Design and dimensioning of dual-homing hierarchical multi-ring networks

A.Proestaki and M.C.Sinclair

Abstract: A nctwork dcsign sludy oiiiployiiig inultiplc hitcl-cotiticctcd rings which exploit the merits of ring topologics i s presented. Ncar-optimal diial-homing structui'cs iirc obkiiiiccl tising ii iiovcl partition, construct and pcr.ltirl3 (PCI') nctwork dcsign mclliod that coiisidcrs both total ring hgt l i and inbx-riiig traffic. I n oidci' (U addrcss sur,vivahility ~SSLICS, two hi-coiincclcd l i i c ~ ~ ~ ~ c h i ~ i d topology sdicincs ;tic identified, tlclxnding OH tlic sclcction ol' the inlcrconnccting r.iiig nodcs. A routing algorithm that nLtcnq>ts IO iiiiniinisr the iiiiixiiiiuni flow mi thc ringss. spccilically dcsigiied li)r dllill- lioinirig struclwes, is dcscribcci, which aims r ~ r hotti lower capiicily ;uid nioir balaijcctl solotiom h n shorkst-path routing. flic PCP dcsign mcthad is showii to give boll1 beltcl- results I11;iin iiii carlicr licul-istic for v:irious iiclwork sizes arid dci1i;tiiti pttcriis, n ~ i d closc to tlie opliinal solutions d>tiii l icd by a n integer-liucar- progl-;imtiiing forlnulation fur sinall prnhlcins. Dimciisioning of networks is also perfortiid, and (he cr'ccts of intcrconncction stratcgy 011 total ring Icngtli, thc ratio of inlra-ring t o total traffic, overiill capacity and ;i.iwiigc lwth leiig~li 01' dificreiit topologies i ~ r c discussctl.

1 Introduction

Ring-biised networks have attracted considcrablc tittciitioii diic to their regular hi-connected strtictiiia, which allows sitnplilictt routing iind riclwvrk control, R S wcll its [;ist ;incl itlativcly simple restoratioii. Rings liave f~.cqiicnlly bceu used Tot the desigti of local iirc'cit iietwoi-ks [I], and for syii- chronoirs optical nelwork (SON 1 C l ' ) scl~-l~caling arcliiw- tiires L2-51. R w n t l y , wavclcngtli divisiori dl ip lcx ing (WDM) rings hnvc :ilso bccn considcred far adoption iii all-opliciil network S C C I I ~ ~ ~ O S [6]$ bccnusc h c y ofycr signifi- cantly hipha capacity. Morcovcr, WDM rings 1 x 1 ~ alt-eady bccti cmployed i t i fieId trials, sitice they rcqtiirc sys- tcm hardware tlial is much easier to build ;tnd nw1tlagc compaced with tlic optical cross-coiiticck nccessriry in iiiosli networks [7].

t-Iowevei; the r c d i ~ i i u i i of 21 large-scale network usiilg it single ring riiay bc impriiclical becausc of the significant iucccase in both thr: capacity required: and the 1~11l1bcr o l hops bctween ~ i i y Lwo nodcs, as Lhc nimibci. of nadcs incrcascs. Thus, it is impor-(ant to invest.igatc cfficicnt inclh- ods to partition thc nctwork noclcs into ~11ii1llcI intercon- ncctcd riiigs- whilc both miintainiiig thc kcncfils of ring- b;iscd stnicturccs and keeping thc hardware coiiiplcxily low. 1 n :iddition, hi-connected archi~ccturcs need to hc consid- ered sincc future networks sIi~iiItI suiliive tlic most likely hilure xcnnrios iis the fibres usd will c;irty I I L I ~ C amounts of tn1ffic.

Severd mcthods of ring inta@onncct.ioii Iiwc hccn pro- poscti. A siiriplc appro;idi bwcd on (lie construction 01' iniiltiplc local rings and just clnc interconricctirig ring is

. - .

dcscribcd in [ I * XI. 'I'lie casc o i owrliippiig Inultiplc rings is prewutcd iii [S, 91. but only Tor. fixed topolngics. In this lat- tcr apprmich, scwfid liodcs and links mity bc shred hctwcc n di fkrc 11 t r i 11 gs, lcading to coni plcn a I I cl ex pci isivc soluliuns i i i term or Iictwork resnwccs tluc to tfic largc nutliber of intcrcuntiuc~ing nodcs. A inarc lmcticitl ;~ppi-oiicIi would I-K. io group the notlcs into ninallcr rings ~ i i d sdcct oiic or two ini~ironnectiiig (coiiiino~i) nodcs to route IIIC iiilcr-ring trnllic, correspoiidiiig tu single-homing (SI-IR) xid d~i;~I-lioining rings (DHR), icspcclivcly. A Iiicc- arcliicwl SIIR structure is proposctl in 121, whcrc ii siniple gi.cL'cly dcsign Iieurjslic is dcscribed. The simie approach i s cxrcnclcd in [-?I 10 DIIRs. Tliesc lead io iiiorc promising struclurcs ~ l ~ n SHlls, siiicc D[ IRs reprcsctll bi-connected topologics, ;ind ;iccordingly ciiii survive all single-oode and single-link Ibilurcs, i i i coiilwsl Lo SI-Itis, which cniiiio~ sttr- vivc w coin nmi- 11 od c ki i I 11 t'c ,

Wc pi'ogosc ;i partition, construct and p c ~ I ~ i r b (PCP) cicsign ii~ctliud for thc conshwlion of Iiicrarchhil bi-cnn- iicctcd nchvorks that c r m l h i multiplc rings, ciiiployitig a i l objcclive that considers both traflic ; i I d ring Ic~lgth, :is in [3]. l'lie idea is to mininiisc (he 1ot;il ring lcrlgth and also c;ipiuir: tlic niexiinum iiiiiount oi' Iriirfic in the inrlividiid ring, in ordcr to rcducc the Iiardwarc rctluircmcii~s HOCCY-

sary to cari-j' tl.:ific bctwccii diffcrcnt rings* 21s well as 10 simplify both primary r i d rcxloriilion i-ouling. Onc possi- blc sceii:ii.io woiild bc to coiisiilcr [lie rings ;it (lie lowest rictwork lcvcl tci be individiml riictropolitim or cnterprisc networks, arid thc upper lcvcls nl' thc tiierarchy tu rcplescrit tlic intcrconnectiiig widc-ilrea nctwork. The lioclcs wc ini- M y partitioned into ringh (level I ) and ~heu two coinin~n IIOLILX iirc sclecled li.oni aicli ring, which iii turn rorm i i

iicw sct of rings (lcvcl 7). Intercoiincction cnniiiiucs in tlic same way through tis nlil~i]' 11ic~iiicIiic;~l lev& as r.cqiiiixd, until a top levcl (f*) with jusl onc or two ring.$ i s rcachcd. In addition, two cl i f lc icnl bi-couneclcd topology sclicincs tiic idcntifictl herc, dcpcnding 011 ~ h c pl;icetiictil 01' Lhc two coiiiiimn nodcs within tlic intcrcoiriiccting rings of tlic higlicr Icvcls. Tticii, alicr dcsigniiig it near-optimal

J l < ! < ~ ' I ' I ~ ~ . - ~ ' u I ~ I I I I ~ ~ ~ I . , VtJi, 147, N r l . 2. ApYii ?(If10

topology, I I K iicst task is 10 idciitiij, :in cfticicnt mcthod to rotitc thc ~rnilic rlziri:iiids aid tlcicrmiiic c;ipxity irqiiirc- iiicnh (diinciisioiiiiig). 111 multi-ring iictwork$ routing citn hc divirlcd into ititrii-iiig and inter-ring rotititig, according io wlietlicr Wlic is conliiicd to a singlc ring or tfiivcrscs clilfcrcnt rings. In DHlis, the acltlition:il decision of sclccL- iiig niic of the two co~iinioii noclcs to raulc intcr-ring lrdlic is rcquircd, which compIic;itcs the routing schciiic. tlic bcsl ol' our knowlcdgc, only shortest-pit11 rwting (Sl'lC) lias so Lir bccii applied in UHlis 131. I-towcvct, we dcsctibc ii routing ;ilgoritliiri tliiil lrics to iiiiiiiinisc the iiiaxiiiiiiiii lloiv and conscqticirlly tlic capacity of the rings, specifically tlcsigncd for duiil-lioining structures, ;ind aiming ti>r inorc hilancctl solulions tli;in sitnplc SPR.

2 Multi-ring network topology design

'I'hc problcni for thc givcti iictwork iioiic Icx;ilions ;mtl skitic lixflic iiiiitrix is lo clclcimiric ;i sct or links ~ l i a t foi-iir rings at c;1cIi ilctwork Icvcl, :liming to iiiitiimiuc t l ic loti11 ring lciigtli ;uid ;ilso tnaxitiiisc the intra-ring Ii-allic so i r s to I C ~ L I C C tlic inlcr--riiig tr>iiiril costs [2, 51. In order to build a tik"cal sti'tichiic that copcs with all singlc-node ; i nd

sitiglc-link liiilurcs and 10 cnsiirc hi-corlricctivi(y (he dud- hcmitig Iccliniqiic is iidoptctl, and mmdiiigly cadi ring s1i:trcs t ~ o iiodcs with high-level rill&). For N, , ii .given

niitiiber of iioclcs tliilt ciin bc includcd in ~ i i c l i ring, i i singlc network level is designcd by both parlilioning (tic nodes into sets R,,>, whcrc it = I ~ .... r, anrl U;:' Rik = N,. and clioosiiig a S C ~ of litiks A, = (( i . ,fl : i, , j f N,} to lorni tlic riiigs. Tlic clioicc of IIT iii:ip hc iiiirdc by l ~ r c l i v ~ i r c liniiki- lions or cost; otlicrwisc. scv~r;il di l l~rc i i l \,illlics ~ 1 1 1 IX used and rhc bcsl resulting tlcsigti sclcclctl. While Iii-dircctionLil rings i i rc considcrcd hcrc (i.c. t l ic t r i i r lk ilows in h u h clircc- tions), our tlesigii approxli could casily bc ; i d a p ~ c d IO iiiii- ciircctional rings. 111 addilion, whilc iutoriition is not cxplicitly lakcii inlo account, wc as~t i i i i c sclf-healing rings with an :iiitoma tic pro~cction nicclxinisiii. TIic objcjccLivc is IO miniiilisc, I'or cach level ! in [he 1Iu twwk hierarchy. thc sciiiic 1ine;ir firtiction cmployetl hy Slii iuitl I :wsckii [3]:

SC~. of / I ! nodes a t 1ictwol-k ICVCI I, i\tid /I? 3, tlic Iiiaxl~i1uIii

y/<, # yw As a result, tlic number of variables is 1'p1 + 2nXq - I), wliik l l i e number or the conslraiiits is O(Y,R~), and thus the sizc of the formulation grows quickly as tlie number of nodcs atid rings iiicreases. Consequently, we have to mort to heurislic methods in order to cope with large-scale pioblcms.

2.2 PCP multi-ring design method O u r proposcd PCi' method for multi-ring topology dcsigii is dcpicted iti thc flow chart or Fig, 1, mil consists of four phascs. Starting with level 1 and tlie se( or all network nadcs, NI = N , thc iictwork is dcsigned one lcvcl at a time. For cach level I , wc use R set of' candidate nodcs V C_ N I and iiodc set5 that will eventually form thc rings. h i - tially, v = AT, atid xi,: = 0, Vk = 1, ,,,, J'/.

.1

1 1: partition V into Rlh

2: construcl all Rlk

I I v e s - last level?

(i) Purtirion phme: Move up to m iiodcs froin V to cacli R, in sequcncc, until Y = 0 (see Fig. 2). Firsl, iiiclucle in cach &. lhc node I E I' with the rnaximuni siiiii of IciigOis froin all nodes in V, i t . which maximises EjErT. dii: j + i. Then, itwativcly selxt tlic node that best conibines ncariicss to, and large traffic with, the nodc(s) in Itjk, i.e. tlic node i E V which miiiiiniscs

f ( i ? k , I ) a: d i j - j F h: j t / I ! &

and hcncc & = l</k 1- { i ) and V = - ( i ] , Next, chcck that cach ll<,kl 2 3. Otherwise, ~ l c c t a node i E R / k r , for tiny k' # k that injniniises the liunctioii flz, k , 0 arid inow it rrom H, to &, until all tlic stts have at lcnst three nodes.

(ii) Xing-cmstrwtion phcasc: Construct e x h ring by iising our g m d y minimum-length ring-constructior~ algorithm, which itcratively sclcc~s the most distant node in cadi set tiol yct added to tlic ring, and connccts it with its closest neighbours. l'lie individual rings itre tlicn modified by two perturbations, adopting any changcs that lead to an impravcnicnt: (1) rciiiove pairs of links and try altcniative ~ 6 l i 1 l ~ C t i O l l S betwccii their elid nodes; and (2) discontiect cach node from thc ring and try reinsertion Ixlwcen each pair or adjacent nodes. (iii) Pwiurlxilion phuse: Repeatedly apply each of tlic fol- lowing pei-turb;ttioi~s to all pairs or ring sets li,,, XI,,, I I f h, in sequence, adapting any that lead to an improvement in the abjeclivc.

98

c7 incroment k

select first node i V=V - {if

Rlk=Rlk+{i)

Fig2

(U) Ivlcrge R,,, it,,,, so that R,. = Rln U XI!, and I$,, = R,,, = 0, Then, pxrlilian them again by lint finding h e nodes i, j that inaxitnise tlic ruiictinn adii - - pio (it. tlie pair of nodcs that best combinc large distana and smell t r a f k with onc another), aticl including them in scpatate sets, so that R,, = { i j and R, = { j j . Next, conipute f'or cadi node h E R!c (in rirbitrary order) the wtlucs,~~h, a, 1) xr~dJlh, h, 0. If,j(h, a, 4 <j@, b, 4, h i s included in R),, otherwise in A',. ( / I ) Swap a11 the pairs or nodes i E &,, j E X, so thaL = Xln - { i } + { j } and R, = X, { j ) -I, { i } , by rearmng- ing links as necessary. (c) Muvc cach of tlie iiodcs i f I</(, in turn Lo Rm so th;tl R,(, = K,, - ( i ) and I$,, = Rlh + { i ) : providd lRj(,l > 3 and lR,/j < I H ! by rcarranging links as ricccssaiy. The itpplicdtion of the Iallcr IWO perturbations is

depict4 in Fig. 3. Although we only cotisider pcrturbations betwocn pairs of rings hcrc, clearly thcsc "Id also bc dcvised between larger sets 01 r ing. However, wc wodd anticipatc that this wwuld grcatly increase thc coinpita- tiorial burden, wilhout a cori-espoiiding improvemenl in thc rcsultiiig network dcsigns. (iv) In~erconncciim phuse: If thc algnrihn results in onc or two rings (depending on which of tlic hvo intercorincchig sclicnics described below is uscd], it stops. Olhct'qke, for cach ring Ii,, sclcct as common iiodcs IWO nodes b, g E R , thtit miniinisc

f ' ( l 2 . l ~ r , 1 ) = (dJij -1. d g j ) - R ( t h , + t g j )

(10) jglila, j $ h k

IEC f'ru(?.-Coninruii . V d 147. h% 2. April 20110

i.e. the nodes ihai hcsi combine iicariics io, tmd hrgc t l d fic with, those i~odcs not included in [\IC I iiig. Finally, usc llic conitnon nodes 21s rlic new canilidaic nndes ( A J / + ~ ) [or the next network lcvcl ( I + 1 ) and i-cpciil thc same inulti- ring design proccss.

a

Thc resulting nutnbcr or rings Formed a t cnch level I = 1, ..., L will be U, = [q'ml, while the nuinbcr of rings ;it Ihc next higher levd is rl.l.l = 12 . ri/m1, sincc thc 2 . r/ coiiitii~ii nodes thausdvcs iieed to bc pai+iitioiied into ring?. I L is apparent h a t grcatcr valucs for m will lead to ii smaller number of rings. I-Iowever, two spccial C H S ~ S CNI hc idcnti- tied before tlw construction o l tlic Iiiial lcvel. If ul, < i i i , just OW ring is built a t this Icvcl, employing our single-ring con- struction algorilhiii. If n,, =. t?? but n,, + 2 s 2 ' ni (sec Fig. 4), tlicn Lwo rings ;ire cuiisiriicted, but instcncl of sclccting two winmoii nodes l'rom cncli one (four in total) to include in thc higher level, we sclcct two coiiiiiioii nodes for both rings and include cacti oiic in the ring LO wliich il does not a l i ~ ~ I y belong. 111 h i s case, the two rings s h e the two coi i i imn nodes, no higlier level is ncccssary, >it id

wnscqucnlly, tlie 1i:irdw:irt rcqiiii.enients rcsultiiig from the coiistriiction of iiinrc interconnccliiig rings w e i-cduccd.

I K K Pr,)~~-[.'fiiiii}ii~,,,, Vu/. (47. A'o~ 2. April 20110

'['hc worst- tw complcxity of 1'CP ;it lcvcl I caii hc esti- m a t d as O(r,+) = U(,$) rot. the pxtitioii phase, wIiicIi is dmiiiatctl by selccl.ion oI' initial i d e s for each node set. Tlic ring-cunslruclion pliasc is O(/ j ) = O(nJ, siiicc all the opcratioiis arc limikil to singlc rings, which I iwc a fixed ~nilxirnuin iiiiiiibcr or nodes TU. Siniilrirly, 2111 thrcc lxttiir- bations xre O($) o(I$)~ as they consider operations Iiin- itcd LO iridiviclutll rings bill over all ring pairs. Finally, ihc intercnnnec~ion pIim is O(rfl,) 4 (I($), as t11e sclcction of coiiiiiion II&S TOY each ring hkcs iIiXoullt of all o t l ~ nutics. E:;ich pliasc is repeated for i i modwi iiiiiiiber of levcls, qlog n), giving an cstimaictl cr\/clall coniplexity of

F:urther impi*ovciiicnls to Wl', inclcasing i hc li kclihoocl of reaching ilic glohal optinium, would bc to iacotporatc ;idditioiial, 11iorc coinplcx Iocd-scarch operations, or LO ciiiploy i11oderii heuristic scaidi mclhods such 21s evolutioii- w y algnrirhins or siinulatctl micaling.

2.3 Comparison with earlier work The heuristic proposccl hy Slii and Voiiseka for SIIRs [Z], iuitl i-ccently extendcd to DI llis [9, iiscs the swliic objcclive iis applied h e . Howcwr, tlicy scqucntia Ily construct lings hy siiiiply connccting norlca iii series anrl forming ii chriin. The nodc pair lhat giva? the bcst. valuc Tor- tlic nbjectivc is first iiicludcd iii the cliain, ;ind h i nndcs tire ~iddcti a[ one of thc chiiin cr~ds. Whcn h c clxiin conlains 117 nodes, llic t w cnils are coi~iicctcil an r l ii IICW clxiin is fartncd. TIE miliii wcalciicss of this approach is tliiit the two cntls Inay corrcspoiid to ilistimt nodcs with low triiftic dcmand. h i d e s , it inay also rcsuli in poor selection of thc links thwi constitiite each ring, wliilc thc ring topology is not niodified for fiirtticr improvcineut. I n teriiis ot' clusbring, the latct rings can oiily hc Ibtiiicd by sclccliiig li-om (hc rcmiiining nudcs, iiI1d coiiscqueiitly, thcy may conlrihutc higher vducs to tlic cllijcctivc firr~c.tioii. Jii i ic ldl im, mcc. tlie topology js cniistrucktl, no multi-ring perLurb;i[iou opcrations arc eniploycd to irnpt'ovc it.

'rhc main tlilTclclicc from oiiI method, apart from our usc or pci~Lulbatious, is 1h;tt in our c : ~ , first thc nodcs tire grouped into xis, and rhen thc rings ;wc consirwlcd by cinploying OUI' single-ring constridoil dgclriihln. 'l'his, iiistexi of coiintxting iiotles in series, conslriicts parts of thc rings, starling f inm the iiiosl dic;lsnl rides : i d moving towards the centre af thc ring. In addition, the sclcction of a\ch i i d e for ii pirlicdar ring depends on dl tlic nodes ;iltcady iiicludctl in il, fii~hcr tliaii just one ol thc cnd nodes or :I chain. An cxaiiiplc of the ;ipplication of Shi and Fon- SC~CR'S inethod and o w iiiclliod to the sill^^^ network design problem ( I I = 4, MI = 4)? liw thc cxtreiiic position 01' n = I, /j = 0 (i.c. iilkii1g only distalice ioio xcoiini), i s showti in Figs. 5rr arid h, rcspcciircly. Both Siii and Fmiscka's over- large final ring K , , iiiid 0111 improved duskring sliould bc noted.

O(12 log n).

2.4 High er- leve I ring in term nn ection 111 Future networks it will bc very important io cnsurc bi- coniiwtivity in ortlct to achicve incretised survivnbility. In parlicular: for niulti-ti ng nctworks this requires two com- inmi i d e s per ling, and has tis 2111 ;iddiiioti;tl variable tho placcrnent 0 1 COIIU" nodcs in the liigher lcvcl interroii- ncctirig riogs. '['WO possihlc sclicmm tire identilicd hcre.

Tlie first one, cniploycd in [3], selects two ;idj;icciit com- i~ioii norks iiiiil ilicludcs theni both, iis wcll as the liiik lxtwcen tliciii, in the ncxt lcvcl ring. I t can he describcil as 'siiiiic coiiiiiioii ring' (SCR), sincc boll1 co~i~iiion nadcs arc iiwrlcrl in tlic snnic ring. PCP can he adaptcd to this

9g

12 b5 4

jiisl 2 lcvcls and 6 rings, but 24 links. I t sliould be noled that will1 DCIZ c1ia.c is ;ilw;iys 21 choice, ;it each etid, of two dilfcrcnt Iiighcr-lcvcl rings to Iouk the t raf tk between il piir ol' lower-level rings. For cxamplc, Tor T>CI< in tig. 6h. Ilic tralTic hclwccn ring XI 1 and c:iii either tt'aversc ring X a l , 01' Rzz3 white Ibr SCR in Fig. G i r , traffic bctweii I-iug

i l n d Kll IllllSt >Illways IISC R3, .

n3 1

10

13

scheme, so tliat cqu. 10 i s coinpukd only for all pairs of xijacciil iiodcs A, g E R)k (inlcrconncction phase), In addi- tion, whcn n nodc i is scloctcd Ihr inclusion in :t ring that I~dongs tcl ii liiglier levcl (tian the first, tlic cotiiiiioii n o d c j acljacciit to i :it the previous level shoiild he includcd in the swne ring (pertition phasc). Thc adjamill coiiiinon noclcs should also rcii1:in in ttie siinie ring during the Iperturba- li011 phasc.

Oia novd second ring intercniiiicction schemc, callcd 'diffci-crit coinmoii ring' (DCR). sclccts a pair of co~niiion nadcs, no1 necessarily tidjwmt, and includes them in dil'fci.- ent rings al thc ncxt Icvcl. I n this casc, PCT should bc mod- ified so 21s to forbid llic inscrtion or ii nodc i into ii ring /<,k tIi:it altrady ~ o i ~ t a i i ~ s ii noclc , j which is part or [tie ~iiiiic ring ns i at tbc piwiniis Icvcl, I - I ,

A key differena: hchccn tlic two sc1wnic.s is L1i;tl SC'R requircs n lowcr number or links, siticc severd links will he used inorc tllnrl oiicc iii difrc~.cni lcvcls, whiic DCR may Icad to OHC lcss intercotmectitig ring and level. Mnrcnvcr, DCR provides better protection qainsl thc po(ciihI hi]- we of B cotnnioii riodc bclonging 10 i t highc~.-lcvcl ring.

Euxamples of inulti-ring nctworits (ti = 18, U I = 4), employing the two interconnection schcmos, a17: shnwri in Figs, 6a and h. I n Lhc first ciisc (SCR) tlicrc arc 3 levcls, 7 rings and 22 links, \vhilc in the scxotiil ( t X R ) + there :~rc

ion

4000

2000

-

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0 - I y -2000 ’ I

2 -4000 - c 3 ; .eo00 -

P -8000 g 2 Y

~

.10000 ’

-1 2000 -

V - - v

I 160000

140000 , 4

-20000

-40000

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9 -1 aoooo

-80000 a - C

-1 20000

2 -I 40DOO

-$6000D bl

5-100000

-2aoooo -220000

A pairwisc sign test [15] for h c diffcrcnces in the objec- tivc h l c i i o n rncdiaris was also applicd. Whcn comparing PCP to Slii and Fonseka's hcurislic, the median differences wrc highly significant in niosl cascs; the exceptions corrc- sponcied to nctworks with a small valuc 01' I I Z . However, without prturlmtione, veiy highly significant differences were still obiaincd in ?nost cases for both cI = p = I and U

= IO, /3 = I , although for a = 1 , (3 -- IO tlic results were inainly iiot sigiificant. Thus, PCP witliout the perturba- tions givcs a better shirting topology (i.e. rings with lower total ring lcngth ;md higher intra-ring traFLic, cspccially for rings with a. gicatcr nuinbcr of nodes) thati Slii ill16 Fonsc- ka's heuristic iii mosl C R S C S , while the perliirbalions rcsult in a notable improvement.

4.2 Comparison of PCP with ILP To find how closc tn optimal our PCP dcsign method approaches, it was compaird with IT R, which obtains the optimum in all cascs, for the lowesl nctwork lcvcl 011 ten tcst problcins with M = 8, 9, 10, 1 I, and tIii*cc problems with n = 12, using n = IS = I (i.e. 43 iichvork design probletns In total). I h c lo ~ h c very long execution hncs [or TLP, we could only obtain rcsults for relat.ively sinall nclwcxks. PCP found Llic optimal resiilt for 81% o f thc nctworks exani- iiicd. The median valucs fool. the total ring length, and thc ratio of intra-ring to totd trafic ([l<), a s well t i s thc per- centage of thc cascs wherc PCP finds the optimum, arc prc- scnlcd in Table 1.

Table 1: Median total ring length and intra-ring traflic ratio for ILP and PCP

- -

- - - -

- -

- - - b

Optimum, N o . of nod= ILP PCP

n m Length, km IR,% Length, km IR,% %

8 4 3364 52.6 3364 52.6 100

9 3 3251 35.9 3391 35.7 70 10 4 3362 40.1 3362 40.1 90

11 4. 3485 42.1 3503 39.6 60

12 4 4082 39.9 4082 39.9 100

4.3 Comparison of ring-interconnection schemes TO cvaluate the two proposed ring-interconntrction schemcs, wc compwed networks with ti = 8, ,,,, 40, YPI = 4 1112

E

m

_v

,-I2000

3 10000 C - c 3

and CY = 0 = 1 ( i t . a single network at t i l & sizc Tor c a d i sdicmc, 66 nctworks in total) iti tcrms of' total ring length otid IR for all lcvcls (Fig. IO). It seem that both schemes lead t.o ii similar Icngih, although higher IR is ohwrvcd in SCR. This is due to the Lict that tlic total number of lings m y bc Iargcr in this case, and thus they caphirc a greater ;unounl of intra-ring truffic. In addition, lhc capacity requirement and also Ihc average path length for both SCR and DCR is shown in Fig. 11, where it can be sccn that SCR results in both liighcr capacity and longer avcragc path Icngth. The above results indicatc that DCR mwy rep- rcsciu a niorc appropriate ring iiilcrconnwtion schetne, iis thc inter-ring traffic bin-tlcn i s inore cvcnly distributed. Additional cxpcrimcntal results, not reported hew, indicatc that out' conchlsions wilh rcspcct to SCII/UCK hold for a wide range of (a, 0) valitcs. Conscquently, in spite of thc incrcascd number of links i i s d in DCR in cornparison with SCR, il inay still provide a more cost-effktivc topology.

"0° r

~

-

t 16000

14000

6000 1 I I I I I I I

10 15 20 25 30 35 40 45 4aoo:

numbaraf nodes &

number of nodes b

Pi . 1 0 -*- SCR

, I - ~ 0 C R

T ( p ) l f ~ rcridf.7 @ I ~ the tii 'o iril~,rtorsir?~fi.ti,rgg . S ~ U ( , . S , SC'H atid I,!!<

II T0l;ll I,i& lcl\glti

4.4 European optical network (EON) case study A 20-node network design prohlcm bawd on that described in [12], wiLh thc network required to caIry all tlic intctna- tional traffic bettvecn tlic inaiii ccntrcs of Europe, is used a s an examplc or our overall multi-ring design approach. Thc traffic matrix empluyd is an cstiinatc or future traffic demands modelled in [MI. Thwc diflci-cnt values of 111, i.e. 4, G and 8, were used, aiid both intcrconncction schemes, with LY = 0 = 1. This particular choicc of (a, f l is simply

I F E r r - ~ c . - c . ~ ~ , , ~ ~ i ~ ~ m , vol. 147, X U , 2, April 2000

11 Tiitla-ring triiific ratiu

250000

200000

c

600 U1 E 2 400-

numbor of nodes a

-

illustrative, with hoth distaiicc and intra-ring l r d k given cqiial wcighting, rather than bcing dcrived from detaikcl lcchno-wonoiiiic niodellitig. Kesulls wcrc obtained for totill ring length and inLi,it-rirIg ttanic nitio for all Icvcls, as ~ c l l as the resulting capiicity rcquiiwicnt and ;ivct-i~gc pall1 length (L’ables 2 and 3). Tlic Iiuinbcr of levcls, rii1g.s and links for the various nclworks is also recorded.

Table 2: Resultsfor the EON employing DCR (a = /3 1)

No.of No. of No. of Longth, IR,O/. Capacity Path, levels rings links km km m

- .. 4 3 10 34 24582 41.3 3187 2003

6 2 6 28 18349 48.4 2857 2390

a 2 4 23 14129 53.1 4678 2873

No. of No. of No. of Length, IR,% Capacity Path, levels rings links km km

4 3 IO 30 23641 40.6 3978 2259

6 2 6 25 17564 50.6 3751 2371

8 2 4 23 14129 53.1 4678 2873

It UII bc sccn that, Tor both SCR and DCR, thc total Icngth of the rings dcci.cascs, wliile lli increuscs, a s 111

incrcascs. ‘l’lzis can be explaiiicd by the corresponding

IET: P ~ ~ ~ ~ . - ~ . ~ i ~ t ~ ~ ~ i f i i . , L’ul, 147, >Vi), 2, April 2111111

dccIease of the number of rings and links in the network. Howcvci; Ihc avcragc path leiigth iiicreases, and this could bc ;I critical cmsidcmtion in WLlM rings, for inst;tncc, given the difliciiltics in mainliiining oplical transparency over long dishticcs. I n tcrms of Ihc capacity rcquircd, the most cost-cffcctive hpology is oblaiiicd Ibr i i i = 6. Corn- paring the two interconnection schcmcs, it scctns (hat SCIE rcsults in R relatively lower total ring length (which miiy bc cltic to thc sninllcr number of links in the nctivork) but. ii higher cap;icity rcrluircmcnt. It should hc iiotcd that for m = 8, ttic rcsults oblnincd for hoth scliancs arc idcritical. since only one intcrconncdjng ring is rcquiiul al the sec- oritl I c i ~ l . I n gcnwal, Lhc sclcctiori d t h c appropriate desigil will bc dctcrmincd by thc cost of capacity aiid link lengths, as well AS the technology iimitalions uti thc maximum link id path Icnglhs lliiil Ciil i bc acliicvctl.

a Athons

Stockholm r-\

Lisbon Madrid Roino

Atliens b

:level-I nods - ~ lsvsl-1 edgo U :level-2 node : level-2 ring-1 edne

..-- : level-2 rlng-2 edgo

Pig. 12 prcscnts thc tqmlogics nhtaitwd for the EON, wiicii Ihc IWO iiitcrcoriricctiiip schemes are employed for rn = I;. It can bc obscrvcd thal in the case of DCR, the cum- 111011 nodcs bclunging lo thc sainc first-levcl ring are placcd in diffcrcnt sccond-lcvcl rings, while ill the case of SCR some links arc iricludcd in both levels, and also the two SE- oiid-level riugs are coiiiicclcd by sliariiig the s:iiiie pail or nodcs.

IO3

5 Conclusions and further work

Multi-ring dcsign has h e n cousidercd, aiming ;it Ihc coil- structioti of' nenr-ophal hi-connccted Iiicfiirchicd IICL- works. A PCP dcsign niclhnci, cinployirig a n objectivc h;d combincs both ring Icnglli m d iritrwring CraClic, which pro- vidcs a sal isfiiclory starling sol ut inn subseclucnily cnIi;inccd by sevcmd pxtiirkitions, has hccn propnsccl for the topol- ogy design. Two dilfcrcnl topology schemes for du;il-Iioiii- iiig striiclures have bccn ictcnlificd wcording to the selection of' Ihc intcrwiinccling ring nodes. '1'he pIoblcm 0 1 trziflic routing and cnpxity wsignnient IIHS i~lso bccn acltlresscd by i i ~ i ;ippIo;ich specifically designed h i - iliial- lioniiiig structurcs, which trics lo ininimisc ~ h c iiiaxiiiiiitii llow on tlic rings sind tliiis obtain molt b a k " solations. Our PCP tlcsign mcthad 1i:is bcen coin partxi ;Lgainsl Slii and Fonscka's c;irlicr. Iicurislic for. various ~n~~wol-k sizcs and dcmand paitcrns, a n d 1x1s been sliawri 10 give bctlcr rcsulls. 111 comparison with an iiitcger-linc;ir progl-animing Ibriiiulalion, oui- method exliibits ii no1;iblc corivcrgcnce to the optiinal r;oiutioris in ~ l i c mjority of cases for siniill probIciii sizes. Dimensioning of thc rings has RISO been Iper- formed, and tlic eflccts or thc diffcrciit intercotitiection schcines on Ihc total ring length, the wtio or itilrit-rhg IO total traffic, uvcrdl capacity and avenge patti length Ii;ivc hcen disciismi.

Futtwc work 111ity includc incorporating the choice of n7 into I'CI', addition;il sludy ol' thc proprtics or our pro- posed inlercor~r~cctio~~ sclien~cs, detcrininiiig thc cxtcnt to which ruinirnuni-flow rc-touting is an imp~~ovcrncn~ over sirllplc shorlcst-path, exploring inorc ltiiIiSIic objcctivc fiinctions, comparing ring-bascd topologies with mesh tict- works, invcs1ig;iling llic problem of fibre and wa\&nglIi d1oc;itim iii multi-ring nctworks, and rleveloping elgo- riltims for multi-ring network construction ha^ intcgratc topology design with f i lm iind wavclcngth allocation.

6 Acknowledgments

The authors woiild likc to Oxink Llr. Colin Soutti 01' Vujitsu Tclcconiin~inications Etuopc Ltrl. (14"1E1,) ror h i s viilu:iblc commcnts 011 an carly draft. A. I'rocstaki is sup- [iorlcd by FTEI, 011 thc 'Futnre Broadkind Nclworks' projcct.

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