An Adaptive Algorithm for Efficient Message Diffusion in Unreliable Environments

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AnAdaptiveAlgorithmforEfficientMessageDiffusioninUnreliableEnvironments

BenoˆıtGarbinatoFernandoPedoneRodrigoSchmidtUniversit´edeLausanne,CH-1015Lausanne,SwitzerlandPhone:+41216923409Fax:+41216923405E-mail:benoit.garbinato@unil.ch

´EcolePolytechniqueF´ed´eraledeLausanne(EPFL),CH-1015Lausanne,Switzerland

Phone:+41216934797Fax:+41216936600E-mail:fernando.pedone,rodrigo.schmidt@epfl.ch

AbstractInthispaper,weproposeanovelapproachforsolv-ingthereliablebroadcastprobleminaprobabilisticunreliablemodel.Ourapproachconsistsinfirstdefin-ingtheoptimalityofprobabilisticreliablebroadcastalgorithmsandtheadaptivenessofalgorithmsthataimatconvergingtowardsuchoptimality.Then,weproposeanalgorithmthatpreciselyconvergestowardtheoptimalbehavior,thankstoanadaptivestrategybasedonBayesianstatisticalinference.Wecomparetheperformanceofouralgorithmwiththatofatyp-icalgossipalgorithmthroughsimulation.Ourresultsshow,forexample,thatouradaptivealgorithmquicklyconvergestowardsuchexactknowledge.

1.IntroductionDiffusinginformationefficientlyandreliablyinanenvironmentcomposedofmanyunreliablenodesin-terconnectedbylossycommunicationlinksisanabil-itysoughtbymanycurrentlarge-scalesystems(e.g.,large-scalepublish-subscribearchitectures).Achiev-ingreliableandefficientinformationdiffusioninsuchcontexts,however,isacomplextask.First,beingcom-posedofmanynodes,itisunrealistictoassumethatanyoneofthemhaspreciseaprioriinformationaboutthenetworktopologyandthereliabilityofthecom-ponents.Second,evenifsuchinformationwereavail-abletonodesatthebeginningoftheexecution,thedy-namicnatureofalargesystemwouldrenderitobso-letequickly.Nodes,forexample,mayleavethesystem

constantly(duetofailuresorexplicitdisconnections),changingitstopology.Finally,asobservedbymanyresearchers,mechanismstraditionallyusedtoreliablybroadcastinformationinsmall-andmiddle-sizenet-worksdonotscalewellwhenthesystemgrows[2].

Manyworkshaveinvestigatedthisproblemfromaprobabilisticperspective(e.g.,[2,4,9,10,11,12]).Probabilisticalgorithmsscalemuchbetterthandeter-ministiconesandachievehighreliability.Intuitively,everynodethatreceivesamessagechoosesasubsetofsystemmembers,forexampleamongthecompletesetofdestinations,andpropagates(i.e.,gossips)themes-sagetothesenodes.Thegossipnatureofthealgorithmcombinedwiththepossibilityofcrashesandmessagelossimpliesthattherearesomechancesthatnotallnodesreceivetheoriginalmessage.Nevertheless,pro-videdthatnodeskeepgossipingtheoriginalmessage“longenough”itcanbeguaranteedthatwithveryhighprobabilityallnodesreceivethemessage.

Inthispaper,weproposeanapproachtoimprovetheperformanceofgossip-basedalgorithmsbytakingintoaccountthetopologyandprobabilisticnature(i.e.,nodefailureandmessagelossprobabilities)oftheen-vironmentinwhichthesealgorithmsexecute.Sincenodesadapttotheenvironmentcharacteristicsduringtheexecution,wecallsuchalgorithmsadaptive.Thisadaptivecharacteristicispreciselywhatdistinguishesourapproachfrompreviousworks,whichingeneraldonottaketopologyandreliabilityaspectsintoac-counttoimproveperformance.Aswediscussinthepaper,ourapproachiscomplementarytopreviousop-timizationsproposedintheliterature(e.g.,[12])andcouldbecombinedwiththem.

Proceedings of the 2004 International Conference on Dependable Systems and Networks (DSN 2004) 0-7695-2052-9/04 $20.00 © 2004 IEEE Themotivationforadaptivealgorithmsisperfor-mance.Large-scalesystemsareusuallycomposedofseveralpartswithvaryingreliabilitycharacteristics(e.g.,local-areanetworklinksareusuallymorereli-ablethanwide-areanetworklinks),andadjustingthegossipmechanismaccordingtothesystemcharacter-isticscanprovidemoreefficientresults.Tobetterspelloutourargument,considerthefollowingsimpleexam-pleinwhichtwonodesareconnectedthroughtwoin-dependentpaths.Pathonelosesmessageswithproba-bility,.Pathtwoislessreliablethanpathoneandlosesmessageswithprobability,where.Withatypicalgossipalgorithm,whichchoosespathsrandomlyforeverysend,afternodeonesendsmessagestonodetwo,theprobabilitythatatleastonemessagereachesnodetwois[5].Us-

inganalgorithmadaptedtothisenvironment,whichchoosesthepathsaccordingtotheirreliabilityprob-abilities(andthereforealwayschoosesthefirstpath),nodeonereachesnodetwowithprobabilityaf-termessagesaresent.

0.75 0.8 0.85 0.9 0.95 1

1 2 3 4 5 6 7 8 9 10L=0.0001

L=0.001L=0.01

Figure1.AdaptivevstraditionalgossipConsequently,toreachthesamereliabilityasanenvironment-adaptedalgorithm,atypicalgossipal-gorithmhastoretransmitmoremessages,wastingthroughputandunnecessarilyconsumingsystemre-sources.Figure1depictstherelationbetweenandasafunctionofwhenbothalgorithmsachievethesamereliability.When,bothpathshavethesamereliabilityandso,thereisnodifferencebetweenthealgorithms.When,evenifpathoneisveryreliable,forexample,anadaptivealgo-rithmonlyneedsabout87%ofthemessagessentbyatraditionalgossipalgorithmtoreachthesameoverallreliability.Furtherimprovementsareobtainedinmorecomplextopologies.Section5discussesthisissueindetail,usingamoresophisticatedtraditionalgossipal-gorithm.