IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS VOL - PDF document

64IEEEJOURNALONSELECTEDAREASINCOMMUNICATIONS,VOL.26,NO.6,AUGUST2008achievedare750units,0.98and898.2respectively,toincreasenetworkutilityby6.5%,wecaneitherincreaselinkcapacityby33%orimprovelinkavailabilityto0.995.Whichnetworkupgrade(linkcapacityincreaseoravailabilityenhancement)ismorecost-effectivedependsonthedetailedcapacityandequipmentcostmodels.Forexample,mostlikelyinwell-deployedopticalnetworks,itislessexpensivetoincreaselinkcapacitybylightingdarkbersthantoenhancelinklevelavailabilitythroughmoreadvancedtransceiveropticalcomponents.GraphssuchastheoneinFigure10willallowoperatorstochoosebetweenalternativemodesofserviceavailabilityenhancementtobestsatisfytheoverallelasticV.CWeestablishtheframeworkofprovisioningelasticserviceavailabilitythroughnetworkutilitymaximization.Thisworkcomplementstheexistingliteratureoneitherbandwidthal-locationforelasticdemandsbutnoavailabilityconcerns,orbandwidthallocationforavailabilityprovisioningbutignoringdemandelasticity.Bydevelopingautilityfunctionofserviceavailabilityinadditiontosourcerate,wetransformoptimalprovisioningintoaconvexoptimizationproblemusingdiffer-entiatedfailurerecovery.Thedesirableserviceavailabilityandsourcerateforeachusercanbeachievedusingaprice-baseddistributedalgorithm,whereeachlinkmaintainsmultipleprices.Wecarryoutnumericalexperimentsoverrealisticnetworktopologies,andpresenttheoptimaltradeoffbetweenthethroughputandtheserviceavailability.Engineeringim-plicationsofthisworkquantifyseveralintuitionsonelasticserviceavailability.Weinitiateautility-basedstudyofnetworkresiliencebyaddressingoptimalprovisioningforelasticserviceavailabilitythroughqualityofprotectionandsharedpathprotection.Itwouldbeinterestingtoinvestigatetheelasticserviceavailabil-ityprovisioningforotherschemes,e.g.employingotherdiffer-entiatedfailurerecoveryschemes,usingrestorationinsteadofprotection,recoveringfrommultiplefailures,etc.Combinedwithdetailedcostmodels,thisworkwillalsoleadtoaquanticationoftheminimum-costtradeoffbetweenaddingcapacityandimprovinglinkavailabilityformaximizationofutilityofserviceavailability.CKNOWLEDGMENTWewouldliketoacknowledgethesupportofNSFCNS-0430487andCNS-0519880,DARPAGrantHR0011-06-1-0008,andAFOSRGrantFA9550-06-1-0297.Wealsoappre-ciatethehelpfuldiscussionswithRubyB.Lee,XinWang,andJiapingLiu.[1]O.GerstelandG.Sasaki,“Qualityofprotection(QoP):aquantitativeunifyingparadigmtoprotectionservicegrades,”inProc.OpticalNet-workingandCommunicationsConference(OPTICOMMÕ03),Denver,CO,2001.[2]G.Holland,“Carrierclassmetronetworking,”RiverstoneNetworks,Technologywhitepaperno.135,July2002.[3]AT&TBusinessServiceGuide,http://new.serviceguide.att.com.[4]L.Z.C.SaradhiandM.Gurusamy,“DifferentiatedQoSforsurvivableWDMopticalnetworks,”IEEECommun.Mag.,vol.42,no.5,pp.8–14,May2004.[5]A.FumagalliandM.Tacca,“Differentiatedreliability(DiR)inWDMringswithoutwavelengthconverters,”inProc.IEEEInternationalConferenceonCommunications(ICCÕ01),Helsinki,Finland,pp.2887–[6]S.Arakawa,J.Katou,andM.Murata,“DesignmethodoflogicaltopologieswithqualityOfreliabilityinWDMnetworks,”inNetworkCommun.,vol.5,no.2,pp.107–121,Mar.2003.[7]F.Kelly,A.Maulloo,andD.Tan,“Ratecontrolincommunicationnet-works:shadowprices,proportionalfairnessandstability,”J.OperationalResearchSociety,vol.49,no.3,pp.237–252,Mar.1998.[8]H.Yaiche,R.R.Mazumdar,andC.Rosenberg,“Agametheoreticframeworkforbandwidthallocationandpricinginbroadbandnetworks,”IEEE/ACMTrans.Networking,vol.8,no.5,pp.667–678,2000.[9]S.Shenker,“FundamentaldesignissuesforthefutureInternet,”J.Select.AreasCommun.,vol.13,no.7,pp.1176–1188,Sept.1995.[10]S.H.Low,“AdualitymodelofTCPandqueuemanagementalgo-rithms,”IEEE/ACMTrans.Networking,vol.11,no.4,pp.525–536,[11]R.Srikant,TheMathematicsofInternetCongestionControl(SystemsandControl:FoundationsandApplications).SpringerVerlag,2004.[12]S.S.KunniyurandR.Srikant,“End-to-endcongestioncontrolschemes:utilityfunctions,randomlossesandECNmarks,”IEEE/ACMTrans.,vol.11,no.5,pp.689–702,2003.[13]R.J.LaandV.Anantharam,“Utility-basedratecontrolintheInternetforelastictrafc,”IEEE/ACMTrans.Networking,vol.10,no.2,pp.272–286,2002.[14]S.H.LowandD.E.Lapsley,“Optimizationowcontrol–partI:basicalgorithmandconvergence,”IEEE/ACMTrans.Networking,vol.7,no.6,pp.861–874,1999.[15]R.T.Rockafellar,NetworkFlowsandMonotropicProgrammingAthenaScientic,1998.[16]M.Chiang,S.H.Low,A.R.Calderbank,andJ.C.Doyle,“Layer-ingasoptimizationdecomposition:amathematicaltheoryofnetworkarchitectures,”Proc.IEEE,Jan.2007.[17]S.Blake,D.Black,M.Carlson,E.Davies,Z.Wang,andW.Weiss,“Anarchitecturefordifferentiatedservice,”IETF,RFC2475,1998.[18]C.BourasandA.Sevasti,“SLA-basedQoSpricinginDiffServnet-works,”ComputerCommun.,vol.27,no.18,pp.1868–1880,2004.[19]X.WangandH.Schulzrinne,“Pricingnetworkresourcesforadaptiveapplications,”inIEEE/ACMTrans.Networking,Apr.2006.[20]L.DaSilva,D.Petr,andN.Akar,“Equilibriumpricinginmultiserviceprioritybasednetworks,”inProc.IEEEGlobalCommunicationsCon-ferenceÕ97,Phoenix,AZ,Nov.1997.[21]——,“Staticpricingandqualityofserviceinmultipleservicenet-works,”inProc.5thConferenceonComputerScienceandInformaticsAtlanticCity,NJ,2000,pp.355–358.[22]J.W.Lee,M.Chiang,andR.A.Calderbank,“Pricing-baseddistributedalgorithmsforrate-reliabilitytradeoffinnetworkutilitymaximization,”IEEEConferenceonComputerCommunications(INFOCOMÕ06)Barcelona,Spain,Apr.2006.[23]V.Marbukh,“Onaggregateutilitymaximizationbasednetworkmanage-ment:challengesandpossibleapproaches,”inProc.IEEEInternationalConferenceonCommunications(ICCÕ04),Paris,France,2004.[24]V.Sharmaetal.,“FrameworkforMPLS-basedrecovery,”Internetdraft,draft-ietf-mpls-recovery-frmwrk-08.txt(workinprogress),Oct.2002.[25]J.MoandJ.C.Walrand,“Fairend-to-endwindow-basedcongestioncontrol.”IEEE/ACMTrans.Networking,vol.8,no.5,pp.556–567,[26]M.KodialamandT.V.Lakshman,“Dynamicroutingofbandwidthguaranteedtunnelswithrestoration,”inProc.IEEEConferenceonComputerCommunications(INFOCOMÕ00),TelAviv,Israel,pp.902–[27]G.Lietal.,“Efcientdistributedpathselectionforsharedrestorationconnections,”inProc.IEEEConferenceonComputerCommunications,NewYork,NY,pp.140–149.[28]C.QiaoandD.Xu,“Distributedpartialinformationmanagement(DPIM)schemesforsurvivablenetworks–partI,”inProc.IEEECon-ferenceonComputerCommunications(INFOCOMÕ02),NewYork,NY,pp.302–311.[29]S.BoydandL.Vandenberghe,ConvexOptimization.NewYork:CambridgeUniversityPress,2004.[30]D.P.Bertsekas,NonlinearProgramming,2nded.AthenaScientic,[31]M.Minoux,MathematicalProgramming:TheoryandAlgorithms.Wi-ley,1986. 60IEEEJOURNALONSELECTEDAREASINCOMMUNICATIONS,VOL.26,NO.6,AUGUST2008 1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 criticality parameter: aq0=q1=98.5% b=1.3 b=1.5 Fig.3.Optimalowonprimarypath()forsingle-userwithdifferentcriticality()andelasticity()parameters.Itiseasytoverifythat ,otherwise,whichmeansthatlinkbefullyutilized. isafunctionoftheparameters,thevaluesoftheparametersmayaffectwhetherlinkfullyutilizedornot.InFig.3below,weshowhowtheparametersmayaffectwhetherlinkisfullyutilizedornot.Wesetunitsandunit.Wecanseethatfor,whichcorrespondstonon-criticalrequirementonavailability,linkcanbefullyutilized.Whenbecomeslargeoruserhashigheravailabilityrequirement,linkbecomenotfullyutilized,especiallyforasmallerelasticityparameter,Theimportantthingillustratedhereisthatgivenbasedonusers’sensitivitytoavailability,theremaybesomecapacitynotfullyutilizedifthecapacitiesforprimaryuseandbackupdonotmatchwell.Wecansavecapacitybymatchingtheprimaryuseandbackupuse.Forinstance,forthissimplescenarioabovewiththegiven,by ,wecangetthesmallestcapacityforbackupsuchthatcanbefullyutilized.Whentherearemultipleuserssharinglinks,thesavedcapacitybymatchingtheratesonprimarypathandbackuppathforoneuser,canbeusedtosupportotherusers.Ourinterestistodothematchingforalltheuserswithelasticdemandonserviceavailabilityinasystematicwayinageneraltopology.F.Algorithms:CentralizedorDistributedItcanbeeasilyveriedthatwhen isastrictlyconcavefunctionofthenalproblem(11)isaconvexoptimizationproblem.Highlyefcientprimal-dualinteriorpointalgorithms[29]canthusbeusedtosolvefortheuniqueglobaloptimumoftheproblem.Suchcentralizedcomputationissuitableforoff-lineprovisioningofelasticserviceavailabilitythroughacentralizednetworkmanagement,whichisthemostprobableapplicationscenarioinpractice.Inadifferentscenario,whentheuserschangetheirprefer-enceorutilityfunctionovertime,inordertoenableregularupdatesthroughdistributedmessagepassingwithinthenet-work,weneedtodevelopdistributedalgorithmstosolve(11)forthejointlyoptimalsourceratesandserviceavailabilities.Mostlikely,suchdistributedupdatesofserviceavailabilityprovisioningisonlyneededonceoveralongtime.ThisisthesubjectofSec.III.III.DISTRIBUTEDInthissection,weuseadualdecompositionapproachtodistributivelysolveproblem(11).Usingbothindexlinks,anddenotingthestackedvectorofdualvariables(orpricingvariables)as,werstwritetheLagrangianassociatedwithproblem(11)asTheLagrangedualfunctionis)=max isthevectorwhoseelementsareallzeros.ThedualproblemisformulatedasTosolvethedualproblem,werstconsiderproblem(15).SincetheLagrangianisseparable,thismaximizationoftheLagrangianovercanbeconductedinparallelateachl,ml,m vars.Then,dualproblem(16)canbesolvedbyusingthegradientprojectionalgorithmas+1)isthestepsizeandaresolutionsofproblem(17)foragivenWenowproposethefollowingdistributedalgorithmforOPTwhereeachsourcesolvesitsownproblemwithonlylocalinformation.ThereisanimportantdifferenceofthefollowingalgorithmcomparedwiththestandardNUMforrateallocationonly:eachlinkmaintainsasetofcongestionpricesl,mforall SUPPLEMENTONOPTICALCOMMUNICATIONSANDNETWORKING 0.2 0.3 0.5 0.6 0.9 1 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Utility Function: Vs(s)Quality of Protection: sq0=q1=98.5% (a=0.7, b=1)Important User(a=1.7, b=1.05)Critical User(a=2.7, b=1.1) Fig.2.Utilityasafunctionof(QualityofProtection)forthreetypicalkindsofusers.achievedbyanyconnectionisjusttheavailabilityofitsprimarypath,SufÞcientAvailability):Asaconservativeapproach,sufcientbackupbandwidthwillbereservedalongbackuppath(i.e.)regardlessofusers’elasticdemandsforserviceavailability.ThemethodsofsolvingproblemOPTcanbeeasilyextendedtotheothertworecoveryschemesbyspecifyingthevalueinadvanceastheadditionalObviously,from(7),wehave=(1,andwithaslightabuseofnotation,wealsousetorepresentthenormalizedutilityfunctionof(QoP).From(3)and(4),)=1)(1)(1Fig.2showsthecurvesofutilityasthefunctionof)forthethreerepresentativeclassesofuserswithelasticserviceavailabilitydemands(sameparametersasthoseinFig.1)assumingtheavailabilitiesforbothprimarypathandbackuppathare98.5%.Notethat,thecurvewillnotbeastraightlineifisnotequalto1.Inaddition,toensureensure,1],thelowerboundofQoPacceptableforuser=max s bsq0 Conrmingourintuition,themoreimportantusersmayhaveastrictlypositive,asillustratedbythe‘criticaluser’curveinFig.2.D.OptimalProvisioningofElasticServiceAvailabilityastheexpectedbackupbandwidthreservedforconnectionalongitsbackuppath.Thentheobjectiveof(2)is))=max whichisequalto,where isastrictlyincreasingfunction,theequalityconstraint(9)canbereplacedby astheconstraintisalwaystightatoptimality.Asweonlyconsidersinglelinkfailure,wehave(10)=maxdenotesthesetofconnectionsusingontheirbackuppathsanddenotesthesetofconnectionsusingontheirprimarypaths.Eq.(10)meansthebackupbandwidthreservedonlinkjustneedtobesufcienttorecovertheworstfailurescenario.Therefore,theformulationforproblemOPTissummarizedasfollows: vars.Notethatcanberecoveredfrom,andconstantsareimplicitlyrepresentedinthefunctionTherestofthispaperexaminesthesolutionmethodsandengineeringimplicationsoftheaboveproblem.E.AnalysisforaSimpleScenarioBeforediscussingsolutionmethodsingeneral,werstillustratesomeoftheinterestingaspectsoftheproblemformulationthroughasimpleexample.Supposewehaveonlyonesource-destinationpair,andtwosingle-linkpaths,,forprimaryandbackuppathsrespectively.Assumetheirpathavailabilitiesareandtheirlinkcapacitiesare,respectively.Forthesingleuser,itscriticalityparameterisandelasticityparameterisForthissimplescenario,theoptimizationproblemis(12),subjectto variablesx,y, xq0)b 1Šq1y ,theoptimalsolutioniswhichistrivial.If,itiseasytoseethattheoptimalsolutionsatisesWith,theproblemisequivalenttomaximizing overrc1,c0].Wetakethederivativeofwithrespectto dxq0)b 1Šq1y xb1y x) 1Šq1y x . SUPPLEMENTONOPTICALCOMMUNICATIONSANDNETWORKING 1.2(99.01%) 1.7(99.31%) 2.2(99.96%) 2.7(99.96%) 0.4 0.6 0.8 Criticality Parameter a (Weighted Average Service Availability)Bandwidth Usage Profile Backup Bandwidth Fig.7.Distribution(percentage)ofbandwidthusagewithvariouscriticality,andthecorrespondingweightedaverageserviceavailabilitiesina15-nodenetwork. 0.98 0.985 0.99 0.995 0.999 700 750 800 850 900 950 1000 1050 Link Availability: r s Us Fig.8.Comparisonoftheachievednetworkutility()amongoptimalrecoveryscheme(OPT),norecoveryscheme()andsufcientavailabilityscheme()fora15-nodenetworkwhereallthelinkshavethesameavailabilitybandwidthisashighas10.5%when(asshownbythe4thand5thbarsinFig.7),i.e.,provisioninghighserviceavailabilityexclusivelyforcriticalusers/applicationsleadstosignicantwasteinbandwidthresource.Therearetwopossiblewaystoreducethebandwidthwaste:1)employingdynamic(andpossiblycomplicated)routingforprimarypathsandbackuppaths,and2)allowingfordemandswithvarioussensitivitiestoserviceavailability,whichisdiscussednext.B.ScenariowithDiverseServiceAvailabilityParametersForthistestscenario,allsourcenodesarecategorizedasnormaluser,importantuserandcriticaluser,withapopulationratioof9:3:1.Theircriticality,,andelasticity,,param-etersaresameasthoseillustratedinFig.2.Allthelinkshavethesameavailability,.Fig.8showsthenetworkutilityachievedina15-nodenetworkwhenthelinkavailabilityvariesfrom0.975to0.999.Obviouslyallcurvesaremonotonically 0.99 0.995 0.999 4000 4200 4400 4600 4800 5000 5200 5400 5600 Link Availability: r s Us Fig.9.Comparisonoftheachievednetworkutilityforthe46-nodeUSnet. 0.98 0.985 0.99 0.995 0.999 750 800 850 900 950 1000 1050 1100 1150 Link Availability: rNetwork Utility: s Us Fig.10.Networkutility()achievedbyoptimalrecoveryschemeforthe15-nodenetworkwithvariouslinkcapacity()andlinkavailability(increasingsincenetwork-wideavailabilityincreasesaseachlink’savailabilityincreases.Itisclearthattheproposedoptimalrecoveryscheme(OPT)isconsistently(andindeedprovably)betterthantheothertworegularschemes:norecov-eryscheme()andsufcientavailabilityscheme(Whenthelinkisnotreliable,byselectivelyprovisioningfailurerecovery,OPTachieves26.9%moreutilitythanMoreover,sufcientavailabilityschemecouldbeevenworsethannorecoveryschemeintermsoftotalutilitywhenlinksareveryreliable.Fig.9showsthenetworkutilityachievedinthe46-nodeUSnetaslinkavailabilityvaries,wheresimilarobservationscanbemade.Fig.10showsthatthenetworkutilityachievedbyopti-malrecoveryschemeinthe15-nodenetworkwillincreasewhenweuniformlyraiselinkcapacity()orimprovelinkavailability().Givenanoperatingpointoflinkcapacities,linkavailabilities,andtheachievednetworkutility,toreachahighernetworkutility,itwillbeinterestingtoinvestigatewhichwayofincreasinglinkcapacityandimprovinglinkavailabilityismorecost-effective.Inthistestsample,ifthecurrentlinkcapacity,linkavailabilityandnetworkutility 62IEEEJOURNALONSELECTEDAREASINCOMMUNICATIONS,VOL.26,NO.6,AUGUST2008 Fig.4.A15-nodenetworkwithheterogneouslinkcapacities. Fig.5.46-nodeUSnetnetworkwithuniformlinkcapacities.near-optimalefciencyinbandwidthusagecomparedtoothercounterpartswithcomplicatedrouting[33].Fortherstandsimplescenariotobeinvestigated,alltheusershavethesameserviceavailabilityparameters,andonlyoptimalrecoveryschemeOPTistested.Theninthesecondscenario,theuserscouldhavevariousserviceavailabilityparametersandtheothertworecoveryschemes,(NoRecovery)and(SufcientAvailability),arealsotestedandcompared.A.ScenariowithUniformServiceAvailabilityParametersInthissetoftests,theavailabilitiesoflinksareall99%andallthedemandsareassumedtohavethesamesettingsoncriticality,,andelasticity,,parameters.Theresultingserviceavailabilitiesachievedbythedemandscouldstillbedifferentsincetheirprimary/backuppathsusedifferentnumberofhopsandthushavedifferentpathavailabilities.Inaddition,thecongestionpriceofusingalinkcouldalsobedifferent.Impactsofelasticserviceavailabilityonthroughput-availabilitytradeoff.WetracethegloballyoptimaltradeoffcurvebetweennetworkthroughputandserviceavailabilitywithoptimalrecoveryschemeOPTonthe15-nodenetwork.Atrst,thevalueofisxedat,andthevalueof 99.00% 99.68% 99.90% 99.97% 2.5 x 104 Weighted Average Service AvailabilityThroughput b=1b=3a=0.7a=2.7a=1.7 b=2 varing a (b=1) varing b (a=1.7) Fig.6.Optimaltradeoffcurvesbetweennetworkthroughput(andweightedaverageserviceavailability()withvariouscriticality,(producingamuchlargerdynamicrange),andelasticity,parametersfora15-nodenetwork.variesfrom0.7to2.7atstepsizeof0.1.Thenwexthevalueofas1.7andvarythevalueof1to3atstepsizeof0.2.ThetworesultingcurvesareshowninFig.6,whichdemonstratethetradeoffbetweenthenetworkthroughput()andtheweightedaverageserviceavailability .Quantifyingourintuition,alargercriticalityparameter(i.e.moresensitivetoserviceavailability)leadstohigherserviceavailabilityattheexpenseoflowerthroughput,sincemorebandwidthhavetobeusedforbackuppurpose.Fromtheleastsensitivity(tothehighestsensitivity(),theweightedaverageserviceavailabilityincreasesfrom98.63%to99.96%whilethenetworkthroughputdecreasesby55.7%.Theresultswithvariouselasticityparameters,,alsoconrmtheaboveobservationonthetradeoffbetweenthroughputandserviceavailability.Notethat,whenislargeenough(),theutilityfunctionsshowninFig.1willbeveryclosetostepfunctions.Suchlackofelasticityinserviceavailabilityleadstolittlevariationinrateallocation,thusthepointswithith,3]areveryclosetoeachotherinFig.6.Impactsofelasticserviceavailabilityonbandwidthusage.Fig.7showsthepercentagesofthetotalbandwidthusedbyallprimarypathsandbackuppathswhenthevalueofisxedandthevalueofvariesfrom0.7to2.7.Itturnsoutthatifthedemandsarenotsensitivetoserviceavailability,almostallthebandwidthcanbeusedbyprimarypaths,andthusanoptimalrecoveryschemewouldhavethesimilarperformanceasnorecoveryscheme.Withtheincreasingsensitivitytoserviceavailabilityforthedemands,morebandwidthhavetobeusedforbackuppurpose.AnotherinterestingobservationofFig.7isthatwhentheusersareverysensitivetoserviceavailability(i.e.,alargevalueof)asignicantfractionofbandwidthiswastedsinceausercannotincreaseitsratealongitsprimarypathifitcannotsimultaneouslyincreaseitsbackupbandwidthreservationtomaintaintheappropriateserviceavailability.Forexample,thepercentageoftheunused SUPPLEMENTONOPTICALCOMMUNICATIONSANDNETWORKINGDistributedAlgorithmforOPTIneachiteration,bysolvingthefollowingproblem(19)over,eachsourcedeterminesitsadjustedrate),rateonprimarypathandrateonbackuppath())thatmaximizeitsnetutilitybasedonthepricesinthecurrentiteration.Sourceproblematsource vars.l,mistheend-to-end(primarypath)congestionpriceatiteration,andl,mistheend-to-end(backuppath)congestionpriceatiterationInaddition,bypriceupdateequation(20),thelinkadjustsitscongestionpricesforthenextiteration.Updateofthesetofcongestionpricesatlink+1)=istheaggregaterateofthoseconnectionsusingontheirprimarypathsatiteration,andl,mistheaggregaterateofthoseconnectionsusingontheirbackuppathsandprimarypaths,respectively. Messagepassingintheabovealgorithmonlyneedstobecarriedoutbetweeneachsourceandthelinksonits(primaryandbackup)paths.Todecidethecongestionpriceaccordingto(20),linkneedstoknowl,mforallTherefore,ifsourcechangesitsrate,itcansendanupdatemessage(containingthenewvalueof)tothelinks()alongitsprimarypath.Incontrast,ifsourceitsrate,ithastosendanupdatemessage(containingthenewvalueofandtherouteofitsprimarypath,i.e.)tonotifythelinks()alongitsbackuppath.Ontheotherhand,tosolvesourceproblem(19),sourceneedstoknowtheend-to-endprimaryandbackupcongestion.First,canbeobtainedbyanoticationmessageoriginatedfromthedestinationthatsummarizesthecongestionpricel,mofeachlink()alongitsprimarypath.Second,beobtainedbythenoticationmessageoriginatedfromthedestinationtosumupthecongestionpricel,mofeachlink()alongitsbackuppath.Inaddition,tocalculateitsutilityonserviceavailabilityaccordingto(6)and(8),thesourcealsoneedstoknowtheavailabilitiesofthelinks()ofitsprimaryandbackuppaths,whichareusuallystaticinwirednetworks.Aftertheabovedualdecomposition,thefollowingresultcanbeprovedusingstandardtechniquesindistributedgradientalgorithm’sconvergenceanalysis:,byDistributedAlgo-rithmforOPT,dualvariablesconvergetotheoptimaldualsolutionsandthecorrespondingprimalvariablesarethegloballyoptimalprimalsolutionsof(11).OutlineoftheProof:Sincestrongdualityholdsforproblem(11)anditsLagrangedualproblem(16),wesolvethedualproblemthroughdis-tributedgradientmethodandrecovertheprimaloptimizersfromthedualoptimizers.ByDanskin’sTheorem[30], l,ml,mHence,thealgorithmin(20)isagradientprojectionalgo-rithmfordualproblem(16).Sincethedualobjectivefunctionisaconvexfunction,thereexistsastepsizetoconvergetotheoptimaldualsolutions[30].Also,ifsatisesaLipschitzcontinuitycondition,i.e.,thereexistsaconstantsuchthatconvergestotheoptimaldualsolutionwithasufcientlysmallconstantstepsize[30].TheLipschitzcontinuityconditionissatisedifthecurvaturesoftheutilityfunctionsareboundedawayfromzero,see[14]forfurtherdetails.Furthermore,sinceproblem(11)isastrictlyconvexop-timizationproblemandproblem(19)haveuniquesolutions,arethegloballyoptimalprimalsolutionsof(11)[31].IV.PVALUATIONANDMPLICATIONSInthissection,wepresentthenumericalresultsinprovi-sioningelasticserviceavailabilities.Recallthatinputstoourproblemare:asetofgivenprimaryandbackuppaths,asetofspeciedprotectionschemes,andtheparametersforeachuserWeconsidertwonetworktopologies.TherstisshowninFig.4,whichisthesameasthatusedin[26]andhas15nodesand28bi-directededges(foratotalof56links).Thecapacityofeachdark(bold)linkis4timesaslargeasthatoftheother(thin)links.ThesecondisalargenetworkcalledUSnetshowninFig.5[32](with46nodesand76bi-directededgesofuniformcapacity)isalsoconsidered.Withoutbeingstatedexplicitly,thecapacitiesofthethinlinksinthe15-nodenetworkandallthelinksinthe46-nodenetworkareassumedtobe1000units.Foralltestscenarios,thereisanelasticdemandbetweeneachnodepair.TheutilityfunctionofuserasdiscussedinSec.II.Weuselog(astheutilityfunctionofadjustedrate.Eachuseralsohasitsowncriticalityparameterelasticityparameterforelasticserviceavailabilitydemand.Alink-disjointpairofprimarypathandbackuppatharechosenforeachdemand.Sincethetrafciscarriedontheprimarypathmostofthetimeandthebackupbandwidthcanbesharedbyseveralconnections,weusetheshorteroneofthedisjointpathpairastheprimarypath[33].Inthesimulation,weuseDijkstra(shortestpath)algorithmtondaprimarypathrstfollowedbyndingabackuppathafterremovingthelinksalongtheprimarypath.Forthecaseofnoutilityfunctionforelasticserviceavailability,previousstudieshaveshownthattheaboveprimary-path-rstheuristiccanachieve 58IEEEJOURNALONSELECTEDAREASINCOMMUNICATIONS,VOL.26,NO.6,AUGUST2008 0 (q=0%) 1 (q=90%) 2 (q=99%) 3 (q=99.9%) 4 (q=99.99%) 5 (q=99.999%) 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Utility Function: Vs(
s)
s: Number of 9’s in Service Availability (qs) (a=0.7, b=1)Important User(a=1.7, b=1.05)Critical User(a=2.7, b=1.1) =8.1 =5.9 =3.5 Fig.1.Utilityasafunctionof(numberof9’sinserviceavailability)forthreetypicalkindsofusers.andachievespercentofsatisfactionatserviceavailability.Thenwehave 100=1Solvingtheequationsabovefor,wecanchoosethefollowingparameters,thusspecifyingtheutilityfunction q AfamilyofutilityfunctionswidelyusedinNUMforresourceallocationformulationsarethe-fairutilities[25],whichcanbenormalizedsuchthat 1
1sŠ Itturnsoutthatsuchutilityfunctionswillresultinaconvexoptimizationproblemforserviceavailabilityprovision-ing,thuslosingthedesirablepropertiesofefcientsolutions(centralizedordistributed)forglobaloptimality.Fortunately,thecurvesoftheutilityfunctionweproposedareveryclosetothoseofnormalizedutilityfunction(5)withappropriateparameters,whichareshownasthedashedlinesinFig.1.Therefore,adifferentparametrizationofutilitycurveswhoseshapesareveryclosetothestandard-faircurvesleadtoamuchmoretractableconvexitystructureintheproblemformulationtobeshownlaterthissection.B.EnhanceServiceAvailabilitywithSharedPathProtectionFailurerecoveryisusuallyrequiredforprovisioninghighserviceavailability.Therearetwomainfailurerecoveryprotectionrestoration.Themajordifferencebetweenthetwoisthat,inprotection,adetouraroundapossiblefailureisdeterminedatthetimeofconnectionsetupandthesparecapacityisallocatedandupdatedperiodicallyalongthedetourpriortothefailure,whereasinrestoration,thedetourisdynamicallydeterminedafterthefailureoccurs.Accordingly,protectionschemescaningeneralrecoverfromafailurequicker(aslongasthedetourisnotaffectedbyanyotherfailures),butarelessbandwidthefcientthanrestorationschemes.Ontheotherhand,restorationschemescansurviveoneormultiplefailures(aslongasthedestinationisstillreachable,withsufcientconnectivityandbandwidth),buttheycannotguaranteetherecoverytime,ortheamountofinformationlossforreal-timeapplications,makingthemun-suitableformission-criticalapplications.Inthispaper,wewillfocusonimprovingserviceavailabilitywithvariousprotectionInmanyapplications,wemainlyconsiderthescenarioofsinglefailure.Thenwecanusesharedprotection[26]–[28]toreducebandwidthusageinameshnetworksincethebackupbandwidthreservedbymultipleconnectionsonasamelinkcanbesharedaslongasnosinglefailurecanaffectthemsimultaneously.C.QualityofProtectionunderSharedPathProtectionWithsharedpathprotection,someschemeswithreliabilityofservice[1],[5],[6]canbeimplementedtodifferentiateserviceavailability.Forexample,inQualityofProtection(QoP),eachconnectionisassociatedwithacontinuousQoPQoP,1],whichisequivalenttotheprobabilityconnectionwillberestoredimmediatelyincaseoffailure.Suchprobabilisticmodelcanbeimplementedinadetermin-isticwaybyreserving,theexpectedbackupbandwidth,alongitsbackuppath[1].Inthiswork,weadoptsharedpathprotectionandQoPtoprovisionelasticserviceavailability.Therefore,foreach,besidesitsxedworking/primarypathithasapre-planneddisjointbackuppath,i.e.,.Incaseoffailureatlink,theconnectiononitsprimarypathwillreroutethetrafcalongitsbackuppathwithaprobabilityofdenotethelinkavailabilityoflinkandalllinkfailuresareassumedtobestatisticallyindependent.Thentheavailabilityoftheprimarypathandbackuppathoftherespectively.Whenatmostonelinkfailureisconsidered,theavailabilityforconnection+(1Tosearchfortheoptimalsolutiontoproblem(2)withthefailurerecoveryscheme()mentionedabove,weneedtoopti-mallydeterminethesourcerates()andserviceavailabilities)foralltheconnectionssimultaneously.WerefertosuchoptimizationprocedureasOPTForcomparisonpurpose,wealsointroducetwoextremecasesofrecoveryschemeasfollows.NoRecovery):Nofailurerecoveryschemeisimplemented,i.e..Thustheserviceavailability IEEEJOURNALONSELECTEDAREASINCOMMUNICATIONS,VOL.26,NO.6,AUGUST200855ElasticServiceAvailability:UtilityFrameworkandOptimalProvisioningDahaiXu,Member,IEEE,YingLi,StudentMember,IEEE,MungChiang,Member,IEEEandA.RobertCalderbank,Fellow,IEEE—Serviceavailabilityisoneofthemostcloselyscruti-nizedmetricsinofferingnetworkservices.Itisimportanttocost-effectivelyprovisionamanagedanddifferentiatednetworkwithvariousserviceavailabilityguaranteesunderauniedplatform.Inparticular,demandsforavailabilitymaybeelasticandsuch SUPPLEMENTONOPTICALCOMMUNICATIONSANDNETWORKINGTABLEIUMMARYOFOTATION s Serviceavailabilityprovidedforsource
s Numberof9’sinserviceavailability s Probabilityofinitiatingfailurerecoveryforsource Us(·) Utilityfunctionofsourcerateandserviceavailability s(·) Normalizedutilityfunctionofserviceavailability, whichmaytakeinargumentsof xs Datarateofsource ys Expectedbackuprateofsource ws Adjustedrateofsource as Criticalityparameter(inserviceavailability)of bs Elasticityparameter(inserviceavailability)of L(s) Primary/workingpathofsource M(s) Backuppathofsource cl Capacityoflink zl Backupbandwidthreservedonlink S(l) Setofconnectionsusinglinkonprimarypath T(l) Setofconnectionsusinglinkonbackuppath tradeoffbetweenthethroughputandtheserviceavail-ability.Engineeringimplicationsofthisworkquantifyseveralintu-itionsonelasticserviceavailability.Forexample,weshowthatindiscriminatelyprovisioningserviceavailabilitiesfordiffer-entkindsofuserswithinonenetworkleadstonoteworthysub-optimalityintermsofmaximizingnetworkutility.Byprolingbandwidthusage,weillustratethatprovisioninghighserviceavailabilityexclusivelyforcriticalusers/applicationsleadstosignicantwasteinbandwidthresource.Therestofthepaperisorganizedasfollows.InSec.II,weincorporatetheelasticserviceavailabilityintotheframeworkofNUMwithdifferentiatedfailurerecovery.InSec.III,aprice-baseddistributedalgorithmisproposedtodeterminede-sirableserviceavailabilityandsourcerateforeachuser.ThenwepresentresultsfromextensivenumericalexperimentsinSec.IV.WeconcludeanddiscussfutureworkonprovisioningofelasticserviceavailabilityinSec.V.ThekeynotationusedthroughoutthispaperissummarizedinTableI.II.SConsiderasimilarsetupasthatforproblem(1),butnowhasautilityfunction,whereisasourcerateandistheserviceavailabilityprovidedforsourceWeassumethattheutilityfunctionisacontinuous,strictlyincreasingfunctionofToprovisionhighnetworkavailability,sparebandwidthhastobereservedinadvance.Suchbandwidthisusuallynotusedundernormalsituationexceptbysomepreemptableconnections.Denoteasthebackupbandwidthreservedon.Letbetherecoveryschemetobeusedincaseoffailure,anddenotealsobythefunctionmappingthesourceratesandbackupbandwidthreservationtheserviceavailabilitiesachievedunderthefailurerecovery.Thentheresultingformulationisasfollows:subjectto=
(variablesThisproblemformulationisthestartingpointofthedevel-opmentinthissection.Next,weneedtospecifyfunctionandfunctionA.UtilityFunctionofServiceAvailabilityWeneedanappropriateutilityfunctiontomea-surethesatisfactionperceivedbyauserfrombothrateandserviceavailabilityilability,1].Inthiswork,wechoosechoose,1]denotesthenormalizedutilityfunctionofserviceavailability.Letbetherate,andbeastrictlyconcavefunction.Obviously,if,thenNotethatserviceavailability,,isgenerallymeasuredinthenumberof9’s.E.g.99.99%hasfour9’s.Weuserepresentthenumberofninesforserviceavailabilityfollows:Withaslightabuseofnotationtodenotethefunctionofaswell:,andisthenormalizedutilityfunctionof,thenumberof9’sinserviceavailabilityNotethatshouldbeastrictlyincreasingfunctionandboundedwithinwithin,1].Moreover,eachuserhasathresholdofacceptableserviceavailability,.Failingtoprovisionsuchserviceavailabilitywillresultinnear-zeroutilitynomatterwhatsourceratecanbeachieved.Baseontheaboveobservations,weproposethefollowingutilityfunction:Theproposedutilityfunction(4),depictedinFig.1,isaconcavefunctionofwithtwoparameters:.InFig.1,threetypicalkindsofusers(normal,importantandcriticalusers)withdifferentsensitivitiestoserviceavailabilityareillustrated.Forexample,homeuserscanbecategorizedasnormalusers,schoolusersareimportantusers,andnancialbusinessarecriticalusers.Thelargervalueofcriticalityparametermeanshigherserviceavailabilityrequirementandthelargervalueofelasticityparametermeanssteepercurveandsuggestslesselasticityinserviceavailabilityrequirement.Notethat,toensureensure,1],wehave bsas Wenowdemonstratehowparameterscanbesetfromcustomer’srequirementsstatedintwootherparametersofdirectengineeringimplications.Givenacustomerhasaminimumrequirementonserviceavailability, 56IEEEJOURNALONSELECTEDAREASINCOMMUNICATIONS,VOL.26,NO.6,AUGUST2008economicsinterpretationofthedual-baseddistributedalgo-rithmforNUM,inwhichtheLagrangedualvariablescanbeinterpretedasshadowpricesforresourceallocation,andeachenduserandthenetworkmaximizehis/hernetutilityandnetrevenue,respectively.Primalanddual-baseddistributedalgorithmshavebeenproposedtosolvefortheglobaloptimumofNUMproblems(e.g.,[12]–[14]).Consideracommunicationnetworkwithlogicallinks,eachwithaxedcapacityofbps,andsources(i.e.,endusers),eachtransmittingatasourcerateofbps.Eachemitsoneow,usingaxedsetoflinksinitspath,andhasautilityfunction.Eachlinksharedbyasetofsources.NUM,initsbasicversion,isthefollowingproblemofmaximizingthenetworkutility,overthesourcerates,subjecttolinearowforalllinkssubjecttovariablesMakingthestandardassumptiononconcavityoftheutilityfunctions,problem(1)isasimpleconcavemaximizationofdecoupledtermsunderlinearconstraints,whichhaslongbeenstudiedinoptimizationtheoryasamonotropicprogram[15].ThebasicNUM(1)hasbeenextendedtoincludeotherlayerstounderstandnetworkarchitecture[16],aswelltoachievefairresourceallocationinthenetworkprovisioningQoSandDifferentiatedService(DiffServ)[17].Thustheutilityfunctionisnotsolelydecidedbythetransmissionrate.Instead,itdependsontheQoS(suchasend-to-enddelay,jitter,packetloss,etc.)guaranteedforthetransmissionaswellasthetransmissionrate[18]–[21].However,amongtheextensiveliteratureonNUManditsgeneralizations,mostworkstreatutilityasafunctionofthroughputorthroughputperunitofenergy,withafewpublicationsexaminingutilityasafunctionofcommunicationreliabilityordelay.Incontrast,thequestionofhowtooptimallyprovisionthenetworkforserviceavailabilityhasnotbeentackledthroughtheutilityformulation.Throughoutthispaper,wewillencounterseveralnewchallengesintacklingthisnewquestion,fromtheintroductionofbothprimaryandbackuppathsforeachsourcetothenonconvexityintheproblemformulation.C.CommunicationReliabilityvs.ServiceAvailabilityIn[22],[23],theQoSofend-to-endcommunicationreliabil-ityisincorporatedintotheframeworkofNUM.Duetochan-nelnoiseorfading,notallthesignalscanbesuccessfullyde-codedatthereceiver.Onsomecommunicationlinks,thephys-icallayer’sadaptiveerrorcorrectionmechanismscanchangethelinkcapacityanddecodingerrorprobability,e.g.,throughadaptivechannelcodinginDigitalSubscriberLoop(DSL)broadbandaccessnetworksoradaptivediversity-multiplexingcontrolinMultiple-Input-Multiple-Output(MIMO)wirelesssystems.Leeetal.investigatetheintrinsictradeoffbetweenrateandcommunicationreliability(end-to-endsignalquality)[22].Marbukhproposedamethodofintegratingdiverserout-ingandretransmissionasanalterativetosinglepathroutingforeachow[23].Communicationreliabilityserviceavailabilityaretwodifferentconcepts.Someoftheirdifferencescanbedemon-stratedbyasimpleexample.Assumingacustomerrequests1Mbpsconnectionservicefromacarrier,butthecarriergrants1.01Mbpsbecauseeitherthecommunicationreliabilityorserviceavailabilityisonly99%.Fortheformerscenario,onaverage,onebitofevery100bitsislostduringthetrans-mission.Suchlosscanbecompensatedbyretransmissionsorappropriatecodinginafasttimescale[22].Incontrast,inthelatterscenario,theconnectionisavailableexceptforanunpredictable7hoursofdowntimeeverymonth.Ingeneral,thecustomerdoesnothavethesamesatisfaction/utilityinthetwoscenarios.Inadditiontotimescaledifference,communicationreliabil-ityandserviceavailabilityalsorelyondifferentmitigationmethods:channelcodingandlostpacketretransmissionareusedtoensurecommunicationreliability,andbackupband-widthprovisioningforpathrestorationandprotectionareusedtoenhanceserviceavailability.D.SummaryofContributionsInthispaper,weaddresstheresourceallocationwhenelasticserviceavailabilityisconsidered.Servicewillbetem-porarilyunavailablebecauseofthefailuresduetohumanmistakes(e.g.,mis-conguration),softwarebugs,hardwaredefects,naturaldisasters(e.g.,oodingorearthquakes),orevenperpetrators(e.g.,terroristsorhackers).Suchfailuresingeneralcannotberepairedimmediatelyorcompensatedbyretransmissionasinthecasesof[22],[23].Toensurethehighavailabilityrequiredbysomecriticalapplications,failurerecoveryhastobeimplementedwheretheaffectedtrafcisreroutedincaseoffailure.Aneffectivefailurerecoveryschemeusuallyconsistsofthreecomponents:establishingbackuppathsdisjointfromtheprimarypaths,provisioningnetworkresource(e.g.bandwidth)priortofailure,andreal-timefailuredetectionandsignalingtoreroutetrafc[24].Therstcomponenthasbeenextensivelystudiedwithgraphtheoreticmethods.Thethirdhasbeeninvestigatedbythesystemresearchcommunity.Inthiswork,wefocusonthesecondcomponent:bandwidthprovisioningtoachievetheoptimalserviceavailabilitythroughNUM.Thisworkisthersttoinvestigateelasticserviceavailabil-ityprovisioningusingdifferentiatedfailurerecovery:Framework:WedeveloptheNUMframeworkforelasticserviceavailability,andpresentautilityfunctionwithcongurableparameterstorepresentthesatisfactionper-ceivedbydifferentusersuponserviceavailabilityandsourcerate.Centralizedsolution:WithQualityofProtection(QoP)andsharedpathprotection,wetransformtheproblemintoaconvexoptimization,thusefcientlysolvableforglobaloptimalitythroughstandardcentralizedalgorithms.Distributedsolution:Withregularupdatesofbackuppathprovisioning,wealsoproposeaprice-baseddistributedalgorithmtooptimallyprovisionelasticserviceavailabil-ityandsourcerate.:Wecarryoutnumericalexperimentsoverrealisticnetworktopologies,andpresenttheoptimal SUPPLEMENTONOPTICALCOMMUNICATIONSANDNETWORKING[32]S.Baroni,P.Bayvel,andR.J.Gibbens,“Onthenumberofwavelengthinarbitrarily-connectedwavelength-routedopticalnetworks,”UniversityofCambridge,StatisticalLaboratoryResearchReport1998-7,availableathttp://www.statslab.cam.ac.uk/reports/1998/1998-7.pdf,1998.[33]Y.Liu,D.Tipper,andP.Siripongwutikorn,“Approximatingoptimalsparecapacityallocationbysuccessivesurvivablerouting,”inProc.IEEEConferenceonComputerCommunications(INFOCOMÕ01),An-chorage,AK,pp.699–708. DahaiXu(S’01-M’05)receivedtheB.Eng.de-greeinAppliedElectronicsin1996andM.Eng.inComputerScienceandEngineeringin1999fromShanghaiJiaoTongUniversity,China,andgothisPh.D.degreeinComputerScienceandEngineeringatStateUniversityofNewYorkatBuffaloin2005.Currently,heisaPostdoctoralResearchAsso-ciateintheDepartmentofElectricalEngineeringatPrincetonUniversity.HisresearchinterestsincludesurvivabilityandrestorationinIP/MPLS,opticalnetworks,networkdesignandprotocoldevelopmentfornextgenerationInternetandperformanceevaluation(modeling,simulationandmeasurements). YingLi(S’05)hasbeenworkingtowardsherPh.D.degreeinElectricalEngineeringatPrincetonUniversity,Princeton,NJ,USA,sinceSeptember2003,supervisedbyProfessorA.RobertCalderbankandProfessorMungChiang.ShereceivedtheB.E.degree(withhonor)andtheM.E.degreeinElec-tricalEngineeringfromXi’anJiaotongUniversity,Xi’an,China,in1997and2000respectively,andtheM.A.degreeinElectricalEngineeringatPrincetonUniversity,Princeton,NJ,USA,in2005.ShewasavisitingPh.D.studentinSwissFederalInstituteofTechnology(EPFL),Switzerland,insummer2007,andinMotorolaMultimediaResearchLab,Schaumburg,IL,USA,infall2007,respectively.SheworkedasafacultymemberofresearchandteachingassistantinDept.ofInformationandCommunicationEngineeringatXi’anJiaotongUniversity,China,from2000to2003,andasavisitingscholarinFujiXeroxCo.Ltd,Japan,from2000to2001.Herresearchinterestsincludecommunications,networking,optimization,informationtheory,andsignalprocessing. MungChiang(S’00-M’03)isanAssistantPro-fessorofElectricalEngineeringandanafliatedfacultyofAppliedandComputationalMathematicsandofComputerScienceatPrincetonUniversity.HereceivedtheB.S.(Honors)inElectricalEngi-neeringandMathematics,M.S.andPh.D.degreesinElectricalEngineeringfromStanfordUniversityin1999,2000,and2003,respectively.Heconductsresearchintheareasofnonlinearoptimizationofcommunicationsystems,theoreticalfoundationofnetworkarchitectures,algorithmsforbroadbandaccessnetworks,andstochasticanalysisofcommunicationsandnetworking.HereceivedCAREERAwardfromtheNationalScienceFounda-tion,YoungInvestigatorAwardfromtheOfceofNavalResearch,HowardB.WentzJuniorFacultyAwardandEngineeringTeachingCommendationfromPrincetonUniversity,SchoolofEngineeringTermanAwardfromStanfordUniversity,NewTechnologyIntroductionAwardfromSBCCommunications,andwasaHertzFoundationFellowandStanfordGraduateFellow.ForhisworkonbroadbandaccessnetworksandInternettrafcengineering,hewasselectedfortheTR35YoungTechnologistAwardin2007,alistoftop35innovatorsintheworldundertheageof35.HisworkonGeometricProgrammingwasselectedbyMathematicalProgrammingSocietyasoneofthetop3papersbyyoungauthorsintheareaofcontinuousoptimizationduring2004-2007.HisworkonLayeringAsOptimizationDecompositionbecameaFastBreakingPaperinComputerSciencebyISIcitation.Healsoco-authoredpapersthatwereIEEEInfocombestpapernalistandIEEEGlobecombeststudentpaper.HehasservedasanassociateeditorforIEEETransactionsonWirelessSpringerJournalofOptimizationandEngineeringleadguesteditorforIEEEJournalofSelectedAreasinCommunicationsguesteditorforIEEE/ACMTransactionsonNetworkingIEEETransac-tionsonInformationTheory,aProgramCo-Chairofthe38thConferenceonInformationSciencesandSystems,andaco-editorofthenewSpringerbookserieson“OptimizationandControlofCommunicationSystems.” A.R.Calderbank(M’89-SM’97-F’98)receivedtheBScdegreein1975fromWarwickUniversity,England,theMScdegreein1976fromOxfordUniversity,England,andthePhDdegreein1980fromtheCaliforniaInstituteofTechnology,allinDr.CalderbankisProfessorofElectricalEngi-neeringandMathematicsatPrincetonUniversitywherehedirectsthePrograminAppliedandCom-putationalMathematics.HejoinedBellTelephoneLaboratoriesasaMemberofTechnicalStaffin1980,andretiredfromAT&Tin2003asVicePresidentofResearch.Dr.Calderbankhasmadesignicantcontributionstoawiderangeofresearchareas,fromalgebraiccodingtheoryandquantumcomputingtowirelesscommunicationandactivesensing.Dr.CalderbankservedasEditorinChiefoftheIEEETransactionsonInformationTheoryfrom1995to1998,andasAssociateEditorforCodingTechniquesfrom1986to1989.HewasamemberoftheBoardofGovernorsoftheIEEEInformationTheorySocietyfrom1991to1996andbeganasecondtermin2006.Dr.CalderbankwashonoredbytheIEEEInformationTheoryPrizePaperAwardin1995forhisworkontheZ4linearityofKerdockandPreparataCodes(jointwithA.R.HammonsJr.,P.V.Kumar,N.J.A.Sloane,andP.Sole),andagainin1999fortheinventionofspace-timecodes(jointwithV.TarokhandN.Seshadri).Hereceivedthe2006IEEEDonaldG.FinkPrizePaperAwardandtheIEEEMillenniumMedal,andwaselectedtotheUSNationalAcademyofEngineeringin2005.