SustainableWireless Network-on-Chip Architectures
PaulWettin
ParthaPratimPande
BehroozShirazi
JacobMurray
MorganKaufmannisanimprintofElsevier
50HampshireStreet,5thFloor,Cambridge,MA02139,USA
Copyright r 2016ElsevierInc.Allrightsreserved.
Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans, electronicormechanical,includingphotocopying,recording,oranyinformationstorageand retrievalsystem,withoutpermissioninwritingfromthepublisher.Detailsonhowtoseek permission,furtherinformationaboutthePublisher’spermissionspoliciesandourarrangements withorganizationssuchastheCopyrightClearanceCenterandtheCopyrightLicensingAgency, canbefoundatourwebsite: www.elsevier.com/permissions
Thisbookandtheindividualcontributionscontainedinitareprotectedundercopyrightbythe Publisher(otherthanasmaybenotedherein).
Notices
Knowledgeandbestpracticeinthisfieldareconstantlychanging.Asnewresearchand experiencebroadenourunderstanding,changesinresearchmethods,professionalpractices, ormedicaltreatmentmaybecomenecessary.
Practitionersandresearchersmustalwaysrelyontheirownexperienceandknowledgein evaluatingandusinganyinformation,methods,compounds,orexperimentsdescribedherein.In usingsuchinformationormethodstheyshouldbemindfuloftheirownsafetyandthesafetyof others,includingpartiesforwhomtheyhaveaprofessionalresponsibility.
Tothefullestextentofthelaw,neitherthePublishernortheauthors,contributors,oreditors, assumeanyliabilityforanyinjuryand/ordamagetopersonsorpropertyasamatterofproducts liability,negligenceorotherwise,orfromanyuseoroperationofanymethods,products, instructions,orideascontainedinthematerialherein.
BritishLibraryCataloguing-in-PublicationData AcataloguerecordforthisbookisavailablefromtheBritishLibrary
LibraryofCongressCataloging-in-PublicationData AcatalogrecordforthisbookisavailablefromtheLibraryofCongress
ISBN:978-0-12-803625-9
ForInformationonallMorganKaufmannpublications visitourwebsiteat https://www.elsevier.com/
Publisher: ToddGreen
AcquisitionEditor: ToddGreen
EditorialProjectManager: LindsayLawrence
ProductionProjectManager: PunithavathyGovindaradjane
TypesetbyMPSLimited,Chennai,India
networksoasinglecoreisnotabletocongesttheentirenetwork, allowingadditionalcorestobeabletotransfertheirdataaswell.
Acontinuationofthebusnetworkistheringandstar-ringnetworks,seenin Fig.1.1bandc,respectively.Foraring,eachcoreis connectedtoitsownindividualnetworkswitchandthenetwork switchesareconnectedtotwoneighbors.Inthecaseofthestar-ringan additionalcentralnetworkswitchconnectstoallotherswitches.The dedicatedswitchinthestar-ringnetworkallowsthecoretosendits dataanddoothertaskswhilethenetworkswitchestakecareofdata delivery.Aninsufficiencywiththeringnetworkisthattheaverage hopcountbetweencoresisrelativelyhighascanbeseenin Table1.1 Hopcountisthenumberoflinksthatdatahastotraversebeforearrivingatthedestinationcorefromthesendingcoreconsideringuniform randomtraffic.Themorecoresthatareinsertedintotheringnetwork, onaverage,themorenumberofhopsittakestoreachanyothercore. Thestar-ringnetworkwascreatedtointroduceshortcutsintothe networktotryandreducetheaveragehopcountwithin thenetwork,reducingtheaveragehopcountfrom6.2to3.8fora16corenetwork,asseenin Table1.1.However,thisrequiresaverylarge networkswitch,with N ports,foran N corenetworktobebuiltthat hastoconnecttoeachoftheothernetworkswitches.Althoughthe centralswitchreducestheaveragehopcount,italsocreatesatraffic bottleneck;allofthetrafficwilltrytousethisnetworkswitchasitcreatesshortcutsinthenetwork.
Increasingtheaveragenumberoflinksperswitchcandecreasethe averagehopcountofthenetwork.Themeshnetworkproducesaregulargrid-likestructurewhereeac hnetworkswitchisconnectedto eachofitscardinalneighbors.Theaveragenumberoflinksper switchisgreaterinmeshthanthatofaringnetwork,3:2fora16corenetwork,whichcanbeseenin Table1.1.A16-coremeshcanbe seenin Fig.1.1d .Themeshlayouthasbeenimplementedinexisting chipsandworkswellasitiseasytoconstructandscaleusinga standardprocessingtile(whichincludesaprocessor,cache,andan NoCswitch).Whileithasrelativelygoodthroughput,asitisscaled, pathsbegintohavelargenumberofhops.Inasimpleexample, communicatingfromonecornerofthemeshtoanothertakes (M 1) 1 ( N 1)hops,where M and N arethenumberofrowsand columnsinthemesh,respectively.Thisgrowthinhopcountcanbe seenin Table1.1 .
N 5 16Averagenumberofconnectionsperswitch1243441.86671.63.4286
Averagehopcount16.26673.86674.66674.13334.13336.53333.64.6667
TotalnumberofswitchesN/A161716161615514
Maxhopcount1104866846
Averagelinklength1611.511.5211.21
Maximumnumberofconnectionsper switch N/A216444356
N 5 32Averagenumberofconnectionsperswitch1243.25441.93551.81823.7333
Averagehopcount110.25813.935565.09685.09688.32264.83876.3871
TotalnumberofswitchesN/A3233323232311130
Maxhopcount118412881068
Averagelinklength321211.62521.03231.23811.125
Maximumnumberofconnectionsper
N 5 64Averagenumberofconnectionsperswitch1243.5441.96831.90483.871
Averagehopcount117.92063.96837.33336.06356.063510.19054.83878.2222
TotalnumberofswitchesN/A6465646464632162
Maxhopcount134416101012610
Averagelinklength6411.812511.7521.09091.33331.1765
Maximumnumberofconnectionsper switch N/A264444356
destinationcolumnistotherightofthefirstswitch.Itcontinuesthis directionforatotalof2hops.Oncethedataisinaswitchthatisin thesamecolumnasthedestination,thedatawillthentrytomatchthe destinationrow.Inthisexamplethedestinationcoreisbelowthe switchassociatedwithcore3,sothedatawillmoveinthedownward directionfor3hops.Oncethedataislocatedintheswitchassociated withcore15,itwilldeliverthedatatothatcore.AvariationonX Y routingisY Xrouting;datawillfirsttrytomatchthedestination rowfirst,followedbydestinationcolumn.Asmentionedearlier,the biggerthenetworkbecomesthelargertheaveragehopcountbecomes inameshnetwork.Thelongerthedatahastomovethroughthenetworktoreachitsdestination,thereisalargerchancethatthereisdata thatwillcompetefornetworkresourceswhichinturnwillleadtoa largerlatencybeforedatacanbedelivered.
Fig.1.2b showsanexampleofUp Down routingfortreenetworks.Datawillrouteupthetree A numberoftimes,where A isanumbergreaterthanorequaltozero,untilacommonsubtreeswitchhas beenreached.Itwillthenroutedownthetree B numberoftimes,where B isanumbergreaterthanorequaltozero.Oncedatahasbegunto moveinthedownwarddirectioninthetree,itwillneverusealinkin theupdirection.Forthisexample,datawasgeneratedincore1whose destinationiscore4.Core1injectsthedataintothefirstswitchwhichis thenroutedupthetreefor3hopsuntilitreachestherootswitch.The datathenmovesdownthetreefor4morehopsuntilitreachescore4. Asmentionedearlierinthischapter,treenetworkshaveabottleneck problemintherootswitch.Asthenetworkbecomeslarger,moretraffic willtrytousetherootswitchincreasingtheaveragenetworklatency.
Routinginaringnetworkistypicallydonebychoosingthelink thatwilltaketheshortestpathtogettothedestinationcore.Asthe networkbecomeslarger,theaveragehopcountincreases.Similarto mesh,thelongerthedataiswithinthenetworkthemorechanceitwill haveforotherdatatocompeteforthesamenetworkresources, increasingnetworklatency.Comparabletotheringnetwork,routing inthestar-ringnetworkwillalsopicktheshortestpath;mostofthe time,thisisthroughthecentralswitch.Thestar-ringnetworkhowever hasnetworkissuessimilartotreenetworks;thecentralswitchisessentiallyonegiantrootswitchconnectedtoalltheotherswitches.Almost alldatawilltrytousethiscentralswitchcreatingabottleneck.This leadstolargeaveragenetworklatency.
Manyroutingvariantsincludingfullyandpartiallyadaptiverouting schemes(Lietal.,2006;Schonwaldetal.,2007;Flich,etal.,2012) andcompacttable-andsegment-basedrouting(Thorupetal.,2001; Flichetal.,2007)havebeenexploredindepth,whichprovideadditionalimprovementsonstandardX YandUp Down routings. Whiletheseexist,onefocusofthisbookisonadopting suitableroutingstrategiesfortopology-agnosticnetworks,whichwill beexploredthroughoutthefollowingchapters.
TRADITIONALNoCBACKBONE
Asastandard,theNoCparadigmhasbeenusedasascalableinterconnectioninfrastructureforthesenewlyintegratedmany-corechips. ManyadvancesinNoCresearch,includingpowerefficiency,reliability,andsustainability,havemadeitavalidchoiceasacommunication backboneinmulticoreandmany-corechips.Althoughtheexisting methodofimplementinganNoCwithplanarmetalinterconnectsisa verymatureprocess,itisdeficientduetothehighlatency,significant powerconsumption,andtemperaturehotspotsarisingoutoflong, multihopwirelinepathsusedindataexchangewithscalingtechnology nodes.Additionalissuesofphysicalwiredefectsandelectromigration worsenthereliabilityofmetalinterconnects.Accordingtothe InternationalTechnologyRoadmapforSemiconductors,forthelonger term,improvementsinmetalwirecharacteristicswillnolongersatisfy performancerequirementsandnewinterconnectparadigmsareneeded. Fig.1.3 presentshowenergydissipatedperbitchangesasafunction
Figure1.3Energy/bitversuswirelengthforaplanarmetalinterconnect.
Fig.2.2 showsthreedifferentnetworksonascaleofhowthelinks interconnectthenodes.Ontheleftof Fig.2.2 isanErd ˝ os Rényinetwork, wherethelinksbetweennodesarecompletelyrandomandanytwonodes canbeconnected,independentofexistinglinksordistancebetweennodes. Ontherightof Fig.2.2 isatorusnetwork,whereeachnodeisconnected toitscardinalneighborsandwheretherowsandcolumnswraparoundto thestartandendofeachroworcolumntoensurethateachnodehasfour connections.Thenetworkinthemiddleof Fig.2.2 isasmall-worldnetworkwherenodesclosetogetherareconnected,butalso,thereareshortcutsthroughoutthenetworksodatacanreachanynodeinasmall numberofhops. Table2.1 summarizesthedifferencesofthesenetworks assuminguniformrandomtraffic.Networkswiththesmall-world
(c)
Figure2.1Various16-coreirregularNoCinterconnecttopologies.
N 5 16Averagenumberofconnectionsperswitch444
Averagehopcount4.44.33334.2667
Totalnumberofswitches161616
Maxhopcount666
Averagelinklength1.59131.54952.1691
Maximumnumberofconnectionsperswitch666
N 5 32Averagenumberofconnectionsperswitch444
Averagehopcount4.41114.54.7419
Totalnumberofswitches323232
Maxhopcount666
Averagelinklength2.14872.20143.2543
Maximumnumberofconnectionsperswitch779
N 5 64Averagenumberofconnectionsperswitch444
Averagehopcount4.71124.7324.8
Totalnumberofswitches646464
Maxhopcount666
Averagelinklength2.46652.86234.1208
Maximumnumberofconnectionsperswitch779
propertyhaveaveryshortaveragepathlength.Thismakessmall-world graphsinterestingforefficientcommunicationwithminimalresources.
Thetrade-offwithusingirregulartopologiesisthatalthoughthe averagenumberofhopsbetweenthenodesdecreases,theaverage lengthofeachhopincreases.Withlargersystemsizes,thetrade-off
Figure2.2Networkconnectivitygraphforirregularnetworks.
onlyusingthe z-dimension,theareaoverheadofthewidebussesis severelyreduced.Widebusesspecificallyalleviatethememorywall problemwhichinturncanmakechipsfaster.Researchinto3DNoCs canbeseenin Chenetal.(2015) and Jabbaretal.(2013).
However,therearemanychallengestoovercomebefore3Dintegrationiswidelyadopted;specifically,manufacturingcost,manufacturing yield,heatdissipationissues,designcomplexity,the3Dlayercommunicationoverhead,andtesting.Currently,manufacturing3Dcircuitsis verycostlyduetothetechnologybeingnewandnontrivial.Breaking downonechip,younowhavetomanufactureasmanydiesasyouhave layerswithallthecostassociatedwithbuildingeachlayer.Notonlydoes eachdielayerhaveitsownyieldbutalsoputtingthewholechiptogether willhaveitsownyieldissues.Heatdissipationwillbethemainchallenge toovercome.Heatgeneratedinthemiddleofthechiplayerscorrelating tothermalhotspotsmustbecarefullymanaged.Thelayercommunicationoverheadcannotbedisregarded.Cuttingachipintofourthstomake afour-layerstackforgetsabouttheareaoverheadittakestocommunicatebetweenthelayers.Atthe45-nmtechnologynode,theareaofa 10 µmby10 µmthrough-siliconvia(TSVs)iscomparabletoabout50 gates;thisdoesnotincludethepadstoconnecttheTSVs,keepoutzones neededtobuildtheTSVs,androutingobstacleswithinthemetallayers. Testing,specificallythetimingcriticalpaths,willbehardertodebugand fixwhenthetimingcriticalpathsgoacrossmultiplelayers.
On-chipphotonicsaddressthescalingchallengebyallowingthe multiplexingofthecorecommunicationmedium.Effectivelythis allowsthecorestohaveanall-to-allnetworkschemewithoutthelong delayoverheadusuallyassociatedwithanall-to-allscheme.Thisfrees upthecoresfromhavingtowaittotransmittheirdatawhilewaiting forcommunicationaccess.Anotherbenefitofusingon-chipphotonics isthesmallareaoverheadofthephotoniccomponents,allowingchips tobemorecompactorenablingchipdesignerstomoreefficientlyuse chiparea,notwastingspaceforcommunicationcomponents. Additionally,communicationbetweenthecoresisdoneatthespeedof lightinanopticalwaveguide;therearenolongwirestochargeordischarge,thusincreasingthebandwidthofthecommunicationmedium. Usingopticalcomponentsalsosubstantiallylowersthepowerdissipationofcommunicationbetweencores;onlydissipatingminimalpower toinjectandreceivedatafromtheopticalmedium,nottomovedata
withinthemedium.ResearchintoopticalNoCscanbeseenin Koohi etal.(2010) and Koohietal.(2011)
However,therearemanychallengestoovercomebeforeon-chip photonicintegrationiswidelyadopted;specifically,silicon-photonic integration,manufacturingcostandyield,temperaturesensitivityofthe photoniccomponents,designcomplexity,testing,andlasersourceintegration.Currently,nontraditionalmethodsareusedwhenconstructing thephotoniclayersuponastandardsiliconwafer.Theintegrationof thephotoniclayersisintegraltoaworkingphotonicchip.Designofthe photoniclayerswillalsobecriticaltophotonicchips.Theopticalwaveguideshavestrictconstructionrulestoallowtheopticalsignaltopropagateproperly.Also,testingofphotonicchipswithtraditionalmethods, likebed-of-nails,willnotwork;newtestingmethodologieswillneedto bedevelopedtotesttheopticalcomponents.Finally,integrationofthe lasersource,whetheron-oroff-chip,needstobetakenintoaccount alongwiththepowerdissipationofthelasersource.
RFinterconnecttechnologiesareverysimilartoon-chipphotonics; however,theyusehigh-frequencywavesinsteadofphotonstotransmit theirdatawithinwaveguides.RFinterconnecttechnologiescanuse currentmanufacturingtechnologiestomaketheroutingwaveguides whichsavesinmanufacturingtimeandcost.Theycanpotentiallyturn multihoppathsintosingle-hop,high-bandwidthpathssavingboth delayandpowerdissipation.
However,therearemanychallengestoovercomebeforeRFinterconnecttechnologiesarewidelyadopted;specifically,waveguide manufacturing,areaoverhead,transmissionlength,andtesting. Althoughmanufacturingthewaveguidescanbedonewithcurrent technologyandtechniques,thelayoutdesignofsuchwaveguidesis nontrivial.Dependingontheexactfrequenciesused,theareaoverhead ofthetransceiversmustbetakenintoaccountwhendesigningthe chip.Theareaoverheadofthetransceiverscanbereducedbyusing higherfrequencies;however,thiscomesatthecostofreducingthe transmissionlengthpossiblewithinthewaveguides.Reducingthe transmissionlengthtoomuchcaninturnmakemultihoppathswhich istheoriginalbottleneck.Also,testingoftheRFcomponentsbecome nontrivial,newtestingmethodologieswillbeneededtoverifythatthe RFcomponentsareworkingasintended.
suitablyvaryingtheirvoltageandfrequencylevels.Consequently,this willenablepowersavingsandloweringoftemperaturehotspotsinspecificregionsofthechip.TheaimistoshowhownovelNoC architectureswithlong-rangewirelesslinksandDVFS-enabledwireline interconnectslowertheenergydissipationofamulticorechip,and consequentlyhelptoimprovethethermalprofile.Afteraddressingthe network-levelissues,theprocessingcoresarealsoaddressedby implementingDVFSamongthemaswell.
ThermaloptimizationintheformofDTMtechniquesalsoappear asasolutiontoavoidhighspatialandtemporalthermalvariations andtherebyavoidlocalizedhotspots(Chaparroetal.,2007).Byimplementingnewthermalmanagementstrategiesinconjunctionwitha dual-levelDVFSstrategyonaWiNoCshouldsignificantlydecrease theoverallthermalprofilewhilenotincurringsignificantperformance penalties.Weproposeapplyingadual-levelDTMstrategytosimultaneouslyaddressprocessor-andnetwork-levelhotspotsinWiNoC architectures.Wedemonstratethatbyincorporatingatemperatureawaretaskallocationheuristictotheprocessingcores,anda dynamicroutingstrategytotheswitches,itispossibletoreducelocal temperaturehotspotsinWiNoCswithoutasignificantperformance impact.Asafinalstep,wefurtherexplorethecapabilitiesofirregular congestion-awareroutingstrategiescoupledwithsuitableDVFStechniquesjointlytofurtherreducetemperaturesoftheNoC.
REFERENCES
Barabasi,A.,Bonabeau,E.,2003.Scale-freenetworks.Sci.Am.50 60.
Bienia,C.,2011.BenchmarkingModernMultiprocessors(Ph.D.dissertation).Dept.Computer Science,PrincetonUniv.,Princeton,NJ.
Chaparro,P.,Gonzalez,J.,Magklis,G.,Qiong,C.,Gonzalez,A.,2007.Understandingthethermalimplicationsofmulticorearchitectures.IEEETrans.ParallelDistrib.Syst.18(8), 1055 1065.
Chen,K.,etal.,2015.Thermal-aware3DNetwork-on-Chip(3DNoC)designs:routingalgorithmsandthermalmanagement.IEEECirc.Syst.45 69.
Deb,S.,etal.,2010.EnhancingperformanceofNetwork-on-Chiparchitectureswithmillimeterwavewirelessinterconnects.In:ProceedingsofIEEEInternationalConferenceonASAP.pp. 73 80.
Erdos,P.,Renyi,A.,1959.Onrandomgraphs.Publ.Math.290 297.
Flich,J.,Skeie,T.,Mejía,A.,Lysne,O.,López,P.,Robles,A.,etal.,2012.Asurveyandevaluationoftopology-agnosticdeterministicroutingalgorithms.IEEETrans.ParallelDistrib.Syst.23 (3),405 425.
Ganguly,A.,etal.,2011.ScalablehybridwirelessNetwork-on-Chiparchitecturesformulti-core systems.IEEETrans.Comput.60(10),1485 1502.
Hanumaiah,V.,Vrudhula,S.,Chatha,K.S.,2009.Maximizingperformanceofthermallyconstrainedmulti-coreprocessorsbydynamicvoltageandfrequencycontrol.In:Proceedingsof ICCAD.pp.310 313.
Jabbar,M.,etal.,2013.Impactof3DIConNoCtopologies:awiredelayconsideration.In: ProceedingsofEuromicroConferenceonDigitalSystemDesign.pp.68 72.
Koohi,S.,etal.,2010.Scalablearchitectureforwavelength-switchedopticalNoCwithmulticastingcapability.In:ProceedingsofEuromicroConferenceonDigitalSystemDesign.pp.399 403.
Koohi,S.,etal.,2011.All-opticalwavelength-routedNoCbasedonanovelhierarchicaltopology.In:ProceedingsofIEEENOCS.pp.97 104.
Lysne,O.,Skeie,T.,Reinemo,S.-A.,Theiss,I.,2006.Layeredroutinginirregularnetworks. IEEETrans.ParallelDistrib.Syst.17(1),51 65.
Marculescu,R.,Ogras,U.Y.,Peh,L.-S.,Jerger,N.E.,Hoskote,Y.,2009.Outstandingresearch problemsinNoCdesign:system,microarchitecture,andcircuitperspectives.IEEETrans. Comput.AidedDes.Integr.CircuitsSyst.17(1),3 21.
Mejia,A.,Flich,J.,Duato,J.,Reinemo,S.-A.,Skeie,T.,2006.Segment-basedrouting:anefficientfault-tolerantroutingalgorithmformeshesandtori.In:Proc.IPDPS.
Mejia,A.,Flich,J.,Duato,J.,2008.Onthepotentialsofsegment-basedroutingforNoCs. In:Proc.ICPP.
Ogras,U.Y.,Marculescu,R.,2006.It’sasmallworldafterall:NoCperformanceoptimization vialong-rangelinkinsertion.IEEETrans.VLSISyst.14(7),693 706.
Watts,D.J.,Strogatz,S.H.,1998.Collectivedynamicsof ‘small-world’ networks.Nature393, 440 442.
Woo,S.C.,Ohara,M.,Torrie,E.,Singh,J.P.,Gupta,A.,1995.TheSPLASH-2programs:characterizationandmethodologicalconsiderations.In:Proc.ofISCA.pp.24 36.
nonuniformtrafficscenarios.Forexample,ifachipwasdesignedtobe usedforweatherprediction,theamountoftrafficeachcoresendsto neighboringcoreswouldnotbeuniform.Utilizing fij isonlyadvantageous ifthechipisdesignedtobeapplicationspecific,ifthechipismadetobe moregeneralpurposeeitherbyremoving fij from(3.1)orbysetting β to0 willensurethatthenetworkismaderegardlessofanytrafficpattern.
ALPHAANDBETA
Theparameters, α and β ,governthenatureofconnectivityand significanceofthetrafficpatternonthetopology,respectively.Alpha governsthenatureoftheconnectivityforthenetwork.Inparticular,as α increases,thenetworkbecomesverylocallyconnectedwithfewor evennolongrangelinks,similartothatofacellularautomata-based topology.Whereas,if α werezero,anidealsmall-worldnetworkwould begeneratedfollowingtheWatts Strogatzmodel(Zhangetal.,2007) withlong-rangeshortcutsvirtuallyindependentofthedistancebetween thecores.Toensurethesmall-worldcharacteristic,ithasbeenshownin PetermannandDeLosRios(2005) that α shouldbelessthan D 1 1, D beingthedimensionofthenetwork.Similartothesmall-worldnetwork, ascale-freenetworkisdefinedasanetworkwithapowerlawdistributionoflinks.Itwasshownin Choromanskietal.(2013) that α typically lieswithintherange2 , α , 3.
Betadeterminesthesignificanceinwhichthenetworktraffic determinesthenetworkconnectivity.Alowervalueof β impliesahigher probabilityofestablishingdirectlinksbetweenswitcheswithhighertrafficexchange.When β iszero, f β ij becomes1making lij theonlydeterminingfactorof P(i,j).Bothoftheseparameters, α and β ,canbeconsidered asdesignknobsthatmaybetunedforaparticularapplicationtogenerateoptimizednetworkarchitecturesdependingonfloorplanandtraffic.
Severalexamplesaredemonstratedinthefollowingsectionsfor threedifferenttrafficscenarios,namely,uniformrandom,transpose, andhotspot.Thedestinationcores2,7,and16werepickedsemirandomlytohighlightsomeofthefeaturesforthedifferenttraffic scenarioswhichareexplainedbelow.Thelocationsofthesedestination corescanbeseenin Figs.3.2 3.4. α waschosentobe1.8(Petermann andDeLosRios,2005)and β waschosentobe1touseanunmodified percentageoftraffictodeterminethenetworkconnectivity.
