Dynamic Lightpath Protection in WDM Mesh Networks under Risk-Disjoint Constraint

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1 Dynamc Lghtpath Protecton n D esh Netors under Rs-Dsont Constrant Shengl Yuan* and Jason P. Jue *Department of Computer and athematcal Scences, Unversty of Houston Donton One an Street, Houston, TX 7700, yuans@uhd.edu Department of Computer Scence, Unversty of Texas at Dallas, Rchardson, TX 7508, ue@utdallas.edu Abstract-- Path protecton requres fndng a orng path and a protecton path that are ln dsont. In ths paper, e consder the dynamc lghtpath protecton problem n D mesh netors here a sngle rs factor may cause multple lns to fal smultaneously. The obectve s to fnd ln-dsont lghtpaths that are also rs dsont. A smlar problem has recently been proven to be NP-Complete. e gve an alternatve proof of the NP-completeness, and formulate the problem as an Integer Lnear Program. e then develop heurstc algorthms and evaluate the performance of the algorthms through computer smulaton. e sho that e can acheve satsfactory performance usng the heurstc technques. Index terms-- Optcal netor, lghtpath protecton, shared rs ln group, rs dsont, nteger lnear program (ILP) I. INTRODUCTION In avelength dvson multplexng (D) netors, end users can communcate th one another va all-optcal channels called lghtpaths [][]. Because of the hgh data rate on lghtpaths, t s mperatve to develop approprate protecton and restoraton schemes to prevent or reduce data loss [][4]. In protecton schemes, bacup resources are pre-computed and reserved for each connecton before a falure occurs [5][6]. In restoraton schemes, an alternate route s dscovered dynamcally for each nterrupted connecton after a falure occurs [7][8]. Compared to restoraton schemes, protecton schemes have faster recovery tme and provde guaranteed recovery ablty but requre more netor resources. Protecton schemes can be dvded nto path protecton and ln protecton based on the level of netor resources nvolved n the protecton. In path protecton, a orng path and a dsont protecton path are establshed for each connecton. In ln protecton, separate bacup resources are reserved for each ndvdual ln on the orng path. Path protecton usually has loer resource requrements and loer end-to-end propagaton delay for the recovered route [5][7]. Protecton schemes can be further dvded nto dedcated protecton and shared protecton based on hether bacup resources are shared by more than one connecton. In dedcated protecton, each ln or node can be reserved as a bacup resource for at most one connecton. In shared protecton, a ln or node can be reserved as a bacup resource for multple connectons, as long as those connectons do not fal smultaneously. Dedcated protecton requres more netor resources but s smpler to mplement, hle shared protecton s more resource effcent but requres complex sgnalng and netor management []. The path protecton problem can be consdered under ether statc or dynamc traffc. Under statc traffc, the entre set of connecton requests s non. The routes and the avelengths for the orng and protecton lghtpaths of all connectons must be determned[5][9][0][][]. Under dynamc traffc, connecton requests arrve one at a tme and each connecton exsts for only a fnte duraton. Subsequently, routes and avelengths are determned ndvdually for the orng and protecton lghtpaths of each connecton request. In an optcal netor thout avelength converson capablty [][4], the establshment of a lghtpath s subect to the avelength contnuty constrant,.e., a lghtpath s requred to be on the same avelength channel throughout ts entre path. In ths paper, e address the dynamc lghtpath protecton problem n D netors th full avelength converson. In ths case, a lghtpath may consst of dfferent avelengths on each ln. A netor falure may be caused by ether a ln falure or a node falure. ost modern node devces have bult-n redundancy hch greatly mproves ther relablty. Therefore ln falure s more of a concern than node falure, and e only consder ln falure n ths paper. In order to fnd to ln-dsont lghtpaths, e may ntutvely use a smple tostep soluton,.e., e fnd one shortest path frst, then remove all lns on that path and fnd the second shortest path. These to paths are guaranteed to be ln dsont. Hoever, ths soluton fals n so-called trap topologes[5]. The correct approach s to use Suurballe's algorthm and ts varatons [6][7], f the probabltes of ln falures are ndependent. The total cost of the resultng to ln-dsont lghtpaths s mnmal among all such path pars. The algorthm runs n O(n log n) tme, here n s the number of nodes. Hoever, n a netor here a sngle factor can cause more than one ln falure, the to lghtpaths found th ths approach may stll fal smultaneously. For nstance, n optcal transport netors, multple fber lns are bundled nto the same underground condut, or span. A cut to the condut can cause all the fber lns to fal. To descrbe ths type of netor phenomenon, transport netor carrers use the notaton of Shared Rs Ln Group (SRLG) [8][9]. The fber lns n the same condut belong to the same SRLG because they all share the same rs of a condut cut. Therefore, n addton to beng ln dsont, the path protecton problem n optcal transport netors has the extra constrant of beng SRLG dsont. For some specal SRLG confguratons, such as fors and express lns, there exst algorthms th polynomal tme complexty [5][7]. If the confguratons are arbtrary, t has IEEE Communcatons Socety Globecom /04/$ IEEE

2 been recently proved that the problem of fndng to SRLGdsont paths s NP-complete [0][]. In ths paper, e gve an alternatve proof usng SAT reducton. Snce the rsdsont constrant also apples to path protecton n D netors and other path-routed netors, e ntroduce the concepts of Rs ID and Rs Set to extend the NPcompleteness result beyond the scope of fber span falure. The or n [] proposes a heurstc to solve the path protecton problem under the optcal fber duct-layer constrant, hch s a specal case of the SRLG-dsont constrant. The heurstcs n [] and [] use a smple tostep approach. The soluton proposed n [4] selects the orng and protecton lghtpaths for each ncomng connecton request from the predefned alternate paths. In ths or, e develop heurstc algorthms for the case n hch rss are arbtrarly dstrbuted. The heurstcs are adaptve to the real-tme netor status. The rest of the paper s organzed as follos. Secton II gves an alternatve SAT reducton to prove the NPcompleteness of the dynamc path protecton problem under the SRLG-dsont constrant. The result s then extended to D mesh netors and general path-routed netors. In Secton III, e formulate the problem as an ILP and develop heurstc solutons. Secton IV presents computer smulatons results for the heurstc solutons and compares the performance of the heurstcs. Secton V concludes the paper. II. NP-COPLETENESS OF THE DYNAIC LIGHTPATH PROTECTION PROBLE UNDER THE RISK-DISJOINT CONSTRAINT For dedcated protecton, the problem s formally defned as follos. Gven netor G = (N, L), here N s the set of nodes and L s the set of fber lns, and gven the SRLGs on all lns n L, fnd to paths from source node s to destnaton node d such that the to paths are SRLG-dsont and do not share any lns on the paths of exstng connectons. A. Proof of NP-Completeness for Dedcated Protecton e reduce the NP-complete SAT problem [5] to the target problem. The SAT problem s stated as follos. Gven a collecton C = C, C,, C of clauses on a fnte set V = v, v,, v N of varables such that C = for, here clause C s the boolean or of three lterals and s satsfed by a truth assgnment f and only f at least one of the three lterals s true, s there a truth assgnment for V that satsfes all the clauses n C? e construct a graph G for an arbtrary nstance of SAT C, such that the graph contans to SRLG-dsont paths P and P from node s to node d, f and only f there s a truth assgnment satsfyng all clauses. Follong are the steps for the graph constructon:. Create source node s and destnaton node d.. Correspondng to the N varables n V, create N+ nodes z, 0 N. There s a ln from s to z 0 and from z N to d. Beteen z - and z, there are nodes x, y, x, y,, x, y, and, hch correspond to the clauses n C. There are lns z - x, x y, y x, x y,, x y, y z and lns z - x y x, x y z. Lns x y and x y each belongs to a unque SRLG other than SRLG- and SRLG-. All other lns created n ths step belong to SRLG-.. Correspondng to each clause C, create nodes u and,. There s a ln from s to u and from to d. There s also a ln from to u +. Other lns are formed accordng to the follong rules: a. A ln from u to x exsts, and a ln from y to exsts, f and only f varable v s n clause C. s b. A ln from u to x exsts, and a ln from exsts, f and only f varable v s n clause C. All lns constructed n ths step belong to SRLG-. x y x y x y x y x y x y z 0 z z z x y x y x y x y x y x y u u Fgure. A graph constructed from a SAT nstance. y to An example s gven n Fg. In ths example, e construct graph G for a SAT nstance C = C, C, V = v, v, v, C = v v v v v, C = v v v v v. The dotted lns belong to SRLG- and the dashed lns belong to SRLG-. Each sold ln belongs to a unque SRLG other than SRLG- and SRLG-. For a truth assgnment v =, v =, v =, the correspondng rs-dsont paths are: p (s-z 0 - z - z - z -d) and p (s -u -x -y - -u -x -y - -d). Lemma : If C s satsfable, then there exst to SRLGdsont paths from node s to node d n graph G. Proof: Let boolean values be assgned to v, v,, v N that satsfy C. The to paths should be routed as follos: P traverses all z nodes for 0 N. Beteen node z - and z, the path s routed va x -y ( ) f and only f v = 0; It s routed va y otherse. P traverses all u, nodes for. Beteen node u and, the path s routed as follos. By constructon, ln u corresponds to clause C hch has three lterals. Each of the lterals corresponds to a path from u to that goes ether through x -y f the lteral s n the form of v, or through y f the lteral s n the negaton form, v. Because C s satsfed, at least one of the three lterals n C must be. Let the varable n that true lteral be v. Then f the lteral s n the form of v, then v =, and route P passes through nodes x, y ; d IEEE Communcatons Socety Globecom /04/$ IEEE

3 f the lteral s n the form of v, then v = 0, and route P passes through nodes y. If more than one lteral s true, then randomly pc one of the true lterals and route P accordngly. Thus, P doesn t traverse any of the nodes u, for, and P doesn t traverse any of the nodes z for 0 N. Furthermore, f P traverses node x, y, then P traverses and vce versa. Therefore P and P each belongs to a dfferent set of SRLGs. Lemma :If there exst to SRLG-dsont paths from s to d n the constructed graph G, then C can be satsfed. Proof:. Snce there are only to lns orgnatng from the source node s, the to lns must each belong to a separate path. Let sz 0 be part of P and su be part of P.. Snce P already belongs to SRLG-, P must not traverse any of the nodes u, for, otherse t ould also belong to SRLG- and volate the SRLG dsont constrant. Therefore, f P traverses x for N, then t must also traverse y, x, y,, x, y, z. Smlarly f P traverses x for N, then t must also traverse, z.. Snce P already belongs to SRLG-, P must not traverse any of the nodes z for 0 N, otherse t ould also belong to SRLG- and volate the SRLG dsont constrant. Furthermore, f P traverses node u ( ) and x ( N), t must also traverse y and then bac to. Smlarly, f P traverses node u and t must also traverse y and then bac to. 4. Loops are not alloed. Therefore once P reaches ( ), t must go to u + f <, or to d f =. 5. If P traverses nodes x, y,, N, t must not also traverse nodes x and, and vce versa; otherse P s bloced and cannot reach the destnaton node d thout volatng the ln dsont constrant. 6. If P traverses nodes x, y,, N, then P must traverses nodes traverses x for N, then t must also traverse,, y. Smlarly f P traverses nodes x then P must traverses nodes x, y, x, y,, x, y,, x, y. 7. Assgn values to v, v,, v N as follos: If P traverses nodes x, y,, N, then assgn v =, mang clause C to be true. If P traverses nodes, N, then assgn v = 0, mang clause C to be true. Varables that are not assgned a value n the frst to steps are randomly assgned ether or 0. Ths assgnment satsfes C. Combnng Lemma and Lemma, e see that the SAT problem s reducble to the problem of fndng SRLG-dsont paths. Therefore ths problem s NP-complete. B. Proof of NP-Completeness for Shared Protecton th shared protecton, one or more protecton paths may traverse a common fber ln. If the problem th shared protecton s solvable, then the problem th dedcated protecton can also be solved snce t s a specal case of that th shared protecton. C. Dynamc Path Protecton n D esh Netors and General Path-Routed Netors In D mesh netors, a sngle rs factor may cause multple lghtpaths to fal smultaneously n stuatons such as the case n hch portons of several lghtpaths are on the same fber ln hen the ln s cut. Therefore the rsdsont constrant s applcable and the NP-completeness perssts. Ths s true for PLS netors as ell. To expand the concept of SRLG to the general path-routed netors, e propose the follong concepts: Rs ID: For each rs factor that may cause a falure n a netor, e assgn a unque nteger number called the Rs ID. Rs Set: The collecton of Rs IDs of the lns on a path s called the Rs Set of that path. The Rs Set represents all the factors that may cause a path to fal. The rsdsont constrant requres that a orng path and ts protecton path contan no common Rs Ids n ther Rs Sets. The concepts of Rs ID and Rs Set are a generalzaton of SRLG. No the dynamc path protecton problem under the rs-dsont constrant n a general path-routed netor can be defned as follos. Gven netor G = (N, L), here N s the set of nodes and L s the set of lns, and gven the Rs IDs of each ln, fnd to rs-dsont paths from source node s to destnaton node d. The proof n Secton II.A and Secton II.B can be easly generalzed to prove the NP-completeness of ths problem. III. ILP FORULATION AND HEURISTIC ALGORITHS A. ILP Formulaton For the ILP formulaton, the obectve s to fnd to rsdsont lghtpaths for a connecton request. An alternatve obectve s to mnmze the total hop count of the to rsdsont lghtpaths. The follong are gven as nputs to the problem. N: number of nodes n the netor. L: collecton of all lns n the netor. : number of free avelengths on ln L. S = s, s,, s,, s T : collecton of all Rs IDs n the netor. T s the number of Rs IDs n the netor. r : f ln has Rs ID s ; 0 otherse. s, d: source node and destnaton node. The ILP solves for the follong varables. α : f avelength on ln s taen by the orng lghtpath from source s to destnaton d; 0 otherse. IEEE Communcatons Socety Globecom /04/$ IEEE

4 β : f avelength on ln s taen by the protecton lghtpath from source s to destnaton d; 0 otherse. Obectve: Fnd a orng lghtpath and a protecton lghtpath that satsfy the rs-dsont constrant. L α + L β > 0 () Constrants: Flo-conservaton thout the avelength contnuty constrant: N l N l, f l = d αl α = l -, f l = s = N l = β l - = N l - = Ln-dsont constrant: α + Rs-dsont constrant: r B. Heurstc Algorthms α + r 0, otherse l N (), f l = d β = -, f l = s l 0, otherse l N () β,, N (4) mn mn β, mn T, L, mn L (5) e dscussed the smple to-step heurstc n Secton I. Ths soluton may fal n the trap topologes because the frst shortest path s obtaned thout consderng the dsont path beng routed next. e develop the Jont-Search To- Step Algorthm (JSTSA) to overcome ths problem by usng Suurballe s algorthm to ontly route both paths. As the frst step of ths algorthm, e ncrease the cost of those lns th hgh-occurrng Rs IDs; hence those lns are avoded henever possble, hch maes t more lely to fnd rsdsont paths. In order to further reduce blocng probablty, e also ncrease the cost of the lns th hgh traffc load so that traffc load s better balanced across all lns. The remanng steps are ncluded n the pseudo code n Fg. and Fg.. Compared to the smple to-step heurstc and other exstng heurstc solutons, the Jont-Search To-Step Algorthm s superor not only because t may fnd to dsont paths n topologes here the smple to-step algorthm fals, but also because t s fully adaptve to netor status and ors on netors th arbtrary rs dstrbuton. If every Rs ID occurs only once n the netor, ths algorthm s equvalent to Suurballe s algorthm. It also has the same order of tme complexty as Suurballe s algorthm. e can further mprove the performance of the Jont- Search To-Step Algorthm th shared protecton [6]. th shared protecton, a netor can accommodate more connectons, and the blocng probablty s reduced. fnd_protecton_path(orng path p ) remove the netor lns along p ; remove the netor lns used by other orng paths; remove the lns that have common Rs IDs th p ; run Dstra s algorthm(s, d). If Succeeds, return path p p. Otherse return FAILURE; Fgure. Subroutne fnd_protecton_path() for (all netor lns) for (all Rs ID r that occurs more than once n the netor) ncrease cost c l on ln l f l contans r; Adust ln cost based on ts traffc load; f ( run Suurballe s algorthm(s, d) and fnd to routes r and r ) r p = fnd_protecton_path(r ); r p = fnd_protecton_path(r ); compare the total cost of the to path pars,.e., (r, r p ) and (r, r p ), and choose the one th smaller total cost; else return(failure); Fgure. Jont-Search To-Step Algorthm (JSTSA) IV. SIULATIONS Computer smulatons ere conducted to evaluate the performance of the algorthms proposed n Secton III. e use the 6-node, 5-ln NSFNET bacbone topology (Fg. 4) for the smulatons. Other netor topologes are also used and yeld smlar results. The cost of every ln s assumed to be, and the capacty on each ln s 8 unts. Every node has full avelength converson capablty. A orng lghtpath and a protecton lghtpath each tae one unt of capacty. Connecton requests arrve accordng to a Posson process, and holdng tmes are exponentally dstrbuted. The prmary performance metrc s the blocng probablty. Snce an optmal soluton s nfeasble due to the NPcompleteness of the problem, e run Suurballe s algorthm thout the rs-dsont constrant and use the resultng blocng probabltes as a loer bound. Note that the dsont lghtpaths obtaned from Suurballe s algorthm may not be rs dsont. The results are obtaned th confdence level beteen 90% to 95% and confdence nterval around 5%. The results are depcted n Fg. 5. The smulaton results sho that, frst of all, shared protecton sgnfcantly mproves the blocng probabltes, regardless of the traffc load. Secondly, hen the traffc load s lo, the Jont-Search To-Step Algorthm s sgnfcantly better than the smple to-step algorthm. As the traffc load ncreases, the blocng probabltes of the to algorthms converge. The performance of the Jont-Search To-Step Algorthm stems from ts ncorporaton of Suurballe s IEEE Communcatons Socety Globecom /04/$ IEEE

5 algorthm and the mnmzaton of the total cost of the orng lghtpath and ts protecton lghtpath..00e-0.00e-0.00e-04.00e-05.00e-06.00e-07.00e-08.00e-09 Blocng Probabltes Fgure 4. 6-node NSFNET bacbone netor. The numbers ndcate Rs IDs. Traffc Load (Erlang) JSTSA th Shared Protecton 7 7 Suurballe's Algorthm JSTSA Smple To-Step Algorthm Fgure 5. Blocng probablty versus load under lo traffc load. The blocng probabltes of the smple tostep algorthm and the JSTSA converge at hgher load. V. CONCLUSION In ths paper e frst consdered the problem of dynamc path protecton n optcal transport netors under the SRLGdsont constrant. e proved that the problem s NPcomplete. The problem as then generalzed to D mesh netors and general path-routed netors th the ntroducton of to ne concepts - Rs ID and Rs Set. To solve the NP-complete problem, e developed an ILP formulaton and heurstc algorthms. e conducted computer smulatons to evaluate the heurstc algorthms and compared ther blocng probabltes under varous traffc loads. The smulaton reveals that, the Jont-Search To-Step Algorthm s superor to the smple to-step algorthm. The smulatons also confrm that shared protecton sgnfcantly mproves blocng probablty over dedcated protecton. One possble area of future or ould be to further mprove the performance of the Jont-Search To-Step Algorthm. The algorthm currently adusts the ln costs based on the occurrences the Rs IDs of the netor lns. e may nclude other factors to mae the adustment more ntellgent. Another area of mprovement mght be usng traffc groomng on the orng lghtpaths and protecton lghtpaths to reduce netor complexty and cost. 8 9 REFERENCES [] B. uheree, Optcal Communcaton Netors. Ne Yor: cgra Hll, 997. [] R. Ramasam and K. N. Svaraan, Optcal Netors: A Practcal Perspectve. San Francsco, organ Kaufmann, 998. [] O. Gerstel, Opportuntes for optcal protecton and restoraton, OFC, Techncal Dgest, pp , February 998. [4] T. u, Fber Netor Survvablty. A: Artech House, 99. [5] S. Ramamurthy and B. uheree, Survvable D mesh netors, part I protecton, Proceedngs, IEEE INFOCO, vol., pp , arch 999. [6] A. Fumagall, et al. Survvable netors based on optmal routng and D self-healng rngs, Proceedngs, IEEE INFOCO, vol., pp. 76-7, arch 999. [7] S. Ramamurthy and B. uheree, Survvable D mesh netors, part II restoraton, Proceedngs, IEEE ICC, vol., pp. 0-00, June 999. [8] R. R. Irascho and. D. Grover, A hghly effcent pathrestoraton protocol for management of optcal netor transport ntegrty, IEEE Journal on Selected Areas n Communcatons, vol. 8, no. 5, pp , ay 000. [9] R.. Karp, On the computatonal complexty of combnatoral problems, Netors, vol. 5, pp , 975. [0] [] Andrea Dacomo, et al. Desgn of statc reslent D mesh netors th multple heurstc crtera, Proceedngs, IEEE INFOCO, vol., June 00. [] Hu Zang, et al., Path-protecton routng and avelength assgnment (RA) n D mesh netors under duct-layer constrants, IEEE/AC Transacton on Netorng, vol., no., Aprl 00. [] R. A. Barry and P. A. Humblet, odels of blocng probablty n all-optcal netors th and thout avelength changers, IEEE Journal on Selected Areas n Communcatons, vol. 4, no. 5, pp , June 996. [4] S. Subramanam, et al. All-optcal netor th sparse avelength converson, IEEE/AC Transactons on Netorng, vol. 4, no. 4, pp , August 996. [5] G. Z. L, et al., Fber span falure protecton n mesh optcal netors, Proceedngs, SPIE OptComm 00, vol. SPIE [6] J.. Suurballe and R. E. Taran, A quc method for fndng shortest pars of dsont paths, Netors, vol. 4, pp. 5-6, 984. [7] Remesh Bhandar, Survvable Netors Algorthms for Dverse Routng. Kluer Academc Publshers. [8] J. Strand, Issues for routng n the optcal layers, IEEE Communcaton agazne, vol. 9, no., pp. 8-87, February 00. [9] P. Sebos, et al. Auto-dscovery of shared rs ln groups, Proceedngs, OFC, vol., pp. DD- - DD-, 00. [0] G Ellnas, et al., Routng and restoraton archtectures n mesh optcal netors, Optcal Netors agazne, vol. 4, January/February 00. [] J. Hu, Dverse routng n optcal mesh netors, IEEE Transactons on Communcatons, vol. 5, no., arch 00 [] S. Yuan and J. P. Jue, Shared protecton routng algorthm for optcal netor, Optcal Netor agazne, vol., no., pp. - 9, ay/june 00. [] E O, et al. A dsont path selecton scheme th shared rs ln groups n GPLS netors, IEEE Communcaton Letters, vol. 6, no. 9, September 00. [4] V. Anand and C. Qao, Dynamc establshment of protecton paths n D netors. Part I, Proceedngs, 9th Intl. Conference on Computer Communcatons and Netors, pp , October 000. [5]. R. Garey and D. S. Johnson, Computers and ntractablty: A gude to the theory of NP-Completeness. Ne Yor:. H. Freeman Company, 979. [6] S. Yuan and J. P. Jue, Dynamc path protecton n D mesh netors under avelength-contnuty and rs-dsont constrants, Techncal Report, no. UTDCS-6-04, Unversty of Texas at Dallas. IEEE Communcatons Socety Globecom /04/$ IEEE