacket2.

1

bypacket

1

1

1.Markpacket

1

asFIXED.

2

do:

(a)Usingthebinarymixingalgorithm,computeabinaryfusionsetforsources

algorithmandreportfailure.(b)Letthebinaryfusionsetbe

1

and

,choosingthe

lowerbinaryfusionsetincaseofachoice.Ifabinaryfusionsetcannotbedetermined,terminatethe

1,

.Mark

asCHOOSABLEiftherehadbeenachoiceoflower

binaryfusionset,elsemarkitFIXED.

3.

(a)Compute

and

asfollows:

max

1

min

1

(b)If

,thenterminatethealgorithmsuccessfullyandreporttheunion

1

2

asaM-aryfusionsetofthe(c)If

mediastreams.

,thenperformthefollowingwindowslidingoperation:

i.Withoutlossofgenerality,letalgorithmandreportfailure.ii.IfpacketasFIXED.iii.Recompute

.Ifpacket

ismarkedFIXED,thenterminatethe

1intheunion,andmarkit

ismarkedCHOOSABLE,thenreplaceitbypacket

and

fortheunion.If

,thenterminatethealgorithm

successfullyandreporttheunionastheM-aryfusionset.iv.Otherwise,gotostep(i).

14

4.2CompletenessofM-aryAlgorithm

ThecorrectnessandcompletenessoftheabovealgorithmindeterminingaM-aryfusionsetisprovedbythefollowingtheorem:

Theorem2Supposethatamixerreceivespackets

1,

2,...,

from

mediasources.TheM-aryMixing

Algorithmproducesafusionsetthatsatisfiesthemixingrule(i.e.itiscorrect).Giventhattherearenoothermessageexchangesbetweenmediasourcesandthemixer,therecannotbeanyotheralgorithmthatproducesaM-aryfusionsetwhenouralgorithmfails(i.e.itiscomplete).Proof:

1.Correctness:Thisisself-evidentfromthecomputationoftheM-aryfusionsetinwhich,theearliestandlatestestimatesofgenerationtimesofpacketsareguaranteedtosatisfyhencesatisfyEquation(6).

2.Completeness:Supposethatthereisanalgorithmthatdeterminesafusionset,containingpacketsources,(

1,

,and

1

2

1.

WewillnowshowthatourM-aryalgorithmwillproducetheabovefusionset.

3),...,

Sincethenewalgorithmproducesafusionset,itcanalsoproducebinaryfusionsetsforpairsof

2),(1,

(

1,

).Bythecompletenesspropertyofourbinarymixingalgorithm,

.Sinceourbinaryalgorithm

ouralgorithmwillalsosucceedindeterminingbinaryfusionsets.Lettheunionofallthesebinaryfusionsetsasdeterminedbyouralgorithmbe

1

2

alwayschooseslowerbinaryfusionsets,weobtainthat,

2

,eitheror

1.

eg (n ’’)sspeg (n ’)11eg (n ’)ssUnion of binary fusion setsM-ary fusion setFigure4:WindowslidingintheM-aryalgorithm

If

1,thenitmustbethecasethat

formsalowerbinaryfusionsetwith

1

andis

is

markedCHOOSABLEinourM-aryalgorithm(ontheotherhand,setwithby

mustformaupperbinaryfusion

1).

Sincetheirbinaryfusionsetsarealllower,theearliestgenerationtimeofallsuch

guaranteedtooccurbelowthatof

1,

whichismarkedFIXED.Everywindowslidewillreplacea

,andwhenthewindowslideoperationreaches

1

1

whichismarkedFIXED,thealgorithm

terminatesafterhaving(1)replacedall

sthataremarkedCHOOSABLE,and(2)performedatmost

1windowslides,yieldingtheset

1

2

.Hence,ifthereisanyalgorithmthatproduces

aM-aryfusionset,sowillourM-arymixingalgorithm,whichgoestoshowthatitiscomplete.

15

Theorem2canbeusedtodeterminethemediapacketsizegivennetworkenvironment:

suchthatthemixingalgorithmiseffectiveina

2

∆

∆

However,inpractice,

cannotbechosentobeverylarge,because,feedbackdelaysinapplicationssuchas

tele-orchestraarerequiredtobesmall,andareboundedbythehumanresponsetime.

5CommunicationArchitecturesforMediaMixing

Theprocessofmixingpassesthroughasequenceoftwophases:(1)atransientphase,duringwhichafusionsetisdetermined,and(2)asteadyphase,inwhichmediapacketsaremixedusingthefusionset.Typically,theprocessofmixingentersthetransientphasewheneveranewsourcejoinsaconference,requiringthatthefusionsetthathadbeencomputedearlierfortheoldersourcesbechangedtoaccommodatethenewsource.Ifthefusionsetdeterminedduringatransientphasecontainspacketsthesteadyphase,

1

and

2

fromsources

1

and

2,respectively,thenduring

0,packets

1

and

2

aremixedtogether.

Thearchitectureforcommunicationamongparticipantsofaconferenceduringthesteadyphasecanbecentralizedatoneendofthespectrum,orfullydistributedattheotherendofthespectrum.Thecentralizedarchitecturerequiresthateachparticipantinaconferencetransmitmediainformationtoacentralmixer.Themixerreceivespacketsfromalltheparticipants,createsacompositepacketbymixingthereceivedpackets,andthentransmitsittoalltheparticipants.Eachparticipant,onreceivingthecompositemediapacket,mayhavetoperformsomemediadependentprocessingofthecompositepacket(suchasremovinghisowncontributioninthecaseofaudio)beforeschedulingitforplayback.

Attheotherendofthespectrumisthedistributedarchitecture,whichrequiresthateachparticipantinaconferencetransmitmediainformationtoeachoftheotherparticipants.Mixingisperformedbyeachparticipantindependently.However,itispossiblethatthefusionsetsderivedbytheparticipantsmaybedifferent.Toresolvethisconflict,oneoftheparticipantsisdesignatedasthemastermixer,andthefusionsetcomputedbythismasterispropagatedtoalltheparticipants.

Whereasthecentralizedarchitectureissimpletoimplementbutinflexible(i.e.,doesnotprovidefeaturessuchasautonomousvolumecontrolofeachmediastream),thedistributedarchitectureisflexiblebutincursduplicationofmixingcomputationandbandwidthusage.Neitherarchitecturescaleswell(witheitherthenumberofparticipantsorthegeographicalseparationbetweenparticipants)ifthenetwork,thenetworkinterface,ortheprocessingpoweratthemixeristhebottleneck.

Byclusteringtogethercloselysituatedparticipants,andusingahierarchicalmixingarchitecture(seeFigure5),wecanboundthebandwidthandprocessingrequirementsatthemixers[7].Inamixinghierarchy,participantsconstitutetheleafnodes,andthemixersconstitutenon-leafnodes.Duringthetransientphase,therootmixercomputesthefusionset(sinceitistheonlynodethatreceivespacketinformationfromalltheparticipants),andpropagatesittoeachoftheintermediatemixers.Duringthesteadyphase,eachmixerreceivesmediapacketsfromitschildren,mixesthem,andsendsthecompositepackettoitsparent.Themixerthatisattherootofthe

16

hierarchyforwardsthefinalmixedpackettoeachoftheleafnodes.Thebandwidthrequiredforpacketreceptionateachmixerisproportionaltothenumberofitschildren,whereasthebandwidthforpackettransmissionisthatofsendingtojustoneparent.(Eventhoughtherootmixerhastosendamixedpackettoeachoftheparticipants,sincethemixedpacketiscommontoalltheparticipants,therootmixerneedstomakeonlyonepackettransmissionbyusingmulticasting).Thus,byincreasingonlytheheightofthehierarchywhileboundingthenumberofchildrenofeachmixer,thehierarchicalarchitecturescanbemadehighlyscalable.

Root mixer :MMixers :M1Multicast to all participantsM2Participants :P1P2P3P4P5Figure5:Ahierarchicalarchitectureformixing

Aspecialcaseofahierarchicalarchitectureisadirectedring,whichcanbethoughtofasamixingtreeinwhicheachnodehasexactlyonechild.Suchaconfigurationisappropriatefortokenringbasednetworks,andisanalyzedbyZiegleretal.[8].

Ageneralizationofthehierarchicalarchitectureyieldsagraph-structuredmixingarchitecture.Inanon-hierarchicalgraph,theremaybemultiplepathsbetweenaparticipantandamixer.Hence,amixermayreceivemultiplemixedpacketscontainingthesameparticipant’spacket.Toeliminatetheduplication,theparticipant’spacketmayhavetobetransmittedinadditiontothemixedpacket,leadingtowastageofbandwidth.Sincegraph-structuredarchitecturesdonotaffordanyspecialadvantagesoverhierarchicalones,theyarenotveryinterestingformixing.

6Real-TimePerformanceofMixing

Theinteractiveandreal-timenatureofcollaborativeapplicationsrequirethattheend-to-enddelayexperiencedbymediapacketsbebounded.Whenamixerreceivesthefirstpacketfromoneofthesourcesthatgoestoformamixedpacket,ithastodelaythecompletionofthemixingprocessuntilitreceivesallotherpacketsthatconstitutethemixedpacket.However,ifthenetworkisunreliable,someofthepacketsthatgotoformamixedpacketmaynotarriveatthemixer.Hence,animportantquestionis:howlongshouldamixerwaitforpacketsfromsourcesbeforedecidingtotransmitapartiallymixedpacket(whichisnotfullymixedbecauseoftheunavailabilityofpacketsfromsomeofthesources)?Asimplesolutionisforthemixertotransmitapartiallymixedpacketwhenamediapacketthatgoestoformasubsequentmixedpacketisreceivedfromoneofthesources.However,this

17

causesmixingdelaysoftheorderofpacketduration()atthemixer.Extensionofthissolutiontoahierarchical

mixingarchitectureofheight

resultsinamixingdelayofateachlevel,leadingtoanoverallmixingdelayof

,andend-to-enddelayof

1

∆

(

∆

forthetransmissiondelayfromaleaftotheroot

upthehierarchy,andanadditional∆

forthemulticastofthefinalmixedpacketfromtherootbacktotheleaf).

Thepacketdurationcannotbechosentobeverysmall(typicalvaluesforvoicepacketsonEthernetare20to150ms)mainlytokeepthepackettransmissionoverheadlow.Hence,eveninsmallmixinghierarchies,themixingdelaywillturnouttobeunacceptablylargeforsupportinginteractiveandreal-timemultimediaapplications.

Wenowpresentasimplealgorithmthatremovestheproportionaldependenceofmixingdelayonmaintainsinformationabouttheexpectedgenerationtimesofpacketsatitschildren.

Whenanewsourceatheight

attime

ina

generalmixinghierarchy(ofwhich,othermixingarchitecturesarespecialcases).Inthisalgorithm,eachmixer

joinstheconference,itsendsaprobepacket

upthehierarchytoenableeach

intermediatemixertocomputetheearliestandlatestgenerationtimesforthepacket.Ifthepacketreachesamixer

,themixercomputesitsearliestandlatestgenerationtimesasfollows:

∆

∆

Considertheprocessofformingthethmixedpacketatthemixer.Sincepacketsaregeneratedregularlyatan

intervalof,themixercanestimatetheearliestandthelatestgenerationtimesofpacket

fromsource

asfollows:

Theminimumearliestandmaximumlatestgenerationtimesofpacketsconstitutingthethmixedpacketare

givenby:

12

min

12

max

Theearliestandlatestarrivaltimesofpacketsconstitutingthethmixedpacketcanbepre-computedasfollows:

∆∆

Hence,allpacketsconstitutingthethmixedpacketmustarriveatamixeratheight

withintheinterval

.Attherootmixer,

(heightoftheentiretree),and

∆

.The

maximumaggregateend-to-enddelaysufferedbyapacketfromaleaftotherootisgivenby,Adding∆

.

forthetransmissionofthefinalmixedpacketfromtheroottoparticipants,weobtainthemaximum

aggregateend-to-enddelayofapacketas:

18

AggregateEnd-to-EndDelay

∆

∆

1

∆

Theabovederivationofmixingdelayhasignoredthecomputationaloverheadofmixingateachmixer,whichisassumedtobesmallcomparedtothecommunicationandwaitingdelays.

7ImplementationandExperience

Wehaveimplementedthemixingalgorithmsonanetworkofmultimediastations,eachconsistingofacomputingworkstation,aPC-AT,avideocamera,andaTVmonitor(seeFigure6).TheworkstationandPC-ATsareconnectedviaEthernets.ThePC-ATsareequippedwithdigitalvideoprocessinghardwarethatcandigitizeandcompressmotionvideoatreal-timerateswitharesolutionof480x200pixelsand12bitsofcolorinformationperpixel,andaudiohardwarethatcandigitizevoiceat8KBytes/sec.

Multimedia StationMultimedia StationVideoMonitorCameraVideoMonitorCameraWorkstationPC-ATWorkstationPC-ATGATEWAYETHERNETSFigure6:Hardwareconfiguration

Wecarriedoutseveralexperimentstoevaluatetheperformancelimitsofmixinginaudioconferencingapplications.AudiosamplesarepacketizedandtransmittedontheEthernet.Inordertostrikeabalancebetweennetworktransmissionoverhead(whichfavorslargepacketsizes),andthepacketizationdelay(whichfavorssmallpacketsizes),theaudiopacketsizewaschosentobe512samples,yieldingcommunicationdelayperpacketiswithin10ms.

Weobservedtheperformanceofcentralizedanddistributedmixingarchitectures,andexperimentallymea-suredthemaximumnumberofparticipantsthattheycansupport.Figure7showsthevariationofthefractionofpacketsreachingamixerinacentralizedarchitecturewithincreaseinthesizeofaconference.Whenthatfractiongoesbelow98%,thereisarapiddeteriorationofvoicequality,andthemixingarchitecturebreaksdown.Thebreakdownpointyieldsamaximumconferencesizeof20inthepresenceofmulticasting,and12initsabsenceforcentralizedarchitecture.Inthepresenceofmulticasting,distributedandcentralizedarchitecturesbehaveinasimilarfashion.However,intheabsenceofmulticasting,theirperformancewillbepoorerduetothegrowthofbandwidthconsumptionasthesquareofthenumberofparticipants.Forhierarchicalarchitectures,givenamaximumallowableend-to-enddelayofabout100ms,theanalysisinSection6yieldscansupportconferenceswithupto202

66.67ms.Themaximum

2,showingthatthey

400participants.

19

Packets recieved at the mixer (%)10090With MulticastingWithout multicasting80706050403020100051015202530Conference size (Number of participants)Figure7:Performanceofaudiomixingwithincreaseinconferencesize

8ConcludingRemarks

Wehavepresentedalgorithmsformixingmediadatatransmittedbymultiplesourcesinmultimediaconferencingapplicationssuchastele-orchestra,carriedoutonpacket-switchednetworks.Thealgorithmsminimizebothdifferencesbetweengenerationtimesofmediapacketsbeingmixed,andend-to-enddelaysofmixedpackets.Thealgorithmsarecomplete,i.e.,therecannotbeamoreeffectivealgorithmformixingintheabsenceofanycontrolmessageexchangesbetweenparticipantsandmixers.

Wehaveimplementedthemixingalgorithmsonanetworkofworkstationsequippedwithdigitalmultimediahardware.Experimentalevaluationsdemonstratethatcentralizedanddistributedmixingarchitecturesarelimitedinthenumberofparticipantsthattheycansupport.Inordertoovercometheirlimitations,wehaveproposedhierarchicalmixingarchitectures,whichcansignificantlyreducebandwidthconsumption,makingthemsuitableforscalablemultimediaconferences.

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