butdequeueselementsfromtheheadElementswithalowerrankaredequeuedrstiftwoelementshavethesamevaluetheelementenqueuedearlierisdequeuedrst2ThecomputationofanelementsrankbeforeitisenqueuedintoaPIFOWemodel ID: 864217
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1 last_finish[f]=p.start+p.length/f.weight![last_finish[f]=p.start+p.length/f.weight](864217/last-finish-f-p-start-p-length-f-weightp.jpg "last_finish[f]=p.start+p.length/f.weight")
last_finish[f]=p.start+p.length/f.weightp.rank=p.start ,butdequeueselementsfromthehead.Elementswithalowerrankarede-queuedÞrst;iftwoelementshavethesamevalue,theelementenqueuedearlierisdequeuedÞrst.2.ThecomputationofanelementÕsrankbeforeitisen-queuedintoaPIFO.Wemodelthiscomputationasapackettransaction[37],anatomicallyexecutedblockofcodethatisexecutedonceforeachelementbeforeenqueuingitinaPIFO. p.rank=p.start schedulingtransactionbeforeenqueuinganelementintothatnodeÕsPIFO;thiselementiseitherapacketorareferencetoachildPIFOofthenode.Second,aschedulingtransactionthatspeciÞeshowtherankiscomputedforelements(packetorPIFOreferences)thatareenqueuedintothenodeÕsPIFO.Figure2bshowsanexampleforHPFQ.Whenapacketisenqueuedintoaschedulingtree,itex-ecut
2 esonetransactionateachnodewhosepacketpre
esonetransactionateachnodewhosepacketpredicatematchesthearrivingpacket.Thesenodesformapathfrom shapingPIFO severalmoreexamples(¤3.1through¤3.4)andalsodescribethelimitationsofourprogrammingmodel(¤3.5).3.1LeastSlack-TimeFirstLeastSlack-TimeFirst(LSTF)[29,31]schedulespacketsateachswitchinincreasingorderofpacketslacks,i.e.,thetimeremaininguntileachpacketÕsdeadline.Packetslacksareinitializedatanendhostoredgeswitchandaredecre-mentedbythewaittimeateachswitchÕsqueue.WecanprogramLSTFusingasimpleschedulingtransaction:p.rank=p.slack+p.arrival_timeTheadditionofthepacketÕsarrivaltimetotheslackal-readycarriedinthepacketensuresthatpacketsaredequeuedinorderoftheirslackatthetimeofdequeue,notenqueue.Then,afterpacketsaredequeued,wesubtractthetimeatwhi
3 chthepacketisdequeuedfromthepacketÕsslac
chthepacketisdequeuedfromthepacketÕsslack,whichhastheeffectofdecrementingtheslackbythewaittimeattheswitchÕsqueue.Thissubtractioncanbeachievedbypro-grammingtheegresspipelineofaprogrammableswitch[17]todecrementoneheaderÞeldbyanother.3.2Stop-and-GoQueueingif(now�=frame_end_time):frame_begin_time=frame_end_timeframe_end_time=frame_begin_time+Tp.rank=frame_end_timeFigure6:ShapingtransactionforStop-and-GoQueueing.Stop-and-GoQueueing[24]isanon-work-conservingal-gorithmthatprovidesboundeddelaystopacketsusingaframingstrategy.Timeisdividedintonon-overlappingframesofequallengthT,whereeverypacketarrivingwithinaframeistransmittedattheendoftheframe,smoothingoutanyburstinessintrafÞcpatternsinducedbyprevioushops.TheshapingtransactioninFigure
4 6speciÞesthescheme.frame_begin_timeandfr
6speciÞesthescheme.frame_begin_timeandframe_end_timearetwostatevari-ablesthattrackthebeginningandendofthecurrentframe Whenapacketisenqueued,weexecuteaFIFOschedul-ingtransactionatitsleafnode,settingitsranktothewall-clocktimeonarrival.Attheroot,aPIFOreference(thepacketÕsßowidentiÞer)ispushedintotherootPIFOusingarankthatreßectswhethertheßowisaboveorbelowitsratelimitafterthearrivalofthecurrentpacket.Todeter-minethis,weruntheschedulingtransactioninFigure7thatusesatokenbucket(thestatevariabletb)thatcanbeÞlledupuntilBURST_SIZEtodecideifthearrivingpacketputstheßowaboveorbelowmin_rate.NotethatasinglePIFOnodewiththeschedulingtransac-tioninFigure7isnotsufÞcient.Itcausespacketreorderingwithinaßow:anarrivingpacketcancauseaßowtomovefromalowertoah
5 igherpriorityand,intheprocess,leavebefor
igherpriorityand,intheprocess,leavebeforelowprioritypacketsfromthesameßowthatarrivedearlier.Thetwo-leveltreesolvesthisproblembyattachingprioritiestotransmissionopportunitiesforaspeciÞcßow,notspeciÞcpackets.Nowifanarrivingpacketcausesaßowtomovefromlowtohighpriority,thenextpacketscheduledfromthisßowistheearliestpacketofthatßowchoseninFIFOorder,notthearrivingpacket.3.4OtherexamplesWenowbrießydescribeseveralmoreschedulingalgo-rithmsthatcanbeprogrammedusingPIFOs.1.Fine-grainedpriorityscheduling.ManyalgorithmsschedulethepacketwiththelowestvalueofaÞeldini-tializedbytheendhost.Thesealgorithmscanbepro-grammedbysettingthepacketÕsranktotheappropri-ateÞeld.ExamplesofsuchalgorithmsandtheÞeldstheyusearestrictpriorityscheduling(IPTOSÞeld),Shortest
6 FlowFirst(ßowsize),ShortestRemainingProc
FlowFirst(ßowsize),ShortestRemainingProcessingTime(remainingßowsize),LeastAttainedService(bytesreceivedforaßow),andEarliestDead- schedulerbasedonPIFOs.Wetargetshared-memoryswitchessuchasBroadcomÕsTridentII[3](Figure8).Intheseswitches,aparserfeedspacketsfromallportsinto schedulingtreeandmostpracticalhierarchicalschedulingalgorithmsweknowofdonotrequiremorethanafewlevels erationsoneachPIFO.Figures11aand12ashowthistreeforFigures2and4respectively.ItthenoverlaysthistreeoveraPIFOmeshbyassigningeverylevelofthetreetoaPIFOblockandconÞguringthelookuptablestoconnectPIFOblocksasrequiredbythetree.Figure11bshowsthePIFOmeshforFigure2,whileFigure12bshowsthePIFOmeshforFigure4.Ifaparticularlevelofthetreehasmorethanoneenqueueordequeuefromanotherlevel,w
7 hicharisesinthepresenceofshapingtransact
hicharisesinthepresenceofshapingtransactions(¤),weallocatenewPIFOblocks .Thiscreatesaconßictbecausetherearetwoenqueueoperationsinthesamecy-cle.Conßictsmayalsooccurondequeues.Forinstance,ifTBF_RightshareditsPIFOblockwithanotherlogicalPIFO,dequeueoperationstothetwologicalPIFOscouldoccuratthesametimebecauseTBF_Rightcanbedequeuedatanyarbitrarywall-clocktime.Inaconßict,onlyoneofthetwooperationscanproceed.WeresolvethisconßictinfavorofschedulingPIFOs.Shap-ingPIFOsareusedforratelimitingtoaratelowerthanthelinerate.Therefore,theycanaffordtobedelayedbyafewclocksuntiltherearenoconßicts.Bycontrast,delayingschedulingdecisionsofaschedulingPIFOwouldmeanthattheswitchwouldidleandnotsatisfyitsline-rateguarantee.Asaresult,shapingPIFOsonlygetbest-effort
8 service.Thereareworkaroundstothis.Oneiso
service.Thereareworkaroundstothis.Oneisoverclockingthepipelineat(say)1.25GHzinsteadof1GHz,providingspareclockcyclesforsuchbest-effortprocessing.AnotheristoprovidemultipleportstoaPIFOblocktosupportmulti-pleoperationseveryclock.Thesetechniquesarecommonlyusedinswitchesforbackgroundtaskssuchasreclaimingbufferspace,andcanbeappliedtothePIFOmeshaswell.5.HARDWAREIMPLEMENTATION isasinglecell.Hence,upto60Kpackets/elementsperPIFOblockcanbespreadoutovermultiplelogicalPIFOs.Basedontheserequirements,ourbaselinedesigntargetsaPIFOblockthatsupports64Kpacketsand1024ßowsthatcanbesharedacross256logicalPIFOs.Further,wetargeta6Packetsinashared-memoryswitchareallocatedinsmallunitscalledcells.Figure13:BlockdiagramofPIFOblockwithaßowsched-ulerandarankstore.
9 LogicalPIFOsandmetadataarenotshownforsim
LogicalPIFOsandmetadataarenotshownforsimplicity.16-bitrankÞeldanda32-bitmetadataÞeld(e.g.,p.lengthinFigure1)forourPIFOblock.Weput5suchblocksto-getherintoa5-blockPIFOmeshthatcansupportupto5levelsofhierarchyinaschedulingalgorithmÑsufÞcientformostpracticalhierarchicalschedulersweknowof.5.2AsinglePIFOblock isonneedsonecomparatorcircuit,andsupporting64Koftheseisinfeasible.Atthesametime,nearlyallpracticalschedulingalgo-rithmsgrouppacketsintoßowsorclasses,7e.g.,basedontrafÞctype,ports,oraddresses.TheythenscheduleaßowÕspacketsinFIFOorderbecausepacketranksincreaseacrossaßowÕsconsecutivepackets.Thismotivatesadesignwithtwoparts(Figure13):1.Aßowschedulerthatpickstheelementtodequeuebasedontherankofthehead(earliest)elementsofeachßow.Theßowschedul
10 eriseffectivelyaPIFOconsistingoftheheade
eriseffectivelyaPIFOconsistingoftheheadelementsofallßows.2.Arankstore,aFIFObankthatstorestheranksofele-mentsbeyondtheheadforeachßowinFIFOorder. mateof200mm2providedbyGibbetal.[23].Inreturnforthis3.7%,wegetasigniÞcantlymoreßexiblepacketsched-ulerthancurrentswitches,whichprovideÞxedtwoorthree-levelhierarchicalscheduling.Our3.7%areaoverheadissimilartotheoverheadforotherprogrammableswitchfunc-tions,e.g.,2%forprogrammableparsing[23]and15%forprogrammableheaderprocessing[ 0.1476(fromsynthesis)OnePIFOblock0.224+0.445+0.148+0.148+0.1476=1.11mm25-blockPIFOmesh5.55300atomsspreadoutoverthe5-blockPIFOmeshforrankcomputa-tions6000µm PriorityFlowControl.PriorityFlowControl(PFC)[7]isastandardthatallowsaswitchtosendapausemessagetoanupstreamswitchrequ
11 estingittoceasetransmissionofpacketsbelo
estingittoceasetransmissionofpacketsbelongingtoparticularßows.PFCcanbeintegratedintoourhardwaredesignbymaskingoutcertainßowsintheßowschedulerduringthedequeueoperationiftheyhavebeenpausedbecauseofaPFCpausemessage,andunmask-ingthemwhenaPFCresumemessageisreceived.Multi-pipelineswitches.Thehighestendswitchestoday,suchastheBroadcomTomahawk[],supportaggregateca-pacitiesexceeding3Tbit/sec.Ataminimumpacketsizeof64bytes,thiscorrespondstoanaggregatepacketrateof~6billionpackets/s.Becauseasingleswitchpipeline(Figure8)typicallyrunsat1GHzandprocessesabillionpackets/s,suchswitchesrequiremultipleingressandegresspipelinesthatshareaccesstotheschedulersubsystemalone.Inmulti-pipelineswitches,eachPIFOblockneedstosup-portmultipleenqueueanddequeueoperatio
12 nsperclockcy- stractions[ aseparateP-hea
nsperclockcy- stractions[ aseparateP-heapinstanceforeachport[].Thisper-portdesignincursprohibitiveareaoverheadonashared-memoryswitch,andpreventssharingofthedatabufferandbinaryheapacrossoutputports.Conversely,itisnÕteasytooverlaymultiplelogicalPIFOsoverasingleP-heap,whichwould (WFQ)orminimumßowcompletiontime(SRPT).PastworkhasdemonstratedsigniÞcantperformancebeneÞtsre-sultingfromswitchsupportforßexibleallocation[12,21,32,39].However,thesebeneÞtshaveremainedunrealized, andmakeitmorepredictable.Thatsaid,ourcurrentdesignisonlyaÞrststepandcanbeimprovedinseveralways. [1]Barefoot:TheWorldÕsFastestandMostProgrammableNetworks.https://barefootnetworks.com/media/white_papers/Barefoot-Worlds-Fastest-Most-Programmable-Networks. com/products/physi
13 cal-ip/embedded-memory-ip/sram.php.[9]Sy![cal-ip/embedded-memory-ip/sram.php.[9]Sy](864217/cal-ip-embedded-memory-ip-sram-php-9-sys.jpg "cal-ip/embedded-memory-ip/sram.php.[9]Sy")
cal-ip/embedded-memory-ip/sram.php.[9]SystemVerilog.https://en.wikipedia.org/wiki/SystemVerilog.[10]TokenBucket.https://en.wikipedia.org/wiki/Token_bucket ,17(6):1030Ð1039,Jun1999.[20]A.Demers,S.Keshav,andS.Shenker.AnalysisandSimulationofaFairQueueingAlgorithm.InSIGCOMM,1989.[21]F.R.Dogar,T.Karagiannis,H.Ballani,andA.Rowstron.DecentralizedTask-awareSchedulingforDataCenterNetworks.InSIGCOMM,2014.[22]S.FloydandV.Jacobson.RandomEarlyDetectionGatewaysforCongestionAvoidance.IEEE/ACMTransactionsonNetworking,1(4):397Ð413,Aug.1993.[23]G.Gibb,G.Varghese,M.Horowitz,andN.McKeown.DesignPrinciplesforPacketParsers.In,2013.[24]S.J.Golestani.AStop-and-GoQueueingFrameworkforCongestionManagement.InSIGCOMM,1990.[25]P.Goyal,H.M.Vin,andH.Chen.Start-time
14 FairQueueing:ASchedulingAlgorithmforInte
FairQueueing:ASchedulingAlgorithmforIntegratedServicesPacketSwitchingNetworks.InSIGCOMM,1996.[26]V.Jeyakumar,M.Alizadeh,D.Mazires,B.Prabhakar,A.Greenberg,andC.Kim.EyeQ:PracticalNetworkPerformanceIsolationattheEdge.InNSDI,2013.[27]C.R.Kalmanek,H.Kanakia,andS.Keshav.RateControlledServersforVeryHigh-SpeedNetworks.InGLOBECOM,1990.[28]S.Keshav.Packet-PairFlowControl.IEEE/ACMTransactionsonNetworking InHotNets,2015.[39]A.Sivaraman,K.Winstein,S.Subramanian,andH.Balakrishnan.NoSilverBullet:ExtendingSDNtotheDataPlane.InHotNets,2013.[40]H.Song.Protocol-ObliviousForwarding:UnleashthePowerofSDNThroughaFuture-proofForwardingPlane.InHotSDN,2013.[41]D.Verma,H.Zhang,andD.Ferrari.GuaranteeingDelayJitterBoundsinPacketSwitchingNetworks.InTRICOMM,1991.