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
Spa ialPa i ioning o P oac i eSpec um
F agmen a ionA oidanceinFlex‐G id/SDM
DynamicOp icalCo eNe wo ks
JaumeComellas,Jo diPe elló,JosepSolé‐Pa e a,Gab ielJunyen
Ad ancedB oadbandCommunica ionsCen e (CCABA),Uni e si a Poli ècnicadeCa alunya(UPC),
Jo diGi ona1‐3,08034Ba celonaSpain,e‐mail:comellas@ sc.upc.edu
Abs ac :Spec um agmen a ionhasalwaysbeenamajo issue oo e come
owa dspec allye icien Flex‐G ido e Single‐ModeFibe (SMF)dynamic
op icalne wo ks,andcon inueslikesowhene ol ing oFlex‐G ido e Spa ial
Di isionMul iplexing(SDM).Apossibles a egy oelimina ei spe niciouse ec s
is odi ide hea ailablespec umin ose e alpa i ions,dedica ingeachoneo
hem oonlysuppo connec ionswi hiden icalspec al equi emen s.In his
way,a i s ‐ i spec umassignmen ensu es ha spec algapsa eachspec al
pa i ionwillalwaysma ch hebandwid hneedso u u econnec ion eques s.
In hispape ,weex end hiss a egy obeapplicable oFlex‐G id/SDMdynamic
op icalne wo ks.Fu he mo e,le e aging hespa ialmul iplici yo e edbySDM,
wealsoin es iga espa ialpa i ioningasane ec i eye simple andmo eeasily
manageablesolu ion oalsoelimina e hespec um agmen a ionnega i e
e ec s.Bo hs a egiesa enume icallye alua edin wo e e enceFlex‐G id/SDM
backbonene wo kswi hx7spa ialmul iplici y,yieldingno ewo hyca ied
ne wo kloadgainsup o18% e susanon‐pa i ionedne wo kscena io.When
inc easing hespa ialmul iplici iesup ox30,suchgains end os abilizea ound
3‐4%.Some esul sa ealsoob ainedunde unexpec ed a icp o ilede ia ions,
showing ha ,e enunde mode a ede ia ions,pa i ioningbecomesbene icial.
Compa ingspec alandspa ialpa i ioning, hey end ope o mqui esimila in
allcases.Thismakesusad oca e o spa ialpa i ioningasamo ein e es ing
solu ion o spec um agmen a iona oidancein hiskindo ne wo ks.
1. INTRODUCTION
Elas icOp icalNe wo ks(EONs)implemen ingFlex‐G id echnology[1][2]ha ebecome op
candida es o ealize heupcomingda a anspo ne wo kin as uc u es,gi en hei supe io
spec ale iciency e suslegacyWa eleng hDi isionMul iplexing(WDM)‐basedones[3].In
Flex‐G id, heop ical ibe spec umisdisc e izedin oF equencySlo s(FSs)o 12.5GHzwid h,
ollowingITU‐TRecommenda ionG.694.1[4],whichcanbecon iguously ese ed o o m
channels ailo ed oanysignalbandwid h.Thisenables hee icien alloca iono sub‐
wa eleng handul a‐highbi ‐ a econnec ions oge he on o hesameop icalne wo k
in as uc u e,being hela e alsocalledsupe ‐channels,composedo mul ipleadjacen sub‐
channelso e sepa a eop icalca ie s.
Howe e , ecen s udiesha e e ealed ha e enadop ingFlex‐G id, hecapaci y equi ed o
This is a pos -pee - e iew, p e-copyedi e sion o an a icle published in Pho onic Ne wo k
Communica ions. The inal au hen ica ed e sion is a ailable online a :
h ps://doi.o g/10.1007/s11107-020-00903-x
suppo mid‐ andlong‐ e m a ic o ecas scangobeyond henonlinea Shannonlimi o
s anda dSingle‐ModeFibe s(SMFs),incu ingapo en ial"capaci yc unch"[5].Toa oid his
si ua ion, hein oduc iono Spa ialDi isionMul iplexing(SDM)in o heop icallaye seems
manda o y[6].Wi h hisobjec i e,SingleModeFibe Bundles(SMFBs)canbeequippedpe link
inanea ‐ e m, husmul iplying heFlex‐G idne wo kcapaci yby henumbe o physically
independen SMFspe bundle.Themid‐andlong‐ e m ully‐SDM isionisexpec ed o elyon
ad ancedop ical ibe echnologies[7],likeMul i‐Co eFibe s(MCFs),Few‐ModeFibe s(FMFs)
ande enFew‐ModeMCFs(FM‐MCFs),whichshould os e in eg a edsys emcomponen slike
ansponde s,ampli ie so Re‐con igu ableOp icalAdd&D opMul iplexe s(ROADMs).
Wi hFlex‐G id/SDMcoming o he o e,newsupe ‐channelalloca ionop ionsappea [8].These
ones ange omspec alsupe ‐channels,asinFlex‐G ido e SMFne wo ks,whe e hei
composingsub‐channelsa ealla angedac oss hespec aldomain, ospa ialoneswi h hei
sub‐channelsa angedac oss hespa ialdomain(o e hesamecen al equency).Mixed
op ions(i.e.,spec al‐spa ialsupe ‐channels)mayalsobepossible,a anging hei sub‐channels
ac ossbo hspec alandspa ialdomains.Among heseop ions,spa ialsupe ‐channelsa e
conside ed hemos cos ‐e ec i e,asasimple SDM‐ROADMa chi ec u e ealizingJoin
Swi ching(JoS)canbeemployed[9].Spec alandspa ial‐spec alsupe ‐channelop ionsshould
yieldhighe spec ale iciency han hespa ialonesbu equi ing,inp inciple,expensi eSDM‐
ROADMa chi ec u esable oswi chanyspec alpo ion omanyinpu ibe /co e/mode oany
ou pu one[10],a echniquecalledIndependen Swi ching(InS).Anal e na i echeape SDM‐
ROADMa chi ec u es illenablingspec alandspec al‐spa ialsupe ‐channelsis heone
pe o mingInSwi hou lanechange[11],which ades ibe /co e/modecon inui y o asimple
SDM‐ROADMa chi ec u e,compa able o ha ealizingJoS.Besides,InSwi hou lanechange
o e saspec ale iciencyclose o ha ob ainedwi hpu eInS[12].
F om he e ybeginning,spec um agmen a ionhasbeeniden i iedasamajo issue o
add ess o deli e inghighspec ume iciencyandu iliza ioninEONs[2].I esul s om he
alloca ion/ eleaseo spec al esou ces oconnec ionswi hdi e en bandwid h equi emen s
upon hei a i al/depa u e,lea ingspec algapso di e en wid hs ha complica e he
alloca iono u u econnec ions,pa icula ly hosewi hhighspec al equi emen s.
Tomi iga e hespec um agmen a ionnega i ee ec s,p oac i eand eac i esolu ionsha e
beenp oposedin heli e a u e[13].Reac i esolu ionsaima de agmen ing heop ical ibe
spec umdu ingne wo kope a ion, e‐a angingac i econnec ionsinaway ha he
agmen a iono hespec umis educed, hus acili a ing hepo en ialalloca iono u u e
connec ion eques s.Du ing hisope a ion,i iso u mos impo anceno odis up ac i e
connec ionsca yingend‐use a ic ha is,pe o minga“hi less”de agmen a ion.
Con e sely,p oac i esolu ionsseek oalloca enewconnec ions ying ominimize he esul ing
agmen a iona e hei alloca ion(e.g.,asin[14][15]).I isno ewo hy ha spec um
agmen a ionisno onlyp esen inpu eEONsbu alsoinFlex‐G id/SDMne wo ks, o which
eac i eandp oac i esolu ions omi iga ei se ec sha ealsobeen ecen lyp oposedin he
li e a u e(e.g.,see[16][17]).
Ap oac i esolu ionp oposedin heli e a u e oa oid hepe niciouse ec so hespec um
agmen a ioninFlex‐G idop icalne wo ksconsis sindi iding hespec al esou ces,so ha
eacho he esul ingpa i ionsisdedica ed oonlysuppo connec ionswi hiden ical
bandwid h equi emen s[18][19].In hisway,byapplyingasimple i s ‐ i spec umassignmen
s a egy, hewid ho hea ailablespec umgapsineachpa i ionwillalwaysma ch he
bandwid h equi emen so u u econnec ions obealloca ed he e.Ac i icalaspec oachie e
highspec alu iliza ionwi h hissolu ionis oassignanapp op ia eamoun o spec um o
eachpa i ion, o example,basedonexpec edloadand a icp o ile.
Thep esen pape hasa h ee‐ oldobjec i e.Fi s o all,weanalyze hebene i sandd awbacks
o ex ending hea o emen ionedp oac i espec um agmen a iona oidancesolu ion
(he ea e gene ically e e ed oasspec alpa i ioning) oFlex‐G id/SDMne wo ks,whe e
spec um agmen a ions illexis sandneeds obeadd essedaswell.Secondly, aking
ad an ageo hespa ialmul iplici yo e edbySDM,wep oposeanal e na i ep oac i e
spec um agmen a ionsolu ion elyingonspa ialpa i ioning,whichaimsa achie ing
iden icalFlex‐G id/SDMne wo kpe o manceas hep e iousspec umpa i ioningsolu ion,
bu beingsimple andmo eeasilymanageable.Thi dly,wenume icallycompa e he
pe o manceo bo hsolu ionsin woFlex‐G id/SDM e e encebackbonene wo kscena ios
wi hspa ialmul iplici iesup ox30,soas oex ac ou inalconclusions.
A hispoin ,weshouldemphasize ha hispape ocusesonsho ‐ e m ealizableFlex‐
G id/SDMne wo ksequippingbundleso independen SMFspe link,whichdono su e om
c oss alk‐ ela edimpai men s.Howe e ,c oss alkcanplayac i ical oleon hemaximum
ansmission eacho op icalsignalswi had ancedSDM echnologieslikeMCFs,FMFso FM‐
MCFs,en isionedinmid‐andlong‐ e mFlex‐G id/SDMne wo k ealiza ions.Hence,al hough
no conside edin hiswo khe ea e ,c oss alkwould equi especiala en ionwhenex ending
ou p oposedsolu ions one wo ksusingsuchad ancedSDM echnologies,demanding heuse
o c oss alk‐awa e ansmission eaches ima ionmodels,as heonesp esen edin[20].
The emainde o hispape con inuesas ollows.Sec ion2p esen s heex ensiono he
spec alpa i ioningsolu ion oFlex‐G id/SDMne wo ks,aswellas henewlyp oposedspa ial
pa i ioningsolu ion.Sec ion3p esen s hee alua ionscena ios,ob ainednume ical esul s
ande en ualcompa ison.Finally,sec ion4d awsup hemainconclusionso hiswo k.
2. PROACTIVEFRAGMENTATIONAVOIDANCE
Acommoncha ac e is ico anyFlex‐G id/SDMscena iois hecoexis enceo he e ogeneous
connec ions,such ha healloca ed esou ces o hemadap o hei bandwid h equi emen s.
Thisisseenasamajo ad an agein e mso ne wo kusee ec i eness,la gelydemons a ed
whenha ing o anspo anygi en a ic.Manyp e iouswo ksdeal wi hmul i‐ a e
connec ions,whosespec alneeds a ydependingon hemodula ion o ma sallowed.In
gene al,di e en bi ‐ a econnec ionsa egene a edandcoexis du ingne wo kope a ion.
Conside ing hea ailable echnology,manywo kscu en ly ocusondynamicne wo kscena ios
suppo ing100G,400Gand1Tb/sconnec ions, ailo ing hespec umassigned o hem
acco ding o hei capaci y,whichp oducesspec al agmen a ion.
Ex ending heideap o idedin[14]and[15] o Flex‐G id/SMFne wo ks oFlex‐G id/SDMones,
wep opose oisola e hedi e en connec ion ypesbyassigningdi e en spec al esou ce
pa i ionsdedica ed oeachoneo hem,wha we e e oasspec alpa i ioning.Acco ding
o he a icp o ileo e ed o hene wo k,di e en spec umpa i ionsa ec ea ed,whose
sizedependson hespeci ico e ed a iccon ibu ionbyeach ypeo connec ions.These
pa i ionscanincludespec al esou ceso mul iplespa ialchannelsp esen in heFlex‐
G id/SDMne wo klinks.
Ino de odesc ibehowspec alpa i ioningcanbepe o medinaFlex‐G id/SDMne wo k,
imagineane wo k a icp o ilecomposedo N a ic ypes(i.e.,bi ‐ a es),T1,T2,…,TN,wi h
espec i ep obabili iesp1,p2,…,pN,beingpnp obabili y ha anincomingdemandiso ypeTn,
nϵ{1,…,N}.
Imaginenow o simplici y ha ixedbaud‐ a emodula o sa eusedin hene wo kandasingle
modula ion o ma isalwaysemployed.Unde heseassump ions, hee ec i ebi ‐ a epe
Op icalCa ie (OC),deno edasC,canbeob ainedbymul iplying he ixedbaud‐ a eo he
modula o s(inGbaud)and hee iciencyo hemodula ion o ma used(inb/s/Hz).In hisway,
henumbe o OCsneeded ocon igu easupe ‐channel(aspec alsupe ‐channelin hiswo k)
able osuppo ademando ypeTn,deno edasNOCn,wouldbeNOCn=ceil(Tn/C),beingceil()
heceiling unc ion.Finally,ha ingNOCn alues o allnϵ{1,…,N},wecannowp oceed o
ob ain he ela i espec um equi emen spe a ic ype,deno edasR1,R2,…,RN,so ha Rn=
pn∙NOCn/(p1∙NOC1+p2∙NOC2+…+pN∙NOCN), o allnϵ{1,…,N}.
Wi h hese ela i espec um equi emen spe a ic ype,spec alpa i ioningcanbe
pe o medinaFlex‐G id/SDMne wo kas ollows.Fi s ly, he o alnumbe o equencyslo s
alongallspa ialchannels,deno edasNFSTo al,shouldbecompu ed.Nex , hespec alwid ho
eachspec alpa i iondedica ed oeach a ic ype,deno edasNFSn, o allnϵ{1,…,N},should
alsoha e obecompu edasNFSn= ound(Rn∙NFSTo al),being ound()anin ege ounding
unc ion.Finally,spec alpa i ionso suchcompu edwid hswouldbecon igu ed.This
p ocedu eisdepic edin he lowcha p esen edinFigu e1.
Figu e1.Flowcha desc ibingspec alandspa ialpa i ioningp ocedu es
Ne wo k a icp o ile:
T
1
(p
1
),T
2
(p
2
)…,T
N
(p
N
)
COMPUTERELATIVESPECTRUMREQUIREMENTSPERTRAFFICTYPE
1. Compu e#o OCs,NOC
1
,NOC
2
,…,NOC
N
,o capaci y CGbps osuppo aT
1
,T
2
,…,T
N
demand,so ha :NOC
n
=ceil (T
n
/C)
2. Compu e ela i e spec um equi emen a iope a ic ype,R
1
,R
2
,…,R
N
,,so ha :
R
n
=p
n
∙NOC
n
/(p
1
∙NOC
1
+p
2
∙NOC
2
+…+p
N
∙NOC
N
)
Spec al
pa i ioning
Spa ial
pa i ioning
3. Ob ain he #o spa ial channels ha
should bededica ed oeach a ic ype
NSC
n
= ound(R
n
∙NSC)
4. Con igu espa ial pa i ions o T
1
,T
2
,…,T
N
along all spa ial channels
Pa .
Type?
3. Ob ain he o al#o FSs inall spa ial
channels,NFS
To al
4. Ob ain spec al pa i ion wid hs o each
a ic ype,NFS
n
= ound(R
n
∙NFS
To al
)
5. Con igu espec al pa i ions o T
1
,T
2
,…,T
N
along all spa ial channels
Thesame ela i espec um equi emen spe a ic ypecouldalsobeemployed ope o man
al e na i eye simple spa ialpa i ioning,speci icallydesigned o Flex‐G id/SDMne wo ks,
whe e ullspa ialchannelsa ededica ed oeach a ic ype,asalsodepic edin he lowcha
p esen edinFigu e1.In hiscase, henumbe o spa ialchannelsdedica ed oeach a ic ype,
NSCn, o allnϵ{1,…,N},wouldha e obecompu edasNSCn= ound(Rn∙NSC),beingNSC he
o alnumbe o a ailablespa ialchannelsand ound() hesamein ege ounding unc ion.
Finally,spa ialpa i ionso suchsizeswouldbecon igu ed.
Imagineanexamplewhe e heo e ed a icp o ileiscomposedo T1=100G(40%),T2=400G
(30%)andT3=1Tb/s(30%)connec ions.Mo eo e ,imagine ha hea ailableop ical
modula o sin hene wo ko e a ixedbaud‐ a eo 25Gbaud,beingPola iza ionMul iplexed
(PM)‐8‐QAMemployedinallcases,wi haspec ale iciencyequal o6bi /s/Hz.Unde hese
assump ions, hee ec i ebi ‐ a epe OCwouldbeC=150Gb/s.Hence,NOC1=1,NOC2=3
andNOC3=7.Thiswouldlead o he ollowing ela i espec al equi emen s,e en ually:R1=
11.75%,R2=26.5%andR3=61.75%.
Now,imagineaFlex‐G id/SDMne wo kscena ioequippingSMFBso 7independen SMFspe
link,o e ingeachone he4THzC‐Band,disc e izedin o320FSso 12.5GHz, o alloca ing
connec ions.The e o e,NFSTo al=2240a ailablealongallspa ialchannels.I aspec al
pa i ioningispe o medin hisscena io,NFS1=263,NFS2=594andNFS3=1383, hus esul ing
in hepa i ioningcon igu a iondepic edinFigu e2.a.
Figu e2.Spec al(2.a) s.spa ial(2.b)pa i ioningexample oalloca e100G,400Gand1Tb/sconnec ions
inanSDMlinkwi h7independen SMFs.O e ed a icp o ile:100G(40%),400G(30%),1Tb/s(30%).
Con e sely,aspa ialpa i ioningwouldo ganize hespa ialpa i ionsasdepic edinFigu e2.b.
BeingNSC=7, hesizeo hedi e en spa ialpa i ionswouldbeNSC1=0.82≈1,NSC2=1.86≈
2andNSC3=4.32≈4.I isob ious ha in hiscase1Tb/sconnec ionsa epenalized,whilemo e
FS han he equi eda eassigned o100Gand400Gconnec ions.Ne e heless, hise ec would
bemi iga edinscena ioswhe e henumbe o spa ialchannelsisinc easedand, he e o e, he
oundinge ec sa esmalle .
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
1Spa ia
l
c
h
anne
l
–
100G
2Spa ial
channels–400G
4Spa ial
channels–1Tb/s
a) b)
Ei he con igu ingspec alo aspa ialpa i ioningasdepic edinFigu e2,whenanew100G,
400Go 1Tb/sconnec iona i esa hene wo k, hespec umallowed osuppo i islimi ed
o hesepa i ions,selec edina i s ‐ i ashion.Twoad an agesa e o eseenwhenadop ing
heses a egies s.gene icFlex‐G id:1)F agmen a ionisa oidedasspec umbands eleased
a e connec ions e mina ionha e hesamesizeinside hedi e en pa i ions;2)The
un ai nessp oblem[19] ypicalo Flex‐G idscena ios,whe ela geconnec ionssu e highe
blocking hansmalle ones,isa oided,sincepa i ionscouldbe ailo ed o une hene wo k
blockingpe o mance.Apo en iald awbacko bo hspec al/spa ialpa i ioningcanappea
unde unexpec ed a icp o ilede ia ions,c ea ingamisma chbe ween heo e ed a icand
hecon igu edspec al/spa ialpa i ions.When hese a icp o ilede ia ionsbecomes able,
ne wo k e‐pa i ioningwouldbeanop ion oallow hene wo kcon inuedeli e inghigh
pe o mance.Las ly,compa ingspec alandspa ialpa i ioning, hela e seemssimple and
easie omanagegi eni scoa se g anula i y,whichmay acili a econnec ionalloca ion
decisionsin hene wo k.
3. NUMERICALRESULTS
Anad‐hocJa a‐basedsimula o hasbeenimplemen ed oob ainaccu a enume ical
pe o mance esul so hep e iouslydesc ibedspec alandspa ialpa i ionings a egies o
Flex‐G id/SDMne wo ks.Ino de oge esul sasgene icaspossible,di e en opologiesas
wellasdi e se a icp o ilesha ebeensimula ed.
3.1. E alua ionscena ios
Twodi e en opologies[12]ha ebeenconside ed o hiss udy,namely, heDT12Ge man
anspo ne wo k(12nodes,20links),whosediame e is1019km,and hepan‐Eu opean
EON16ne wo k(16nodes,23links),wi hadiame e o 2663km.Fo hesakeo simplici y,a
singlemodula ion o ma isemployedineachne wo k.Acco ding o[20], hemaximum
ansmission eacho PM‐8QAMis1340kminSDMne wo ksdeployingSMFBlinks,while his
eachisinc eased o3796kmwhenPM‐QPSKisused.The e o e,when heDT12issimula ed,
hemaximumpa hleng hislimi ed o1340kmandPM‐8QAMisalwaysused.Incon as ,when
simula ing heEON16, hemaximumpa hleng hinc eases o3796kmandPM‐QPSKisalways
employed.
Weassume hea ailableop icalmodula o sin hene wo ko e a ixedbaud‐ a eo 25Gbaud.
So,i wein oduceagua d‐bandbe weenadjacen OCsequal o1FS,eachOCendsoccupying
a o alspec alwid ho 3FSs,o e ingane ec i e ansmissioncapaci yo 150o 100Gb/s
whenPM‐8QAM(asin heDT12)o PM‐QPSK(asin heEON16)isemployed,wi hspec al
e iciencieso 6and4b/s/Hz, espec i ely.Asa esul , osuppo 100G,400Gand1Tb/s
incomingdemandsin heDT12ne wo k,supe ‐channelscomposedo 1,3and7OCswillbe
needed,occupying3,9and21FSs.Incon as ,in heEON16ne wo k,supe ‐channels osuppo
100G,400Gand1Tb/sincomingdemandswillneed obecomposedo 1,4and10OCs, ha is,
occupying3,12and30FSs.Allconnec ionswillbesuppo edo e spec alsupe ‐channelsin
bo hne wo ks.So, hea o emen ionednumbe so FSswillalwaysneed obecon iguously
alloca edinaspeci icspa ialchannelincludedin heallowedspec al/spa ialpa i ion.
ASMFBisassumed obedeployedpe ne wo klinkineachdi ec ion,includinganumbe o
s anda dSMFs ha can a y om7 o30dependingon heexpe imen .The4THzC‐Bandis
usedineachSMF,which esul sin320FSso 12.5GHzwid h.Insomecases, hisnumbe o FSs
issligh lyadjus ed obe e i hespec al equi emen so incomingconnec ion eques s.Fo
example,wi hspa ialpa i ioning,324FSsa eenabledin hoseSMFdedica ed osuppo 400G
and1Tb/sconnec ions,s illwi hin heC‐Bande ec i ely.Thisnumbe o FSsbe e ma ches
he9o 12FS equi edby400Gconnec ionswhenPM‐8‐QAMo PM‐QPSKisused.O he wise,
asigni ican amoun o spec al esou ceswoulddi ec lybewas edpe SMF.Inanycase, obe
o ally ai , hesamesligh lymodi iednumbe o FSsisequippedpe SMFwhen es ingspec al
pa i ioningo nopa i ioningcases.
Rega ding heRou ing,Spa ialchannelandSpec umAssignmen (RSSA)algo i hm,weemploy
aK‐Sho es Pa h ou ingalgo i hm,cons aining hecandida epa hsby hea o emen ioned
maximumpa hleng h alues.Once heKcandida epa hs osuppo agi enconnec iona e
ob ained, heseonesa eexplo eds a ing om hesho es o helonges one.No ehe e ha
hespeci icnumbe o pa hs oexplo eby healgo i hmcanbeless hanKe en ually,when
someo hecompu edpa hsexceed hemaximum ansmission eachimposedby heemployed
modula ion o ma .As o hespa ialchannelandspec umassignmen ,a i s ‐ i s a egyis
used,assuming ha cos ‐e ec i eInSwi hou lanechangeSDM‐ROADMsa ep esen in he
ne wo k.Hence,spa ialchannelcon inui ymus beensu edend‐ o‐endalong hecandida e
pa hs,besides hespec umcon inui yandcon igui ycons ain simposedby heFlex‐G id
echnology.
Thewo s ‐case imecomplexi yo hisRSSAalgo i hmcanbeexp essedas ollows.I |N|and
|E|deno e henumbe o nodesandlinksin hene wo k, he imecomplexi yo compu ing he
Kcandida epa hsusing hewell‐knownYen’salgo i hm[21]isO(K∙|N|∙(|E|+|N|∙log(|N|)).As
o hespa ialchannelandspec umassignmen , he( e yunlikely)wo s ‐casewouldbegi en
when he eisonlyonespec al/spa ialpa i ionencompassingallspa ialchannelsand he
incomingdemand equi esasingleFS,needingup oO(K∙FSTo al)con inuousFSa ailabili ychecks
along heKcandida epa hs( ecall ha FSTo aldeno es he o alnumbe o a ailableFSsalong
allspa ialchannels).The e o e, hewo s ‐case imecomplexi yo heRSSAalgo i hmbecomes
O(K∙|N|∙(|E|+|N|∙log(|N|)+K∙FSTo al)e en ually.
Inou simula ions, wodi e en a icp o ilesha ebeenconside ed,whosepa ame e sa e
summa izedinTable1,whe eABRCandAFSC e e oA e ageBi ‐Ra epe Connec ionand
A e agenumbe o FSpe connec ion, espec i ely.
Table1.O e ed a icp o iles
T a icP o ileConnec ionsRa io(%)Spec umUsedDT12
(%)
Spec umUsedEON16
(%)ABRC
(Gb/s)
AFSC
DT12
(FS)
AFSC
EON16
(FS)
100G400G1Tb/s1004001Tb/s1004001Tb/s
TP1(Cu en )70201035303528324025067.5
TP2(Fu u e)40303011.76526.4761.7658.726.165.246010.213.8
I isimpo an ohighligh ha he ac iono spec umexpec ed obe equi edpe connec ion
ypedi e s om hei con ibu ion o he o alo e ed a icin heDT12ne wo k,bu no in
heEON16one.Fo example,unde TP1,100G,400Gand1Tb/sconnec ionswillcon ibu e o
28%,32%and40%o he o alo e ed a ic,whichma ches hei ela i espec um
equi emen sin heEON16.Thisisdue o he ac he a ioo FSsneeded(3,12and30FSs) s.
connec ionbi ‐ a e(100G,400G,1Tb/s)keepscons an whenPM‐QPSKisemployedin he
EON16.Howe e , hisdoesno happenwhenemployingPM‐8QAMin heDT12.
Asexplainedbe o e,oneo heobjec i eso hiswo kis ogauge hee ec o inc easing he
numbe o spa ialchannelson he esul sob ained.The e o e,di e en aluesha ebeen
simula ed.Speci ically,5illus a i eSDMspa ialmul iplici ies,namely,7,12,19,22and30,ha e
beene alua ed,assumingSMFBspe linkcomp isingsuchnumbe so pa allelSMFs.
3.2. Nume ical esul sandcompa ison
Fi s simula ionsha e ocusedon hee ec so di e en esou cepa i ionings a egies.Th ee
di e en casesa eshowninFigu e3,whe eTP1(seeTable1)hasbeeno e ed:
NOP(Nopa i ioning):Theconnec iondemandsa ealloca edwi hou anydis inc ion,
usingall hespa ialchannelsandoccupying hem omlow ohighspa ialchannelsin
a i s ‐ i spa ialchannelandspec umassignmen .
SPAP(Spa ialpa i ioning):Each ypeo connec ionsusesi scon igu edspa ial
pa i ion,asdesc ibedinFigu e2.b.In hecaseshowninFigu e3,wi h7spa ial
channels,100Gconnec ionsa ealloca edo e he wo i s spa ialchannels,400Gones
o e spa ialchannels3and4,and1Tb/sconnec ionscanusechannels om5 o7.
SPECP(Spec alPa i ioning):Each ypeo connec ionsusei scon igu edspec al
pa i ion,asdesc ibedinFigu e2.a.
(a) (b)
Figu e3.Bandwid hblockingp obabili y s.a e agesuppo edne wo kloadin heDT12(a)andEON16
(b)ne wo kswhenTP1isgene a ed.
Someconclusionscanbeex ac ed omFigu e3.Fi s and o emos ,bo hSPAPandSPECPa e
alwaysbene icialin e mso suppo edloada anyBBP alue e susNOP,p o idingSPECP
sligh lybe e pe o mance.Speci ically,i isobse ed ha gainsin heEON16ne wo ka e
clea lyhighe han hoseob ainedin heDT12,whe e hepe o manceo allop ionsissimila .
Thishappensasa esul o hehighe di e encesbe weenla ge andsmalle connec ionssizes
whenemployingPM‐QPSKin heEON16.Lookinga heload alues o BBP=1%, hesea e795,
855and860Tbi /s o NOP,SPAPandSPECPin heDT12, espec i ely(asseeninFigu e3.a,
di e encesbe weenSPAPandSPECPa e e ysmall).Incon as ,in heEON16(Figu e3.b) he
ela i edi e encesbe ween heNOPcaseand hoseusingpa i ions(SPAPandSPECP)isclea ly
highe ,namely,610,705and710Tbi /sa BBP=1%.Whileloadgainsa ea ound8%in he
DT12, hey ise oabou 16%in heEON16.
Asimila beha io isobse edwhenTP2isgene a ed,bu in hiscasedi e encesbe weenSPAP
andSPECPa ehighe (seeFigu e4).Thisisdue o he ac ha ,byha inghighe di e encesin
hep opo ionso spec umdedica ed oeachkindo connec ions(seeTable1), hedi e ences
be weenassigningcomple e ibe so heexac numbe o slo sbecomela ge .
(a)(b)
Figu e4.Bandwid hblockingp obabili y s.a e agesuppo edne wo kloadin heDT12(a)and
EON16(b)ne wo kswhenTP2isgene a ed.
The e o e, omFigu e4i canbeconcluded ha hedi e encesbe ween heSPAPandSPECP
s a egiesa ela ge unde TP2.Lookinga heexac load alues o BBP=1%, hesea e845,875
and900Tbi /s o NOP,SPAPandSPECPinDT12, espec i ely(Figu e4.a).Incon as ,in he
EON16(Figu e4.b) he ela i edi e encesa eclea lyhighe ,namely,630,730and740Tbi /s
a BBP=1%.Whileloadgain aluesob ainedbyspec umpa i ioning ange om3% o6%in
heDT12, hey ise oa ange om15% oalmos 18%in heEON16.
Asmen ionedbe o e,onepo en iald awbacko spec al/spa ialpa i ioningcoulds em oma
misma chingbe ween hepa i ionsand heo e ed a icp o ile.Wi h heaimo quan i ying
hise ec ,someaddi ionalsimula ionsha ebeenalsoconduc edwhe e heo e edload
de ia es om heexpec edone,bu wi hou modi ying hecon igu edpa i ions.Theob ained
esul sa esumma izedinFigu e5,conside ing heEONne wo kunde TP1andBBP=5%,
whe eSPAPandNOPha ebeencompa ed.Please ecall omFigu e3.b ha negligible
pe o mancedi e encesbe weenSPAPandSPECPexis in heEONunde TP1.The e o e, e y
simila esul swi hSPECPwouldalsobeobse ed.
The a icp o ilede ia ionssimula edconsis indec easing he a ioo 100Gconnec ions
(whose alueinTP1is70%)ins epso 5%,inc easing ha o 400Gand1Tb/sconnec ionsby
2.5%each.Fo example, he i s de ia ed a icp o ilebecomes100G(65%),400G(22.5%)and
1Tb/s(12.5%).