Spatial partitioning for proactive spectrum fragmentation avoidance in flex-grid/SDM dynamic optical core networks
Abstract
Spectrum fragmentation has always been a major issue to overcome toward spectrally efficient Flex-Grid over Single-Mode Fiber dynamic optical networks and continues like so when evolving to Flex-Grid over Spatial Division Multiplexing (SDM). A possible strategy to eliminate its pernicious effects is to divide the available spectrum into several partitions, dedicating each one of them to only support connections with identical spectral requirements. In this way, a first-fit spectrum assignment ensures that spectral gaps at each spectral partition will always match the bandwidth needs of future connection requests. In this paper, we extend this strategy to be applicable to Flex-Grid/SDM dynamic optical networks. Furthermore, leveraging the spatial multiplicity offered by SDM, we also investigate spatial partitioning as an effective yet simpler and more easily manageable solution to also eliminate the spectrum fragmentation negative effects. Both strategies are numerically evaluated in two reference Flex-Grid/SDM backbone networks with ׿7 spatial multiplicity, yielding noteworthy carried network load gains up to 18% versus a non-partitioned network scenario. When increasing the spatial multiplicities up to ׿30, such gains tend to stabilize around 3–4%. Some results are also obtained under unexpected traffic profile deviations, showing that, even under moderate deviations, partitioning becomes beneficial. Comparing spectral and spatial partitioning, they tend to perform quite similar in all cases. This makes us advocate for spatial partitioning as a more interesting solution for spectrum fragmentation avoidance in this kind of networks.
Full text
SpatialPartitioningforProactiveSpectrum FragmentationAvoidanceinFlex‐Grid/SDM DynamicOpticalCoreNetworks JaumeComellas,JordiPerelló,JosepSolé‐Pareta,GabrielJunyent AdvancedBroadbandCommunicationsCenter(CCABA),UniversitatPolitècnicadeCatalunya(UPC), JordiGirona1‐3,08034BarcelonaSpain,e‐mail:[email protected] Abstract:Spectrumfragmentationhasalwaysbeenamajorissuetoovercome towardspectrallyefficientFlex‐GridoverSingle‐ModeFiber(SMF)dynamic opticalnetworks,andcontinueslikesowhenevolvingtoFlex‐GridoverSpatial DivisionMultiplexing(SDM).Apossiblestrategytoeliminateitsperniciouseffects istodividetheavailablespectrumintoseveralpartitions,dedicatingeachoneof themtoonlysupportconnectionswithidenticalspectralrequirements.Inthis way,afirst‐fitspectrumassignmentensuresthatspectralgapsateachspectral partitionwillalwaysmatchthebandwidthneedsoffutureconnectionrequests. Inthispaper,weextendthisstrategytobeapplicabletoFlex‐Grid/SDMdynamic opticalnetworks.Furthermore,leveragingthespatialmultiplicityofferedbySDM, wealsoinvestigatespatialpartitioningasaneffectiveyetsimplerandmoreeasily manageablesolutiontoalsoeliminatethespectrumfragmentationnegative effects.BothstrategiesarenumericallyevaluatedintworeferenceFlex‐Grid/SDM backbonenetworkswithx7spatialmultiplicity,yieldingnoteworthycarried networkloadgainsupto18%versusanon‐partitionednetworkscenario.When increasingthespatialmultiplicitiesuptox30,suchgainstendtostabilizearound 3‐4%.Someresultsarealsoobtainedunderunexpectedtrafficprofiledeviations, showingthat,evenundermoderatedeviations,partitioningbecomesbeneficial. Comparingspectralandspatialpartitioning,theytendtoperformquitesimilarin allcases.Thismakesusadvocateforspatialpartitioningasamoreinteresting solutionforspectrumfragmentationavoidanceinthiskindofnetworks. 1. INTRODUCTION ElasticOpticalNetworks(EONs)implementingFlex‐Gridtechnology[1][2]havebecometop candidatestorealizetheupcomingdatatransportnetworkinfrastructures,giventheirsuperior spectralefficiencyversuslegacyWavelengthDivisionMultiplexing(WDM)‐basedones[3].In Flex‐Grid,theopticalfiberspectrumisdiscretizedintoFrequencySlots(FSs)of12.5GHzwidth, followingITU‐TRecommendationG.694.1[4],whichcanbecontiguouslyreservedtoform channelstailoredtoanysignalbandwidth.Thisenablestheefficientallocationofsub‐ wavelengthandultra‐highbit‐rateconnectionstogetherontothesameopticalnetwork infrastructure,beingthelatteralsocalledsuper‐channels,composedofmultipleadjacentsub‐ channelsoverseparateopticalcarriers. However,recentstudieshaverevealedthatevenadoptingFlex‐Grid,thecapacityrequiredto This is a post-peer-review, pre-copyedit version of an article published in Photonic Network Communications. The final authenticated version is available online at: https://doi.org/10.1007/s11107-020-00903-x
supportmid‐ andlong‐termtrafficforecastscangobeyondthenonlinearShannonlimitof standardSingle‐ModeFibers(SMFs),incurringapotential"capacitycrunch"[5].Toavoidthis situation,theintroductionofSpatialDivisionMultiplexing(SDM)intotheopticallayerseems mandatory[6].Withthisobjective,SingleModeFiberBundles(SMFBs)canbeequippedperlink inanear‐term,thusmultiplyingtheFlex‐Gridnetworkcapacitybythenumberofphysically independentSMFsperbundle.Themid‐andlong‐termfully‐SDMvisionisexpectedtorelyon advancedopticalfibertechnologies[7],likeMulti‐CoreFibers(MCFs),Few‐ModeFibers(FMFs) andevenFew‐ModeMCFs(FM‐MCFs),whichshouldfosterintegratedsystemcomponentslike transponders,amplifiersorRe‐configurableOpticalAdd&DropMultiplexers(ROADMs). WithFlex‐Grid/SDMcomingtothefore,newsuper‐channelallocationoptionsappear[8].These onesrangefromspectralsuper‐channels,asinFlex‐GridoverSMFnetworks,wheretheir composingsub‐channelsareallarrangedacrossthespectraldomain,tospatialoneswiththeir sub‐channelsarrangedacrossthespatialdomain(overthesamecentralfrequency).Mixed options(i.e.,spectral‐spatialsuper‐channels)mayalsobepossible,arrangingtheirsub‐channels acrossbothspectralandspatialdomains.Amongtheseoptions,spatialsuper‐channelsare consideredthemostcost‐effective,asasimplerSDM‐ROADMarchitecturerealizingJoint Switching(JoS)canbeemployed[9].Spectralandspatial‐spectralsuper‐channeloptionsshould yieldhigherspectralefficiencythanthespatialonesbutrequiring,inprinciple,expensiveSDM‐ ROADMarchitecturesabletoswitchanyspectralportionfromanyinputfiber/core/modetoany outputone[10],atechniquecalledIndependentSwitching(InS).AnalternativecheaperSDM‐ ROADMarchitecturestillenablingspectralandspectral‐spatialsuper‐channelsistheone performingInSwithoutlanechange[11],whichtradesfiber/core/modecontinuityforasimpler SDM‐ROADMarchitecture,comparabletothatrealizingJoS.Besides,InSwithoutlanechange offersaspectralefficiencyclosetothatobtainedwithpureInS[12]. Fromtheverybeginning,spectrumfragmentationhasbeenidentifiedasamajorissueto addressfordeliveringhighspectrumefficiencyandutilizationinEONs[2].Itresultsfromthe allocation/releaseofspectralresourcestoconnectionswithdifferentbandwidthrequirements upontheirarrival/departure,leavingspectralgapsofdifferentwidthsthatcomplicatethe allocationoffutureconnections,particularlythosewithhighspectralrequirements. Tomitigatethespectrumfragmentationnegativeeffects,proactiveandreactivesolutionshave beenproposedintheliterature[13].Reactivesolutionsaimatdefragmentingtheopticalfiber spectrumduringnetworkoperation,re‐arrangingactiveconnectionsinawaythatthe fragmentationofthespectrumisreduced,thusfacilitatingthepotentialallocationoffuture connectionrequests.Duringthisoperation,itisofutmostimportancenottodisruptactive connectionscarryingend‐usertrafficthatis,performinga“hitless”defragmentation. Conversely,proactivesolutionsseektoallocatenewconnectionstryingtominimizetheresulting fragmentationaftertheirallocation(e.g.,asin[14][15]).Itisnoteworthythatspectrum fragmentationisnotonlypresentinpureEONsbutalsoinFlex‐Grid/SDMnetworks,forwhich reactiveandproactivesolutionstomitigateitseffectshavealsobeenrecentlyproposedinthe literature(e.g.,see[16][17]). Aproactivesolutionproposedintheliteraturetoavoidtheperniciouseffectsofthespectrum
fragmentationinFlex‐Gridopticalnetworksconsistsindividingthespectralresources,sothat eachoftheresultingpartitionsisdedicatedtoonlysupportconnectionswithidentical bandwidthrequirements[18][19].Inthisway,byapplyingasimplefirst‐fitspectrumassignment strategy,thewidthoftheavailablespectrumgapsineachpartitionwillalwaysmatchthe bandwidthrequirementsoffutureconnectionstobeallocatedthere.Acriticalaspecttoachieve highspectralutilizationwiththissolutionistoassignanappropriateamountofspectrumto eachpartition,forexample,basedonexpectedloadandtrafficprofile. Thepresentpaperhasathree‐foldobjective.Firstofall,weanalyzethebenefitsanddrawbacks ofextendingtheaforementionedproactivespectrumfragmentationavoidancesolution (hereaftergenericallyreferredtoasspectralpartitioning)toFlex‐Grid/SDMnetworks,where spectrumfragmentationstillexistsandneedstobeaddressedaswell.Secondly,taking advantageofthespatialmultiplicityofferedbySDM,weproposeanalternativeproactive spectrumfragmentationsolutionrelyingonspatialpartitioning,whichaimsatachieving identicalFlex‐Grid/SDMnetworkperformanceasthepreviousspectrumpartitioningsolution, butbeingsimplerandmoreeasilymanageable.Thirdly,wenumericallycomparethe performanceofbothsolutionsintwoFlex‐Grid/SDMreferencebackbonenetworkscenarios withspatialmultiplicitiesuptox30,soastoextractourfinalconclusions. Atthispoint,weshouldemphasizethatthispaperfocusesonshort‐termrealizableFlex‐ Grid/SDMnetworksequippingbundlesofindependentSMFsperlink,whichdonotsufferfrom crosstalk‐relatedimpairments.However,crosstalkcanplayacriticalroleonthemaximum transmissionreachofopticalsignalswithadvancedSDMtechnologieslikeMCFs,FMFsorFM‐ MCFs,envisionedinmid‐andlong‐termFlex‐Grid/SDMnetworkrealizations.Hence,although notconsideredinthisworkhereafter,crosstalkwouldrequirespecialattentionwhenextending ourproposedsolutionstonetworksusingsuchadvancedSDMtechnologies,demandingtheuse ofcrosstalk‐awaretransmissionreachestimationmodels,astheonespresentedin[20]. Theremainderofthispapercontinuesasfollows.Section2presentstheextensionofthe spectralpartitioningsolutiontoFlex‐Grid/SDMnetworks,aswellasthenewlyproposedspatial partitioningsolution.Section3presentstheevaluationscenarios,obtainednumericalresults andeventualcomparison.Finally,section4drawsupthemainconclusionsofthiswork. 2. PROACTIVEFRAGMENTATIONAVOIDANCE AcommoncharacteristicofanyFlex‐Grid/SDMscenarioisthecoexistenceofheterogeneous connections,suchthattheallocatedresourcesforthemadapttotheirbandwidthrequirements. Thisisseenasamajoradvantageintermsofnetworkuseeffectiveness,largelydemonstrated whenhavingtotransportanygiventraffic.Manypreviousworksdealtwithmulti‐rate connections,whosespectralneedsvarydependingonthemodulationformatsallowed.In general,differentbit‐rateconnectionsaregeneratedandcoexistduringnetworkoperation. Consideringtheavailabletechnology,manyworkscurrentlyfocusondynamicnetworkscenarios supporting100G,400Gand1Tb/sconnections,tailoringthespectrumassignedtothem accordingtotheircapacity,whichproducesspectralfragmentation. Extendingtheideaprovidedin[14]and[15]forFlex‐Grid/SMFnetworkstoFlex‐Grid/SDMones,
weproposetoisolatethedifferentconnectiontypesbyassigningdifferentspectralresource partitionsdedicatedtoeachoneofthem,whatwerefertoasspectralpartitioning.According tothetrafficprofileofferedtothenetwork,differentspectrumpartitionsarecreated,whose sizedependsonthespecificofferedtrafficcontributionbyeachtypeofconnections.These partitionscanincludespectralresourcesofmultiplespatialchannelspresentintheFlex‐ Grid/SDMnetworklinks. InordertodescribehowspectralpartitioningcanbeperformedinaFlex‐Grid/SDMnetwork, imagineanetworktrafficprofilecomposedofNtraffictypes(i.e.,bit‐rates),T1,T2,…,TN,with respectiveprobabilitiesp1,p2,…,pN,beingpnprobabilitythatanincomingdemandisoftypeTn, nϵ{1,…,N}. Imaginenowforsimplicitythatfixedbaud‐ratemodulatorsareusedinthenetworkandasingle modulationformatisalwaysemployed.Undertheseassumptions,theeffectivebit‐rateper OpticalCarrier(OC),denotedasC,canbeobtainedbymultiplyingthefixedbaud‐rateofthe modulators(inGbaud)andtheefficiencyofthemodulationformatused(inb/s/Hz).Inthisway, thenumberofOCsneededtoconfigureasuper‐channel(aspectralsuper‐channelinthiswork) abletosupportademandoftypeTn,denotedasNOCn,wouldbeNOCn=ceil(Tn/C),beingceil() theceilingfunction.Finally,havingNOCnvaluesforallnϵ{1,…,N},wecannowproceedto obtaintherelativespectrumrequirementspertraffictype,denotedasR1,R2,…,RN,sothatRn= pn∙NOCn/(p1∙NOC1+p2∙NOC2+…+pN∙NOCN),forallnϵ{1,…,N}. Withtheserelativespectrumrequirementspertraffictype,spectralpartitioningcanbe performedinaFlex‐Grid/SDMnetworkasfollows.Firstly,thetotalnumberoffrequencyslots alongallspatialchannels,denotedasNFSTotal,shouldbecomputed.Next,thespectralwidthof eachspectralpartitiondedicatedtoeachtraffictype,denotedasNFSn,forallnϵ{1,…,N},should alsohavetobecomputedasNFSn=round(Rn∙NFSTotal),beinground()anintegerrounding function.Finally,spectralpartitionsofsuchcomputedwidthswouldbeconfigured.This procedureisdepictedintheflowchartpresentedinFigure1. Figure1.Flowchartdescribingspectralandspatialpartitioningprocedures Networktrafficprofile: T 1 (p 1 ),T 2 (p 2 )…,T N (p N ) COMPUTERELATIVESPECTRUMREQUIREMENTSPERTRAFFICTYPE 1. Compute#ofOCs,NOC 1 ,NOC 2 ,…,NOC N ,ofcapacity CGbps tosupport aT 1 ,T 2 ,…,T N demand,sothat:NOC n =ceil (T n /C) 2. Computerelative spectrum requirement ratiopertraffic type,R 1 ,R 2 ,…,R N ,,sothat: R n =p n ∙NOC n /(p 1 ∙NOC 1 +p 2 ∙NOC 2 +…+p N ∙NOC N ) Spectral partitioning Spatial partitioning 3. Obtain the #ofspatial channels that should bededicated toeach traffic type NSC n =round(R n ∙NSC) 4. Configurespatial partitions for T 1 ,T 2 ,…,T N along all spatial channels Part. Type? 3. Obtain the total#ofFSs inall spatial channels,NFS Total 4. Obtain spectral partition widths for each traffic type,NFS n =round(R n ∙NFS Total ) 5. Configurespectral partitions for T 1 ,T 2 ,…,T N along all spatial channels
Thesamerelativespectrumrequirementspertraffictypecouldalsobeemployedtoperforman alternativeyetsimplerspatialpartitioning,specificallydesignedforFlex‐Grid/SDMnetworks, wherefullspatialchannelsarededicatedtoeachtraffictype,asalsodepictedintheflowchart presentedinFigure1.Inthiscase,thenumberofspatialchannelsdedicatedtoeachtraffictype, NSCn,forallnϵ{1,…,N},wouldhavetobecomputedasNSCn=round(Rn∙NSC),beingNSCthe totalnumberofavailablespatialchannelsandround()thesameintegerroundingfunction. Finally,spatialpartitionsofsuchsizeswouldbeconfigured. ImagineanexamplewheretheofferedtrafficprofileiscomposedofT1=100G(40%),T2=400G (30%)andT3=1Tb/s(30%)connections.Moreover,imaginethattheavailableoptical modulatorsinthenetworkofferafixedbaud‐rateof25Gbaud,beingPolarizationMultiplexed (PM)‐8‐QAMemployedinallcases,withaspectralefficiencyequalto6bit/s/Hz.Underthese assumptions,theeffectivebit‐rateperOCwouldbeC=150Gb/s.Hence,NOC1=1,NOC2=3 andNOC3=7.Thiswouldleadtothefollowingrelativespectralrequirements,eventually:R1= 11.75%,R2=26.5%andR3=61.75%. Now,imagineaFlex‐Grid/SDMnetworkscenarioequippingSMFBsof7independentSMFsper link,offeringeachonethe4THzC‐Band,discretizedinto320FSsof12.5GHz,forallocating connections.Therefore,NFSTotal=2240availablealongallspatialchannels.Ifaspectral partitioningisperformedinthisscenario,NFS1=263,NFS2=594andNFS3=1383,thusresulting inthepartitioningconfigurationdepictedinFigure2.a. Figure2.Spectral(2.a)vs.spatial(2.b)partitioningexampletoallocate100G,400Gand1Tb/sconnections inanSDMlinkwith7independentSMFs.Offeredtrafficprofile:100G(40%),400G(30%),1Tb/s(30%). Conversely,aspatialpartitioningwouldorganizethespatialpartitionsasdepictedinFigure2.b. BeingNSC=7,thesizeofthedifferentspatialpartitionswouldbeNSC1=0.82≈1,NSC2=1.86≈ 2andNSC3=4.32≈4.Itisobviousthatinthiscase1Tb/sconnectionsarepenalized,whilemore FSthantherequiredareassignedto100Gand400Gconnections.Nevertheless,thiseffectwould bemitigatedinscenarioswherethenumberofspatialchannelsisincreasedand,therefore,the roundingeffectsaresmaller. 123 320 123 320 123 320 123 320 123 320 123 320 123 320 263 264 263FSs(11.75%)– 100G 207 208 594FSs(26.5%)– 400G 1383FSs(61.75%)–1Tb/s s 1 s 2 s 3 s 4 s 5 s 6 s 7 123 320 123 320 123 320 123 320 123 320 123 320 123 320 s 1 s 2 s 3 s 4 s 5 s 6 s 7 1Spatia l c h anne l – 100G 2Spatial channels–400G 4Spatial channels–1Tb/s a) b)
EitherconfiguringspectraloraspatialpartitioningasdepictedinFigure2,whenanew100G, 400Gor1Tb/sconnectionarrivesatthenetwork,thespectrumallowedtosupportitislimited tothesepartitions,selectedinafirst‐fitfashion.Twoadvantagesareforeseenwhenadopting thesestrategiesvs.genericFlex‐Grid:1)Fragmentationisavoidedasspectrumbandsreleased afterconnectionsterminationhavethesamesizeinsidethedifferentpartitions;2)The unfairnessproblem[19]typicalofFlex‐Gridscenarios,wherelargeconnectionssufferhigher blockingthansmallerones,isavoided,sincepartitionscouldbetailoredtotunethenetwork blockingperformance.Apotentialdrawbackofbothspectral/spatialpartitioningcanappear underunexpectedtrafficprofiledeviations,creatingamismatchbetweentheofferedtrafficand theconfiguredspectral/spatialpartitions.Whenthesetrafficprofiledeviationsbecomestable, networkre‐partitioningwouldbeanoptiontoallowthenetworkcontinuedeliveringhigh performance.Lastly,comparingspectralandspatialpartitioning,thelatterseemssimplerand easiertomanagegivenitscoarsergranularity,whichmayfacilitateconnectionallocation decisionsinthenetwork. 3. NUMERICALRESULTS Anad‐hocJava‐basedsimulatorhasbeenimplementedtoobtainaccuratenumerical performanceresultsofthepreviouslydescribedspectralandspatialpartitioningstrategiesfor Flex‐Grid/SDMnetworks.Inordertogetresultsasgenericaspossible,differenttopologiesas wellasdiversetrafficprofileshavebeensimulated. 3.1. Evaluationscenarios Twodifferenttopologies[12]havebeenconsideredforthisstudy,namely,theDT12German transportnetwork(12nodes,20links),whosediameteris1019km,andthepan‐European EON16network(16nodes,23links),withadiameterof2663km.Forthesakeofsimplicity,a singlemodulationformatisemployedineachnetwork.Accordingto[20],themaximum transmissionreachofPM‐8QAMis1340kminSDMnetworksdeployingSMFBlinks,whilethis reachisincreasedto3796kmwhenPM‐QPSKisused.Therefore,whentheDT12issimulated, themaximumpathlengthislimitedto1340kmandPM‐8QAMisalwaysused.Incontrast,when simulatingtheEON16,themaximumpathlengthincreasesto3796kmandPM‐QPSKisalways employed. Weassumetheavailableopticalmodulatorsinthenetworkofferafixedbaud‐rateof25Gbaud. So,ifweintroduceaguard‐bandbetweenadjacentOCsequalto1FS,eachOCendsoccupying atotalspectralwidthof3FSs,offeringaneffectivetransmissioncapacityof150or100Gb/s whenPM‐8QAM(asintheDT12)orPM‐QPSK(asintheEON16)isemployed,withspectral efficienciesof6and4b/s/Hz,respectively.Asaresult,tosupport100G,400Gand1Tb/s incomingdemandsintheDT12network,super‐channelscomposedof1,3and7OCswillbe needed,occupying3,9and21FSs.Incontrast,intheEON16network,super‐channelstosupport 100G,400Gand1Tb/sincomingdemandswillneedtobecomposedof1,4and10OCs,thatis, occupying3,12and30FSs.Allconnectionswillbesupportedoverspectralsuper‐channelsin bothnetworks.So,theaforementionednumbersofFSswillalwaysneedtobecontiguously allocatedinaspecificspatialchannelincludedintheallowedspectral/spatialpartition.
ASMFBisassumedtobedeployedpernetworklinkineachdirection,includinganumberof standardSMFsthatcanvaryfrom7to30dependingontheexperiment.The4THzC‐Bandis usedineachSMF,whichresultsin320FSsof12.5GHzwidth.Insomecases,thisnumberofFSs isslightlyadjustedtobetterfitthespectralrequirementsofincomingconnectionrequests.For example,withspatialpartitioning,324FSsareenabledinthoseSMFdedicatedtosupport400G and1Tb/sconnections,stillwithintheC‐Bandeffectively.ThisnumberofFSsbettermatches the9or12FSrequiredby400GconnectionswhenPM‐8‐QAMorPM‐QPSKisused.Otherwise, asignificantamountofspectralresourceswoulddirectlybewastedperSMF.Inanycase,tobe totallyfair,thesameslightlymodifiednumberofFSsisequippedperSMFwhentestingspectral partitioningornopartitioningcases. RegardingtheRouting,SpatialchannelandSpectrumAssignment(RSSA)algorithm,weemploy aK‐ShortestPathroutingalgorithm,constrainingthecandidatepathsbytheaforementioned maximumpathlengthvalues.OncetheKcandidatepathstosupportagivenconnectionare obtained,theseonesareexploredstartingfromtheshortesttothelongestone.Noteherethat thespecificnumberofpathstoexplorebythealgorithmcanbelessthanKeventually,when someofthecomputedpathsexceedthemaximumtransmissionreachimposedbytheemployed modulationformat.Asforthespatialchannelandspectrumassignment,afirst‐fitstrategyis used,assumingthatcost‐effectiveInSwithoutlanechangeSDM‐ROADMsarepresentinthe network.Hence,spatialchannelcontinuitymustbeensuredend‐to‐endalongthecandidate paths,besidesthespectrumcontinuityandcontiguityconstraintsimposedbytheFlex‐Grid technology. Theworst‐casetimecomplexityofthisRSSAalgorithmcanbeexpressedasfollows.If|N|and |E|denotethenumberofnodesandlinksinthenetwork,thetimecomplexityofcomputingthe Kcandidatepathsusingthewell‐knownYen’salgorithm[21]isO(K∙|N|∙(|E|+|N|∙log(|N|)).As forthespatialchannelandspectrumassignment,the(veryunlikely)worst‐casewouldbegiven whenthereisonlyonespectral/spatialpartitionencompassingallspatialchannelsandthe incomingdemandrequiresasingleFS,needinguptoO(K∙FSTotal)continuousFSavailabilitychecks alongtheKcandidatepaths(recallthatFSTotaldenotesthetotalnumberofavailableFSsalong allspatialchannels).Therefore,theworst‐casetimecomplexityoftheRSSAalgorithmbecomes O(K∙|N|∙(|E|+|N|∙log(|N|)+K∙FSTotal)eventually. Inoursimulations,twodifferenttrafficprofileshavebeenconsidered,whoseparametersare summarizedinTable1,whereABRCandAFSCrefertoAverageBit‐RateperConnectionand AveragenumberofFSperconnection,respectively. Table1.Offeredtrafficprofiles TrafficProfileConnectionsRatio(%)SpectrumUsedDT12 (%) SpectrumUsedEON16 (%)ABRC (Gb/s) AFSC DT12 (FS) AFSC EON16 (FS) 100G400G1Tb/s1004001Tb/s1004001Tb/s TP1(Current)70201035303528324025067.5 TP2(Future)40303011.76526.4761.7658.726.165.246010.213.8 Itisimportanttohighlightthatthefractionofspectrumexpectedtoberequiredperconnection typediffersfromtheircontributiontothetotalofferedtrafficintheDT12network,butnotin theEON16one.Forexample,underTP1,100G,400Gand1Tb/sconnectionswillcontributeto
28%,32%and40%ofthetotalofferedtraffic,whichmatchestheirrelativespectrum requirementsintheEON16.ThisisduetothefacttheratioofFSsneeded(3,12and30FSs)vs. connectionbit‐rate(100G,400G,1Tb/s)keepsconstantwhenPM‐QPSKisemployedinthe EON16.However,thisdoesnothappenwhenemployingPM‐8QAMintheDT12. Asexplainedbefore,oneoftheobjectivesofthisworkistogaugetheeffectofincreasingthe numberofspatialchannelsontheresultsobtained.Therefore,differentvalueshavebeen simulated.Specifically,5illustrativeSDMspatialmultiplicities,namely,7,12,19,22and30,have beenevaluated,assumingSMFBsperlinkcomprisingsuchnumbersofparallelSMFs. 3.2. Numericalresultsandcomparison Firstsimulationshavefocusedontheeffectsofdifferentresourcepartitioningstrategies.Three differentcasesareshowninFigure3,whereTP1(seeTable1)hasbeenoffered: NOP(Nopartitioning):Theconnectiondemandsareallocatedwithoutanydistinction, usingallthespatialchannelsandoccupyingthemfromlowtohighspatialchannelsin afirst‐fitspatialchannelandspectrumassignment. SPAP(Spatialpartitioning):Eachtypeofconnectionsusesitsconfiguredspatial partition,asdescribedinFigure2.b.InthecaseshowninFigure3,with7spatial channels,100Gconnectionsareallocatedoverthetwofirstspatialchannels,400Gones overspatialchannels3and4,and1Tb/sconnectionscanusechannelsfrom5to7. SPECP(SpectralPartitioning):Eachtypeofconnectionsuseitsconfiguredspectral partition,asdescribedinFigure2.a. (a) (b) Figure3.Bandwidthblockingprobabilityvs.averagesupportednetworkloadintheDT12(a)andEON16 (b)networkswhenTP1isgenerated. SomeconclusionscanbeextractedfromFigure3.Firstandforemost,bothSPAPandSPECPare alwaysbeneficialintermsofsupportedloadatanyBBPvalueversusNOP,providingSPECP slightlybetterperformance.Specifically,itisobservedthatgainsintheEON16networkare clearlyhigherthanthoseobtainedintheDT12,wheretheperformanceofalloptionsissimilar. Thishappensasaresultofthehigherdifferencesbetweenlargerandsmallerconnectionssizes whenemployingPM‐QPSKintheEON16.LookingattheloadvaluesforBBP=1%,theseare795, 855and860Tbit/sforNOP,SPAPandSPECPintheDT12,respectively(asseeninFigure3.a, differencesbetweenSPAPandSPECPareverysmall).Incontrast,intheEON16(Figure3.b)the relativedifferencesbetweentheNOPcaseandthoseusingpartitions(SPAPandSPECP)isclearly higher,namely,610,705and710Tbit/satBBP=1%.Whileloadgainsarearound8%inthe
DT12,theyrisetoabout16%intheEON16. AsimilarbehaviorisobservedwhenTP2isgenerated,butinthiscasedifferencesbetweenSPAP andSPECParehigher(seeFigure4).Thisisduetothefactthat,byhavinghigherdifferencesin theproportionsofspectrumdedicatedtoeachkindofconnections(seeTable1),thedifferences betweenassigningcompletefibersortheexactnumberofslotsbecomelarger. (a)(b) Figure4.Bandwidthblockingprobabilityvs.averagesupportednetworkloadintheDT12(a)and EON16(b)networkswhenTP2isgenerated. Therefore,fromFigure4itcanbeconcludedthatthedifferencesbetweentheSPAPandSPECP strategiesarelargerunderTP2.LookingattheexactloadvaluesforBBP=1%,theseare845,875 and900Tbit/sforNOP,SPAPandSPECPinDT12,respectively(Figure4.a).Incontrast,inthe EON16(Figure4.b)therelativedifferencesareclearlyhigher,namely,630,730and740Tbit/s atBBP=1%.Whileloadgainvaluesobtainedbyspectrumpartitioningrangefrom3%to6%in theDT12,theyrisetoarangefrom15%toalmost18%intheEON16. Asmentionedbefore,onepotentialdrawbackofspectral/spatialpartitioningcouldstemfroma mismatchingbetweenthepartitionsandtheofferedtrafficprofile.Withtheaimofquantifying thiseffect,someadditionalsimulationshavebeenalsoconductedwheretheofferedload deviatesfromtheexpectedone,butwithoutmodifyingtheconfiguredpartitions.Theobtained resultsaresummarizedinFigure5,consideringtheEONnetworkunderTP1andBBP=5%, whereSPAPandNOPhavebeencompared.PleaserecallfromFigure3.bthatnegligible performancedifferencesbetweenSPAPandSPECPexistintheEONunderTP1.Therefore,very similarresultswithSPECPwouldalsobeobserved. Thetrafficprofiledeviationssimulatedconsistindecreasingtheratioof100Gconnections (whosevalueinTP1is70%)instepsof5%,increasingthatof400Gand1Tb/sconnectionsby 2.5%each.Forexample,thefirstdeviatedtrafficprofilebecomes100G(65%),400G(22.5%)and 1Tb/s(12.5%).