Dynamic Wavelength Routing in WDM Networks under Multiple Signal Quality Constraints

Transcription

1 Dynamc Wavelength Routng n WDM Networks under Multple Sgnal Qualty Constrants Wey Zhang, Guolang Xue, Senor Member, IEEE, Jan Tang, Krshnayan Thulasraman, Fellow, IEEE Abstract Most research works n routng and desgn of optcal networks assume that the optcal medum can carry sgnals wthout any bt error. However, the physcal mparments on the optcal sgnal qualty ntroduced by optcal components, such as erbum-doped fber amplfers (EDFA) and optcal cross connects (OXCs), must be consdered n the routng and desgn problems of WDM networks n practce. In ths paper, we studed the dynamc connecton provsonng problem n WDM networks under multple sgnal qualty constrants. We present a polynomal tme optmal algorthm that fnds an actve path for an ncomng connecton request wth mnmum network resource consumpton. Smulaton results show that our soluton outperforms the prevously best soluton to the problem. Keywords: WDM networks, lghtpath, routng algorthm, OEO modules, path provsonng. INTRODUCTION Fber optcs have replaced copper to be the prmary transmsson medum. Wavelength Dvson Multplexng (WDM) networks effectvely ncrease sngle-lnk bandwdth from Mbps to over 6Gbps, consequently have been consdered as a promsng canddate for the next-generaton backbone network by researchers n the feld. There have been many prevous works on routng and wavelength assgnment (RWA) problem [2], [7], [8]. Most prevous works have nvestgated the problems under the assumpton that the optcal medum s an deal one whch can carry data sgnals wthout any bt error. Under ths assumpton, the effects of transmsson mparments on the sgnal qualty of a connecton do not need to be consdered. However, at the present tme, a wavelength-routed network faces several techncal dffcultes n overcomng the physcal mparments ntroduced by optcal components such as erbum-doped fber amplfers (EDFA) and optcal cross connects (OXCs). Physcal mparments, e.g., power loss, noses, and dspersons, mpose fundamental constrants on the qualty of sgnals n WDM optcal networks [5], [], [4]. Therefore, at the destnaton node, the receved sgnal qualty may be so poor that the bt-error rate (BER) could be too hgh to be acceptable, thereby makng the lghtpath unusable [], [5], [9], []. In [9], the authors analyzed the mpact of transmsson performance n WDM networks under dfferent routng strateges. In [5], the authors consdered the mpact of transmsson mparments on the teletraffc performance n WDM networks. Huang et al. [4] proposed a physcal layer herarchcal RWA Wey Zhang s wth the Department of Computer Scence, North Dakota State Unversty, Fargo, ND 585. Emal: wey.zhang@ndsu.edu. Guolang Xue s wth the Department of Computer Scence and Engneerng, Arzona State Unversty, Tempe, AZ Emal: xue@asu.edu. Jan Tang s wth the Department of Computer Scence, Montana State Unversty, Bozeman, MT Emal: tang@cs.montana.edu. Krshnayan Thulasraman s wth the School of Computer Scence, Unversty of Oklahoma, Norman, OK 739. Emal: thulas@ou.edu. model to evaluate optcal sgnal-to-nose rato (OSNR) and polarzaton mode dsperson (PMD) on a canddate lghtpath, and decde whether to set up the lghtpath on network layer. However, the aforementoned works cannot recover the optcal sgnal n a lghtpath. Wth current technology, only OEO (optcal-electrcal-optcal) converson can solve such a problem [4], [3], [4]. The concept of translucent networks was proposed n [6]. In a translucent WDM mesh network, a small number of OEO modules are placed sparsely. Wth sparse OEO regeneraton, an optcal sgnal can travel as long as possble before ts sgnal qualty falls below a threshold. How to provde lghtpaths wth sparse OEO converson n translucent WDM mesh networks has been studed recently. In [], consderng a sngle sgnal constrant, a new 2-D Djkstra s algorthm was provded to fnd a connecton. In [4], consderng the OSNR constrant, the authors provded several smple heurstcs to fnd paths for connecton requests. We note that both works consdered only one sgnal constrant and both used a smple regeneraton model. They also assumed that there s at most one regenerator on each node, and do not consder the regenerator shareablty ssue [3]. In [2], the authors provded a practcal network model. Wth the consderaton of multple lnear sgnal constrants, the authors proposed several heurstcs to fnd paths for connecton requests. None of the prevous works guarantees a feasble actve path for an ncomng connecton request even when feasble paths exst. In ths paper, we use the sophstcated network model proposed n [2], and propose a novel algorthm whch can fnd workng paths for ncomng requests f feasble paths exst. Moreover, our algorthm can fnd an optmal soluton whch uses the mnmum number of OEO modules. The rest of the paper s organzed as follows. In Secton 2, we ntroduce the transmsson mparments n optcal networks, and descrbe the network model used and the problem we study. Ths s followed by Secton 3 wth a study of the dynamc path provsonng problem. Performance evaluaton of our algorthms s presented n Secton 4. We conclude our work n Secton 5, summarzng our contrbutons. 2. PROBLEM FORMULATION A. Transmsson Imparments n Optcal Networks Two lnear mparments are consdered n ths paper: Amplfer Spontaneous Emsson (ASE) and Polarzaton Mode Dsperson (PMD), whch are regarded as the two key lnear mparments that can be practcally used to constran optcal layer routng []. These two mparments have been extensvely dscussed n many prevous works [4], [6], [], [3]. ) Polarzaton Mode Dsperson: PMD management requres that the tme-average dfferental tme delay between /8/$ IEEE. Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE "GLOBECOM" 28 proceedngs.

2 two orthogonal states of polarzatons, [Δ t ], be less than a fracton α of the bt duraton, T = /B, where B s the bt rate. A typcal value for α s. []. Assume that a transparent segment conssts of M fber spans, where the kth span has length L(k) and fber PMD parameter D PMD (k). The average dfferental delay s expressed as: B M D PMD (k) 2 L(k) α () k= Assume that the length of a fber span s nteger, and all fber spans have the same PMD parameters,.e., D PMD (k) = D PMD, PMD gves the constrant on the length of a lghtpath wth acceptable BER: M α 2 L = L(k) B 2 D 2 = C PMD (2) k= PMD 2) Amplfer Spontaneous Emsson: ASE s the domnant nose n optcal networks, and degrades the sgnal to nose rato. An acceptable optcal SNR level (SNR mn ) whch depends on the bt rate and transmtter-recever technology needs to be mantaned at the recever. The upper bound on M, the maxmum number of spans, s obtaned usng the OSNR constrant n []: M P L n sp(k)(g(k) ) (3) 2hvB k= osnr mn where P L s the average optcal power at the transmtter, G(k) and n sp (k) are the amplfer gan and excess nose factor, respectvely, on the kth span, h = J/Hz s the Planck s constant, v s the carrer frequency, and B o s the optcal bandwdth. Assume the M optcal spans ntroducng the same nose power and that each optcal amplfer has the same power gan G. Then P L M = C 2SNR mn n sp hv(g )B ASE (4) o ASE can be understood as the constrant for the maxmum number of lnks a lghtpath may have. B. Network Model In ths paper, we consder a translucent network, whch s a wavelength-routed mesh network wth the capablty of sparse OEO regeneraton [3]. Such a network conssts of a number of wavelength-routng nodes wth optonal OEO modules and nterconnected by optcal fber lnks. We assume that each lnk has a sngle fber n each drecton, whle each fber has a fxed number of wavelengths that are used to carry data. Each node has a fxed number of add and drop ports, through whch the user data can access the network. The node has nherent regeneraton resources because t provdes the basc regeneraton resource of Tx/Rx pars. 3R (regenerate, reshape and retme) regenerators can be attached between a Tx-Rx par to mplement sgnal regeneraton n the electronc doman. The combnaton of a transmtter, a recever and an electronc 3R regenerator s called an OEO module [3]. Such a node model allows all-optcal swtchng, by WRS swtchng, as well as OEO regeneraton by usng an OEO module on the node. The path from the source node to the destnaton node s dvded nto several segments by OEO regeneratons at ntermedate nodes, whch are named regeneraton nodes. Each segment s defned as a regeneraton segment [3]. C. Problem Statement We study a dynamc WDM routng problem of great nterest to network servce provders. A wavelength on a fber s called as a channel. Terms OEO module and regenerator are used nterchangeably n ths paper. Throughout ths paper, W, m, n denote the number of wavelengths per fber, the number of lnks and the number of nodes of a network, respectvely. Defnton 2.: An r-node s a node wth OEO modules equpped. R-nodes s the set of all r-nodes. Defnton 2.2 (Dynamc Relable WDM Routng Problem): Gven the followng nformaton of a translucent network: ) New connecton requests that arrve dynamcally; 2) The network topology and the number of wavelengths W on each fber; 3) The R-nodes n the network, and the number of OEO modules on each r-node; 4) Current network accommodaton status. In other words, we know whether a channel s free or used. The objectve of the problems s to satsfy each comng connecton request wth an actve path, on whch the sgnal qualty receved at each node must be recognzable. A path whch satsfes the sgnal qualty constrants s a feasble soluton. An optmal soluton to ths problem s a feasble path whch uses the mnmum number of regenerators, and consumes the mnmum number of free wavelengths among all paths that use the mnmum number of regenerators. 3. DYNAMIC RELIABLE WDM ROUTING SCHEME In ths secton, we propose a novel scheme to fnd an optmal soluton to the Dynamc Relable WDM Routng problem f there exsts any feasble path. The request wll be dropped by our scheme f there s no feasble soluton. A. Novel Graph Transformaton PMD and ASE constrants are bounded by C PMD and C ASE, whch are both ntegers. In our algorthms, we use C and C2 to represent C ASE and C PMD, respectvely. ASE u and PMD u denote the ASE and PMD cost on node u for the comng connecton request. ASE(u, v) and PMD(u, v) are the ASE and PMD costs on edge (u, v). Our algorthm uses a novel graph transformaton to combne all nformaton; OEO and channel usage, PMD and ASE cost, nto a sngle auxlary graph. We frst present Algorthm to construct an auxlary graph G aux from the orgnal graph G. In Lne 2 and 3, on each wavelength plane, we splt each node u n G nto W (C+) (C2+) copes n the form u λ (c,c2), where (c,c2) s a possble (ASE, PMD) combnaton. For each node u G, we process t accordng to two cases. CASE : f u s NOT a r-node: From Lne 4 through Lne, for each edge (u, v) n the orgnal graph, a group of edges, from u λ (ASE to vλ u,pmd u) (ASE, are added nto Gaux v,pmd v). Each of these edges means that, gven a path from s to node u wth sgnal costs ASE u and PMD u on node u, f we extend the path by usng (u, v) for the connecton (s, d), then t has sgnal costs ASE v and PMD v when reachng node v, where ASE v =ASE u +ASE(u, v) and PMD v =PMD u +PMD(u, v) because no regeneraton can be appled on node u. The cost of such an edge s, whch s the cost of consumng a new channel /8/$ IEEE. Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE "GLOBECOM" 28 proceedngs.

3 Algorthm Setup Aux Graph(G, G aux, R-nodes) : for (each wavelength ) do 2: From the wavelength graph G λ of G, set up a wavelength graph G aux wth node set 3: Vλ Gaux =V G {,,...,C} {,,...,C2} and edge set Eλ Gaux : 4: for (each node u/ R-nodes) do 5: for (each undrected edge (u, v) n G λ do 6: Add drected edges from u v nto EGaux (ASE u,pmd u) ff: (ASE v,pmd v) 7: ASE v=ase u+ase(u,v) C and PMD v=pmd u+pmd(u,v) C2; 8: Assgn cost to ths edge; 9: end for : end for : for (each node u R-nodes) do 2: f (there s free Tx-Rx par on node u) then 3: Add a drected edge nto E Gaux from vertex u (ASE to vertex u,pmd u u) (,) ; 4: Assgn cost to the edge; 5: end f 6: for (each undrected edge (u, v) n E G ) do 7: Add drected edges from u (ASE u,pmd u) v nto EGaux (ASE v,pmd v) such that: 8: ASE v=ase u+ase(u,v) C and PMD v=pmd u+pmd(u,v) C2; 9: Assgn cost to ths edge; 2: end for 2: end for 22: end for 23: for (each par of wavelengths and λ j) do 24: for (each node u R-nodes) do 25: Connectng u, and uλ j, wth a new edge; 26: Assgn cost to ths edge; 27: end for 28: end for 29: The constructed auxlary graph G aux s composed by node set V Gaux = Vλ Gaux, and edge set E Gaux = W W E Gaux We do not add an edge f ASE v >C ASE or PMD v >C PMD because obvously such an edge s not on any feasble path. CASE 2: f u s a r-node: From Lne through Lne 2, f there s a free Tx-Rx par on node u, t can apply regeneraton. Thus, new edges are added from u λ (ASE to uλ u,pmd u) (,), whch represents that the sgnal s cleared and restored. The cost of such an edge s (>> ), whch means usng a regenerator has cost. Meanwhle, node u can choose not to apply regeneraton, Ths case s handled the same as the case that node u s not a r-node (Lnes 6-2). In the FOR-loop n Lnes 23-28, for each r-node u, we connect u λ, and uλj, for any two wavelength and λ j. Such an edge represents that a wavelength converson, together wth regeneraton, s appled at node u. The cost of such an edge s because we do not allow the wavelength converson n ths work. Let us use an example to llustrate Algorthm. The orgnal network s shown n Fg. (a), whch conssts of 4 nodes and 4 edges. Assume that only node x s a r-node. There are 2 to to wavelengths on each edge, and the costs of ASE and PMD are shown as the edge label for each edge. Both C and C2 are set to be n the example. s (,) (,) x y (,) (2,) d d y y y s s s s x x x x d d d Wavelength plane y y y y y d s s s s x x x x d d d Wavelength plane 2 (a) Network G (b) The constructed auxlary graph G aux Fg.. Novel Graph Transformaton There are 2 wavelength planes n G aux. Intally, all channels are free. We use wavelength plane G λ for llustraton snce the operatons are the same on both planes. For each node n the orgnal network G, t s spltted nto (C+) (C2 +) copes. Each of them represents a possble (ASE, PMD) combnaton on the node. For example, node y means that the ASE cost at node y s, and the PMD cost s. Then we need to add edges nto G aux. Edges from s λ, to xλ, and y λ,, as well as edge (xλ,, dλ, ) are added. The edge (sλ,, x λ, ) mples that by takng edge (s, x) n G from source s, the ASE and PMD wll both be on node x. Each such edge has cost, whch means that we consume one free channel by utlzng ths edge for the connecton. But no other edges can be added because ether bound C or C2 would be volated. For the r-node x, we add edges from x λ (ASE x,pmd x) to xλ (,) wth cost, where M and N are the number of edges and nodes n G aux, respectvely. Usng such an edge represents that a regenerator on node x wll be used wth a large cost, whch mples that we would take all free channels for a connecton f possble rather than use a regenerator. Next,we connect x λ (,) to xλ2 (,) by a -cost edge because wavelength converson s not allowed n our algorthm. The constructed auxlary graph G aux s shown n Fg. (b). B. Optmal Soluton for Actve Path Provsonng After the auxlary graph constructon, Algorthm 2 s presented to fnd an optmal soluton for actve path provsonng. To fnd an actve path for request (s, d), we frst need to have the auxlary graph (Lnes - 3). Then from Lne 4 through Lne, we add some new edges whch are partcularly used for the ncomng request. On each wavelength plane, we have new edges from d λ ASE d,pmd d to d λ C,C2. Such an edge means that f we can fnd a path to node d wth sgnal costs less than threshold, we can reach the destnaton node n G aux, wth no more cost. Moreover, from Lne to Lne d λ C,C2 4, vertcally we connect s λ, to sλ+, and d λ C,C2 to dλ+ C,C2. These edges represent that we can start from source node s at any wavelength plane, and stop at destnaton node d at any wavelength plane too. Once we fnsh addng the new edges, n Lne 5 we use Algorthm 3 to fnd an optmal path for the request from s λ, to dλw (C,C2). Wth the found path AP n Gaux from Algorthm 3, Algorthm 2 can get the path actvep and OEO utlzaton n orgnal graph G (Lnes 6-8), or there s no feasble soluton and the request s dropped n Lne 2. In Lne 8 of Algorthm 2, all edges added for ths specfc request (s, d) wll be removed, and G aux s changed back to ts orgnal verson for future connecton requests /8/$ IEEE. Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE "GLOBECOM" 28 proceedngs.

4 Algorthm 2 Actve Path Provson(G, s, d, R-nodes) : f (auxlary graph G aux has not been constructed) then 2: Setup Aux Graph(G, G aux, R-nodes); 3: end f 4: for (each wavelength ) do 5: for (ASE d =; ASE d < C; ASE d ++) do 6: for (PMD d =; PMD d < C2; PMD d ++) do 7: Add zero-cost edges from node d to d ASE d,pmd C,C2 ; d 8: end for 9: end for : end for : for ( =;< W; ++) do 2: Add a zero-cost edge from node s, to node s+, ; 3: Add a zero-cost edge from node d C,C2 to node d+ C,C2 ; 4: end for 5: QualfedWorkngLP(G, G aux, s λ,, dλ W (C,C2) ); 6: f (an actve path AP s found) then 7: return AP; 8: Change the orgnal G aux back by removng edges added from Lne 4 to Lne 4; 9: else 2: Drop the connecton request (s, d); 2: end f Algorthm 3 QualfedWorkngLP(G, G aux, s λ,, dλw (C,C2) ) : for (each lnk e n G aux ) do 2: f (the channel on e s not free) then 3: remove e from G aux ; 4: end f 5: end for 6: for (each node u R-nodes) do 7: f (u has no more free OEO module) then 8: remove all ncomng edges to node u, and ts all nterlayer edges; 9: end f : end for : Compute the shortest path actvep from source s λ, to destnaton d λ W (C,C2) n auxlary graph Gaux ; 2: f (there does not exst such a path actvep) then 3: block the connecton request; 4: else 5: Return the path AP correspondng to actvep n G as workng path canddate; 6: end f In Algorthm 3, at frst all used channels are removed because actve paths cannot share channels (Lnes -5). Then n the FOR-loop startng from Lne 6, f a r-node u has no more free OEO module, we remove all edges to u λ, because no regeneraton can be appled, and u λ, can not be reached. After updatng the network, n Lne, shortest path algorthm, say Djkstra algorthm, can be used to fnd a shortest path from s λ, to dλw (C,C2) n Gaux. We return the found path as an actve path for the request (Lne 5). Let us use Fg. 2 for llustraton of our approach on the network shown n Fg. (a). Once we have the auxlary graph n Fg. (b), we add some new edges, whch are marked by the dashed edges n Fg. 2. For example, we add an edge from d to d on each wavelength plane, and connect s λ to sλ2. Then, a shortest path actvep ((s λ,xλ,xλ,dλ,dλ2 ))s found from node s λ (,) to node dλ2 (,) n ths graph, whch s marked by the thck red edges n Fg. 2. The path AP n G Fg. 2. y y y y s s s s x x x x d d d d Wavelength plane y y y y s s s s x x x x d d d d Fndng actve path for connecton (s, d). Wavelength plane 2 for ths example s (s, x, d) wth cost +2. We know that one OEO module needs to be utlzed on node x wth cost, and the number of the consumed free channels s two. Theorem 3.: For any connecton request, Algorthm 2 can correctly fnd a connecton n O(W C C2 m) tme f a feasble path exsts. In addton, the connecton uses the mnmum number of regenerators. Among all possble connectons whch use the mnmum number of regenerators, the computed path uses the mnmum number of free wavelengths. PROOF. Followng the constructon of G aux n Algorthm, we observe that G aux has a path actvep from s λ (,) to dλw (C,C2) f and only f there s a correspondng feasble path AP from s to d n graph G. In addton, because n G aux we remove all edges whch would brng the volaton to sgnal constrants, any path must reach a node d λ (pmd,ase) where pmd C and ase C2. Ths proves the correctness of the algorthm. To construct an auxlary graph (Lne 2 of Algorthm 2), each wavelength plane of the auxlary graph has O(n C C2) nodes, and O(C C2 (m+n)) edges. Totally G aux has O(W n C C2) nodes and O(W C C2 (m + n)+w 2 ) edges. In next two FOR-loops (Lne 4-4), we add O(W C C2) more edges. Then Algorthm 3 s called n Lne 5 to fnd a path. In Algorthm 3, frst t takes O(W C C2 m) tme to remove the used edges (Lnes 2-4). Then O(W C C2 n) tme s spent to update the edges ncdent wth the regeneraton nodes. In Lne of Algorthm 3, t takes O(W C C2 (m + n)) tme to fnd a shortest path n the acyclc graph G aux [3]. Fnally we use O(n) tme to fnd the path AP and return. Thus, Lne 5 of Algorthm 2 takes O(W C C2 (m + n)) tme. In total, we can fnd that the tme complexty of Algorthm 2 s O(W C C2 m) because m s larger than n snce the network G s connected. In our approach, the cost of usng a free channel s, and the cost of usng a free OEO module s. Hence for a connecton, we would use as many as free channels nstead of one free OEO module (note that there are at most N free channels can be used on a path). Therefore our algorthm can fnd a soluton wth the mnmum usage of regenerators, and the mnmum consumpton of channels whle usng the mnmum number of OEO modules. 4. PERFORMANCE EVALUATION We mplemented our algorthm of ths paper (denoted by AP-OPT n the fgures), and compared t wth the prevously best heurstc n [2] (denoted by HW-SPF+Trace-back n the fgures). A well-known network s used to study the routng capablty of the algorthms. Thus, connecton blockng probablty s the man performance crtera. Dfferent numbers of wavelengths (W ) on each fber and dfferent numbers of r-nodes are tested. For each test case, we generated dfferent /8/$ IEEE. Ths full text paper was peer revewed at the drecton of IEEE Communcatons Socety subject matter experts for publcaton n the IEEE "GLOBECOM" 28 proceedngs.

5 random connecton requests. A connecton request s generated at each tme unt wth random source and destnaton, and has a lfe tme whch s set to a random nteger unformly dstrbuted n [,]. The network used for our tests s the Pacfc Bell network (5 nodes and 2 lnks), shown n Fg. 3. Each lnk s labeled by ts length n klometers. The system parameters are set to typcal values as n [] Fg. 3. The 5-node/2-lnk Pacfc Bell network. When a connecton request arrves, we use both algorthms to compute a path. If we can fnd a feasble path, we reserve the correspondng network resources, ncludng regenerators and free channels. Otherwse the connecton request s dropped. Once a connecton s expred, all resources used by t are released. Our numercal results are presented n Fg. 4, where each fgure shows the average of runs. It s worth notng that we have also tested both algorthms on some randomly generated network topologes. The results are smlar. Therefore we only present the results for Pacfc Bell Network here due to the page lmt. In Fg. 4(a) and 4(b), we compared Blockng probablty (%) HW SPF,W=8,R node=25% AP OPT,W=8,R node=25% HW SPF,W=6,R node=25% AP OPT,W=6,R node=25% Number of connecton requests Blockng probablty (%) HW SPF,W=8,R node=33% AP OPT,W=8,R node=33% HW SPF,W=6,R node=33% AP OPT,W=6,R node=33% Number of connecton requests (a) Wth 25% r-nodes (b) Wth 33% r-nodes Fg. 4. Performance comparsons between AP-OPT and HW-SPF the routng capablty between two algorthms wth randomly generated r-nodes whch consttutes 25% and 33% of all nodes, respectvely. On each r-node, as n [3], the number of OEO modules s assumed the same as the number of wavelengths on a fber. 4 to connectons were generated and njected nto the network one by one. We can observe that AP-OPT has notceable lower blockng probablty than HW- SPF+trace-back heurstc for all scenaros. For example, wth the settng of W=6, R-nodes consttutng 25% of all nodes, and the number of connecton requests beng 7, AP-OPT acheved the blockng probablty of 2%. Note that a blockng probablty obtaned by HW-SPF+Trace-back heurstc s about 22%. Another nterestng observaton s that the number of r-nodes has more sgnfcant effect than the number of wavelengths per fber at reducng the blockng probablty. For example, gven 33% R-nodes and W=8, HW-SPF+Traceback has better performance than t has wth more wavelength (W =6) but less R-nodes (25%). Smlar property can also be observed from the results of our algorthm. In Fg. 5, we compare the consumptons of OEO modules and free channels between two algorthms, whch s represented by the y-axle. And x-axle represents the rato of the number of r-nodes n the network. Dynamc connecton requests are kept beng nserted nto the network untl both algorthms accommodated Fg Wavelength and OEO consumpton Wavelength by HW SPF Wavelength by AP OPT OEO by HW SPF OEO by AP OPT r node rato (%) Network resource consumpton wth satsfed connectons connectons. From the Fg. 5, t shows that AP-OPT uses less number of OEO modules and free channels than HW- SPF+Trace-back does n all testng cases. Ths confrms our analyss at the end of Secton CONCLUSIONS In ths paper we consdered the dynamc relable routng problem n WDM networks under multple sgnal qualty constrants. We proposed a novel algorthm that can return a lghtpath for a connecton request f one exsts. The connecton uses the mnmum number of OEO regenerators. Also the computed path consumes the mnmum number of free wavelengths, among all connectons whch use the mnmum number of regenerators. Smulaton results demonstrated that our algorthm outperforms the prevously best heurstc n [2]. REFERENCES [] I. Cerutt, A. 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