Performance Evaluation of Survivable Multifiber WDM Networks

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1 erformnce Evluton of Survvble ultfber WD Networks Yunqu Luo nd Nrwn Ansr Advnced Networkng Lbortory Deprtment of Electrcl nd Computer Engneerng New Jersey Intute of Technology Unvery Heghts, Newrk, NJ 070 USA Abrct Ths rtcle proposes survvblty evluton model for multfber WD networks, n whch the extended lyered grph s developed to jontly optmze the wvelength routng nd wvelength ssgnment problems, nd three dfferent edge co functons re evluted n terms of trffc engneerng. Lner progrmmng (L) equtons re formulted to optmlly determne the workng lghtpth nd the correspondng protecton lghtpth under the schemes of shred protecton nd dedcted protecton. The extensve smultons show tht shred protecton wth the fber nd wvelength-bsed co functon provdes the be survvblty. Keywords multfber WD networks; lyered grph; L; survvlblty. I. INTRODUCTION By dynmclly provsonng tremendous mount of bndwdth wth tens of terbts per second, wvelength dvson multplexng (WD) s plyng mjor role n the expnson of our networks. ore bndwdth n ech optcl chnnel of WD networks mens more serous dt loss ech tme when fult occurs. Ths s why the survvblty performnce of WD networks s n mportnt reserch ssue. A number of reserch results on survvble WD networks hve been reported n the lterture. odno nd Nrul-Tm [] proved tht the survvblty ssue for WD networks s N-complete. yo nd Sto [] proposed the optml desgn scheme for survvble WD networks. The utomtc protecton swtchng (AS) functon for survvble WD networks s relzed by protecton cycles []. The vlblty nlyss of the spn-bsed recovery s presented n []. The mplementton of spn reorton nd prorty-bsed recovery ssures tht the WD networks re survvble n the cse of multple flures. There hs been recent ntere n ssessng the survvblty performnce mprovement of multfber WD networks. Ths s motvted by the economc dvntge of deployng bundles of fbers for the purpose of fult tolernce nd network growth. In multfber networks, ech node ncludes dynmclly confgurble optcl swtch tht supports fber swtchng nd wvelength swtchng. Wvelength converson s not confgured functon, nd thus the connecton between two nodes mu be ssgned the sme wvelength n ll the ntermedte edges. Ths s the so-clled wvelength contnuty conrnt. A wvelength-routng node of nodl degree two (two nput bundles nd two output bundles), three fbers per bundle, nd four wvelengths per fber s depcted n Fgure. ultfber WD networks re n lterntve soluton to overcome the wvelength contnuty conrnt [5], [6]. An F-fber W-wvelength network s functonlly equvlent to n FW-wvelength network wth prtl wvelength converson of degree F [7]. The reserch n [8] shows tht multfber WD networks ctully ncrese wvelength utlzton. demultplexers multplexers bundle bundle swtch λ swtch λ swtch λ swtch λ Fgure. Wvelength node wth degree, fbers per lnk, nd wvelengths per fber bundle bundle In ths pper, we focus on the survvblty ssue of multfber WD networks wth the purpose of evlutng the survvblty performnce. We shll fr defne the followng terms. ultfber network: A network tht utlzes multple fbers n ech lnk. Our udy s focused on the even multfber network, n whch the number of fbers n ech lnk s the sme, nd the number of wvelengths n ech fber s the sme. An esy extenson nd the smlr nlyss cn be ppled to the uneven multfber networks. Lnk: A bundle of fbers n the optcl network between two nodes. Lghtpth: An optcl communcton pth between two nodes, eblshed by lloctng the sme wvelength throughout the route of the trnsmsson. There s no wvelength converson n the ntermedte nodes, nd wvelength contnuty conrnt s ppled on lghtpth. Lyered grph: The vrtul logcl topology of physcl network. In lyered grph, ech lyer represents the sme wvelength connectons mong the network nodes. Ths work hs been supported n prt by the New Jersey Commsson on Hgher Educton v the NJI-TOWER project nd the New Jersey Commsson on Scence nd Technology v NJWINS. GLOBECO /0/$ IEEE

2 Edge: The connecton between two nodes n the lyered grph. An edge s n ctul wvelength between two nodes. The re of the pper s orgnzed s follows. The evluton model for survvble multfber WD networks s proposed n Secton II. Formultons for shred protecton nd for dedcted protecton re derved by L equtons n Secton III. The smultons nd correspondng dscussons re presented n Secton IV. Conclusons re gven n Secton V. II. THE EVALUATION ODEL A network s survvble f ny sngle lnk flure does not dsconnect the trffc n the network. To cheve such survvblty, protecton lghtpth s ssgned to workng lghpth. In the cse of ny ntermedte lnk flure, the trffc s gurnteed by swtchng t nto the protecton lghtpth. Dsjont protecton lghtpth s desred recovery scheme, whch resolves the wor cse when ll the ntermedte lnks fl. The network survvblty ssue cn be descrbed s follows: gven the network trffc mtrx, the problem s to () fnd lghtpth s the workng lghtpth for ech trffc, nd (b) fnd dsjont lghtpth s the protecton lghtpth for ech trffc. Selectng the workng nd correspondng protecton lghtpth s routng nd wvelength ssgnment (RWA) problem, whch s N-complete. In ths secton, model wth two components s developed to resolve the bove survvblty ssue. The extended lyered grph component supports the jont optmzton of wvelength routng nd wvelength ssgnment problems. The workng lghtpth nd the dsjont protecton lghtpth cn be esly selected n the extended lyered grph, nd wvelength contnuty n ech lghtpth s gurnteed. The edge co functon component fclttes trffc dmsson nd trffc engneerng. By properly choosng the edge co functon, trffc lod n ech lnk could be blnced ccordng to the network tus nformton. A. The Extended Lyered Grph Consder grph G(N, E, F, W) for gven multfber WD network, where N s the node set, N s the totl number of nodes; E s the lnk set, E represents the b-drectonl lnk numbered, E s the totl number of lnks; F s the number of fbers per lnk; W s the number of wvelengths per fber. The lyered grph G L cn be obtned from gven grph G by the followng procedure: ) Replcte the gven grph G for W tmes n G L. Ech lyer represents the s th wvelength,.e., λ s, λ s {λ, λ,,λ W }. ) In ech lyer, replcte lnk E for F tmes. Ech edge n the lyered grph denotes n ctul wvelength connecton n the network. Fgure shows n exmple of n even -fber - wvelength WD network wth nodes N, N,, nd lnks E,,,,. Ech lnk s bundle of two fbers, nd ech fber ccommodtes four wvelengths λ, λ, λ, λ. Fgure shows the lyered grph of ths network. We replcte the orgnl grph four tmes, wth the fr lyer for wvelength λ, the second lyer for λ, the thrd lyer for λ, nd the fourth lyer for λ. In ech lyer, replcte ech lnk twce s the edges n G L. For exmple, the lnk n G s denoted s edges E (s=, ; t=,,, ) n the lyered grph G L, where s nds for the fber number, nd t for the wvelength number (e.g., lnk hs two edges n lyer three: E nd E ). E N E N N E N N E Fg.. hyscl network N E Fg.. Lyered grph In the lyered grph, ech route s one ctul lghtpth wth wvelength contnuty. By usng such route, there s no requrement for wvelength converson. As smple exmple, f we need to fnd route for the node pr (N, ) wth wvelength λ, we cn set up such route by usng the lyer two n G L. Ined of consderng wvelength routng nd wvelength ssgnment seprtely n G, the lyered grph G L provdes scheme to combne these two problems together. In the lyered grph, whenever route s found, ts wvelength contnuty s gurnteed. Therefore, the lyered grph model tghtly couples the wvelength routng nd wvelength ssgnment eps together. It provdes frmework for obtnng the exct optml soluton for the number of requeed lghtpths s well s for the throughput tht gven network cn support. It s esy to see tht f set of workng nd protecton lghtpths s found n the lyered grph, then ll of them cn be supported n the correspondng physcl network. If two lghtpths do not shre the sme lnk (one lnk hs F fbers n ech lyer) nd the sme ntermedte nodes (one node hs one replcton n ech lyer), they re dsjont n the physcl network. Therefore, the network survvblty ssue cn be reduced nto the problem of fndng pr of dsjont lghtpths n the lyered grph for ech trffc. B. The Edge Co Functon A prmount concern of survvble network s to ensure the end-to-end vlblty of lghtpths n the cse of lnk E N E N N E N E GLOBECO /0/$ IEEE

3 flures wth the le co. The co for trffc trnsmsson s the sum of ll the edge cos long the lghtpth. The co functon of edges flls nto one of two ctegores: tc co, where the edge co s fxed wthout consderng the network tus, nd dptve co, where the co of n edge s updted by the network te nformton (e.g., vlble bndwdth). For the tc edge co functon, ech edge s co functon s fxed, nd there s not much dfference between sngle fber nd multfber networks. For the dptve co functon, the edge co functon n multfber networks s much more complex thn n the sngle fber networks. Ined of updtng the co functon by wvelength vlblty nformton n sngle fber networks, the co functon cn be dynmclly updted s combnton of the wvelength vlblty nd fber vlblty. We ctegorze the edge co functon n multfber networks nto the followng three types: ) Connt co: the co functon of edge E,.e., C(E ), s defned s follows:, f s not occuped α E CE ( ) =, (), otherwse where α s connt for edge E. The co functon s fxed no mtter wht the network tus s. When the edge s occuped, the edge co s set to nfnte to vod future utlzton. ) Wvelength-bsed co: the co s updted by the wvelength utlzton nformton n fber,.e., W o α + β, f W < W CE ( ) = W o t, () t, otherwse where W t s the totl number of wvelengths n specfc fber E s, W o s the number of occuped wvelengths n ths fber, nd α nd β re connt weght fctors for edge E. The rto β / α determnes how much the edge co depends on the vlble wvelength n one fber. The co wll ncrese s the number of occuped wvelengths n fber ncreses. When ll of the wvelengths re used up, the co s nfnte. ) Fber nd wvelength-bsed co: the edge co s updted by the combnton of vlble wvelengths n fber nd vlble fbers n lnk,.e., W F o o α + β + γ, f W < W CE ( ) = W F o t, () t t, otherwse where F t s the totl number of fbers n lnk E, F o s the number of occuped fbers n lnk E ( fber s occuped f t le one of ts wvelengths s used), α, β, nd γ re connt weght fctors for edge E. The rto β / α determnes how much the edge co depends on the vlble wvelength n one fber, nd the rto γ / α determnes how much the edge co depends on the vlble fbers n one lnk. The co wll ncrese f more number of wvelengths re used or more number of fbers re occuped. Ths co functon tkes consderton of the occuped wvelengths n specfc s fber E nd the occuped fbers n specfc lnk E. When ll of the wvelengths re occuped, the co s nfnte. The connt co rtegy s tc one, n whch the co of ech edge s fxed throughout the tme. The wvelengthbsed co s n dptve one, whch consders the nfluence of the number of occuped wvelengths n fber; t ncludes the locl wvelength vlblty n one fber. The fber nd wvelength-bsed co s lso n dptve one wth two dynmc fctors: the number of occuped wvelengths n specfc fber, nd the number of occuped fbers n specfc lnk. Ths rtegy s motvted by the common prctce tht n bundle of fbers connectng two nodes,.e., lnk, the vlblty of one wvelength chnnel s decded by the unoccuped fbers n ths lnk nd the unoccuped wvelengths n the vlble fbers. If we use the le co routng polcy, the mjor dfference between the connt nd the dptve co functon s tht, under the connt co functon, some lnks re more often selected whle others re reltvely dle, whle under the wvelength-bsed co nd the fber nd wvelength-bsed co, the trffc wll be llocted to the less congeed lnks bsed on the network te nformton. In Secton IV, we evlute the performnce of these three dfferent co functons. III. NETWORK SURVIVABILITY ROBLE FORULATIONS To survve lnk flures, one dsjont protecton lghtpth mu be ssgned to specfc workng lghtpth. The schemes to ssgn the protecton lghtpth cn be ctegorzed nto two types: the dedcted protecton lghtpth, n whch ech workng lghtpth s protected by dsjont protecton lghtpth (ths protecton lghtpth s dedcted only to specfc workng lghtpth, nd cnnot be shred by other workng lghtpths); the shred protecton lghtpth, n whch the protecton lghtpths cn hve common lnks. A. Nottons For n even multfber network G(N, E, F, W), ts correspondng lyered grph s G L (N, E, F, W), node set W W s N = { N, N,..., N,..., N, N,..., N }, edge set s L n n n E = { E, E,..., E, E, E,..., E,..., E }, n= N L s the L W W FW e totl number of nodes, e= E L s the totl number of lnks, F s the totl number of fbers n ech lnk, nd W s the totl number of wvelengths n ech fber. For the trffc mtrx, we ntroduce the followng nottons: {,,..., }: the set of workng lghtpths for trffc mtrx, {,,..., }: the set of protecton lghtpths for trffc mtrx, : the trffc n the workng lghtpth, : the trffc n the protecton lghtpth, GLOBECO /0/$ IEEE

4 th E : lnk n G( N, E, F, W), s th th E : s fber n lnk, E : the edge n G ( N, E, F, W),.e., t wvelength n s L L L th fber of lnk, CE ( ) : the co of edge E, C ( ) : the co of lghtpth,, f workng lghtpth uses edge E I =, E 0, otherwse, f protecton lghtpth uses edge E Q =. E 0, otherwse th th B. L Formultons In the followng formultons, we ssume tht ech trffc n requres one wvelength bndwdth. The shred protecton scheme s then formulted s follows. nmze the co:, () = = mn( C ( ) + C ( )) where the workng lghtpth co: e F W C ( ) = CE ( ) I, {,,..., }, (5) E = s= t= the protecton lghtpth co: e F W C ( ) = CE ( ) Q, {,,..., }, (6) = s= t= subject to the followng conrnts: wvelength conrnt: W = t= E I W, E E, s {,,..., F}, (7) E bndwdth requrement conrnt: I, E E, (8) = E lnk cpcty conrnt: F W I FW, (9) = s= t= E trffc recovery conrnt: =, (0) = = dsjont protecton conrnt: F F W W I Q = 0, {,,..., }, {,,..., e}. () xy s= y= t= x= E E For n F-fber W-wvelength network, mnmzng the totl co for the workng lghtpths nd the protecton lghtpths s the objectve of L (). The totl co s the sum of the co for the workng lghtpths (5) nd the protecton lghtphs (6). Ech fber E s only ccommodtes t mo W workng lghtpths (7). Ech workng lghtpth only requres t mo one wvelength bndwdth (8). Conrnt (9) lmts the trffc lod n lnk; the totl lod of ll the workng lghtpths n lnk cnnot be lrger thn the lnk cpcty of FW wvelengths. We consder 00% protecton for ech trffc (0) to vod the serous dt loss per flure. Full protecton s relzed by ssgnng dsjont protecton lghtpth for ech workng lghtpth (); no common lnks nd no common ntermedte nodes ex between the workng lghtpth nd the correspondng protecton lghtpth. The bove equtons re the formulton for the shred protecton scheme. rotecton lghtpths for dfferent workng lghtpths cn be ssgned common edges f possble. Ths shred protecton cn ensure survvblty of ny sngle flure n the network. In the cse of multple flures, the dedcted protecton scheme mu be deployed, nd the followng conrnt re lso requred n ddton to ()-(): Q. () = E Ths nequlty ensures tht ech edge t mo ccommodtes one protecton lghtpth. The edges of one protecton lghtpth re not shred wth other protecton lghtpths. IV. NUERICAL RESULTS Smultons re conducted on the NSFNET topology wth three dfferent fber-wvelength combntons: -fber 8- wvelength, -fber -wvelength, nd 8-fber -wvelength. The trffc mtrx hs 55 connecton requrements, nd ech requres bndwdth of one wvelength nd protecton lghtpth. Four lgorthms re mplemented to compre ther survvblty performnce. Algorthm I pples the the connt co functon. α n () s set to be. The lghtpth s ssgned by the shorte pth scheme; dsjont protecton s dedcted for workng lghtpth. Algorthm II mplements the wvelength-bsed co functon, where α nd β n () re both equl to. A dedcted le co protecton lghtpth s ssgned for workng lghtpth. Algorthm III ccommodtes the fber nd wvelength-bsed co functon, where α, β nd γ n () re ll set to be, nd the dedcted protecton scheme s deployed. Algorthm IV s shred protecton verson of lgorthm III; t dopts the sme edge co functon s Algorthm III except tht the protecton lghtpth could shre common edges f possble. Tble I ()-(c) summrzes the survvblty performnce for ech scenro. The unprotected soluton decreses s the number of fbers ncreses. Incresng the number of fbers results n hgher connectvty n the lyered grph, nd therefore less hop count for ech lghtpth. Among Algorthms I, II, nd III, Algorthm I s the greede one; t serches for the lghtpth wth the le hop, nd thus the verge hop count s the le. On the other hnd, the network lod for ech fber s serously uneven for the shorte routng scheme, nd GLOBECO /0/$ IEEE

5 ths leds to more unprotected connectons n Algorthm I. The shred protecton llows Algorthm IV to protect more workng trffc wth less network resources, s compred wth Algorthm III. However, the protecton n Algorthm IV s only pplcble to sngle flure whle the protectons n other three lgorthms re effectve for multple flures. TABLE I. Survvbkty performnce comprson (). -fber 8-wvelength network Algorthm I II III IV Unprotected connecton Ave. lghtpth hop (b). -fber -wvelength network Algorthm I II III IV Unprotected connecton Ave. lghtpth hop (c). 8-fber -wvelength network Algorthm I II III IV Unprotected connecton Ave. lghtpth hop TABLE II. Network lod drbuton (). -fber 8-wvelength network Algorthm I Algorthm II Algorthm III Averge 6.6 lod/fber 7. lod/fber 7 lod/fber Stndrd devton.50 lod/fber.6 lod/fber 0.8 lod/fber (b). -fber -wvelength network Algorthm I Algorthm II Algorthm III Averge. lod/fber.5 lod/fber.5 lod/fber Stndrd devton 0.85 lod/fber 0.66 lod/fber 0.6 lod/fber (c). 8-fber -wvelength network Algorthm I Algorthm II Algorthm III Averge.5 lod/fber.7 lod/fber.7 lod/fber Stndrd devton 0.75 lod/fber 0.58 lod/fber 0.9 lod/fber Tble II ()-(c) llurtes the trffc drbuton for ech scenro. Wth the connt co functon nd the shorte pth routng, Algorthm I drbutes the trffc lod unevenly n ech fber. By tkng consderton of the wvelength utlzton of ech fber, Algorthm II reduces the trffc lod ndrd devton compred wth Algorthm I. Algorthm III uses the globl resource nformton, nd ths scheme genertes the be lod blncng result. When n ncomng trffc rrves, Algorthm II routes t nto the fber wth more vlble wvelengths, whle Algorthm III routes t nto the fber wth more vlble wvelengths, nd ths fber s locted n the lnk wth more dle fbers. The dptve co functons (Algorthms II nd III) re superor to the connt co functon (Algorthm I) n terms of the network lod blncng. Ths s becuse, s the network trffc lod ncreses, the dptve co functons tend to drbute the lod to lghtly loded edges nd vod the hevly loded ones. Between the two dptve schemes, the fber nd wvelength-bsed co functon (Algorthm III) employs much more ccurte globl network te nformton, nd therefore results n more evenly loded trffc; the lod vrton mong ll edges s less. V. CONCLUSIONS The common prctce of nllng bundles of multple fbers motvtes the recent reserch on the multfber WD networks. ultfber WD networks wthout wvelength converson re ttrctve lterntve for sngle fber networks wth wvelength converson cpblty. In ths pper, we ddress the survvblty ssue of multfber networks wth the purpose of protectng ech workng lghtpth by dsjont protecton lghtpth. To evlute the survvblty performnce, the extended lyered grph s proposed to jontly optmze the wvelength routng nd wvelength ssgnment problems. Bsed on L, the mthemtcl formultons for survvble multfber networks re derved. Shred protecton recovers the trffc from ny sngle edge flure, whle dedcted protecton recovers multple flures. To relze network trffc engneerng, dfferent edge co functons re proposed. Our extensve smultons verfy tht the fber nd wvelength-bsed co functon results n mrgnl mprovements n the lod blncng drbuton, becuse t ncorportes more network te nformton bout fber utlzton nd wvelength utlzton. REFERENCES [] E. odno nd A. Nrul-Tm, Survvble lghtpth routng: new pproch to the desgn of WD-bsed networks, IEEE Journl on Selected Ares n Communctons, vol. 0, no., pp , y 00. [] Y. yo nd H. Sto, Optml desgn nd evluton of survvble WD trnsport networks, IEEE Journl on Selected Ares n Communctons, vol. 6, no. 7, pp , Sept [] G. Ellns, A.G. Hlemrm, nd T.E. Stern, rotecton cycles n mesh WD networks, IEEE Journl on Selected Ares n Communctons, vol. 8, no. 0, pp. 9-97, Oct []. Clouqueur nd W.D. Grover, Avlblty nlyss of spnreorble mesh networks, IEEE Journl on Selected Ares n Communctons, vol. 0, no., pp. 80-8, y 00. [5] L. L nd A.K. Somn, A new nlytcl model for multfber WD networks, IEEE Journl on Selected Ares n Communctons, vol. 8, no. 0, pp. 8-5, Oct [6] S. Xu, L. L, nd S. Wng, Dynmc routng nd ssgnment of wvelength lgorthms n multfber wvelength dvson multplexng networks, IEEE Journl on Selected Ares n Communctons, vol. 8, no. 0, pp. 0-7, Oct [7] A. okhtr nd. Azzoglu, Adptve wvelength routng n lloptcl networks, IEEE/AC Trnsctons on Networkng, vol. 6, no., pp , Aprl 998. [8] G. L nd R. Smh, On the wvelength ssgnment problem n multfber WD r nd rng networks, IEEE/AC Trnsctons on Networkng, vol. 9, no., pp , Feb. 00. GLOBECO /0/$ IEEE