Path-Based Protection for Surviving Double-Link Failures in Mesh-Restorable Optical Networks

Transcription

1 Path-Based Protection for Surviving Doube-Link Faiures in Mesh-Restorabe Optica Networks Wensheng He and Arun K. Somani Dependabe Computing and Networking Laboratory Department of Eectrica and Computer Engineering Iowa State University Ames, Iowa Emai: Abstract we consider path-based protection methods for twoink faiures in mesh optica networks. Two ink-disjoint backup paths are pre-computed for each source and destination node pair. We identify the scenarios where the backup paths can share their waveengths without vioating 100% restoration guarantee (backup mutipexing). We use integer programming to optimize the tota capacity requirement for both dedicatedand shared-path protection schemes. Our resuts indicate that backup mutipexing significanty improves the efficiency of tota capacity utiization. For the randomy generated demand sets, the shared-path scheme provides up to 37.5% saving in tota capacity utiization over dedicated-path scheme. Backup mutipexing provides more saving for the demand set that has connection requests distributed more eveny. For the doube ink faiure recovery methods, path-based methods are more efficient in capacity utiization than ink-based methods. Dedicated-path scheme performs better than shared-ink scheme in tota capacity utiization on average. I. INTRODUCTION A-optica networks empoying dense waveength division mutipexing (DWDM) have fundamentay changed the economics of transport networking, as they can effectivey satisfy the growing demand for bandwidth. A WDM optica network consists of a set of waveength cross-connects interconnected by point-to-point fiber inks. A waveength-seective crossconnect (WSXC) is capabe of opticay switching an optica signa from an incoming fiber to an outgoing fiber on the same waveength. Unike a WSXC, a waveength-interchange cross-connect (WISC) is capabe of changing the waveength of an incoming signa by using waveength converters. In the absence of converters, the same waveength has to be assigned on a inks aong the route. In this work, we assume that there is no waveength transation in the network. WDM networks are prone to component faiures, and the faiures woud cause catastrophic effects due to the high voume of traffic. The protection methods for surviving ink faiures in mesh-based networks can be cassified by their route computation and execution mechanisms as centraized or distributed, by their re-routing as path- or ink-based, by their computation timing as pre-computed or rea time, and by their capacity sharing as dedicated or shared [1][2][3]. There has been some research in surviving two-ink faiures. The probem of spare-channe design schemes for a sef-heaing network in the case of doube ink faiures was soved using inear programming method in [4]. In [5], the two-ink faiures restorabiity of mesh networks designed to fuy restore any singe ink faiure was studied by experimenta computationa approach. Three ink-based protection methods were presented in [6]. In [7], three different modes were deveoped to address the design of the networks for surviving dua faiures. In our previous study[8], backup mutipexing technique was deveoped for ink-based protection methods in the case of doube-ink faiures. The tota capacity for providing 100% protection was optimized. In this work, we present a pathbased doube-ink faiure recovery mode. We first show that sharing backup resources among backup paths is possibe, and then deveop the rues to identify the scenarios when the sharing of backup capacity wi not vioate 100% restoration guarantee. We formuate the optimization of the tota capacity utiization as an Integer Linear Programming (ILP) probem. Our resuts demonstrate the significant saving in tota capacity by empoying backup mutipexing technique. II. DOUBLE-LINK FAILURE RECOVERY MODEL AND BACKUP MULTIPLEXING A. Doube-Link Faiure Recovery Mode We consider a centraized recovery mode with 100% restoration guarantee against any arbitrary two-ink faiures. The network is represented by a directed graph. For the graph to remain connected when two edges fai, the graph must be 3-connected. We assume this is the case. To provide 100% protection against any two-ink faiures, two inkdisjoint backup paths must be provided for each s-d pair. We assume that both inks fai simutaneousy (the mode aso works for the scenario when the second ink fais during the physica repair of first faied ink). We assume that each path, primary or backup, aways accommodates an OAM (operation, administration, and maintenance) channe terminated at the same s-d pair as the path. When a primary path fais, an aarm indication signa is generated by the node that detects the ink faiure and is transferred over OAM channe. When the source receives the aarm signa in its OAM channe, it prepares to set up the first backup path. The first backup path may aso fai due to another ink faiure. Therefore, run time search is needed. Run time search aso detects if the backup capacity on the first backup path is not avaiabe due to the sharing, in the case of shared-path scheme (detaied in the foowing). If the source detects the above scenarios using run time search, it wi prepare to set up the second backup path; otherwise, it wi use the first backup path to reroute the traffic on the primary. The backup paths may or may not use the same waveength as the primary path.

2 B. Backup Mutipexing Reserving dedicated capacity on two backup paths for every primary path, however, coud reserve excessive capacity in some situations. Fig.1 depicts an exampe to iustrate this probem. Suppose paths and are 2 Fig A 5-node 8-ink network two primary paths p and r. 1 2 and are two backup paths for p, denoted as b p1, b p and are two backup paths for r, denoted as b r1, b r2. The ony faiure scenario that coud cause two primary paths to go down simutaneousy is when one of inks on p, and one of the inks on r fai at the same time. b p1 and b r1 can be used to reroute the working traffic on p and r, respectivey. Thus b p2 and b r2 wi not be used at the same time for a possibe two-ink faiures, therefore they can share backup capacity for primary p and r on ink (4,2). On the other hand, backup capacity sharing is not aways aowed if we want to provide 100% restoration guarantee against any two-ink fais. Suppose the other two primary paths p and r are and 4 5 1, respectivey. The two backup paths for p are, b p1 : 2 1, and b p2 : The two backup paths for r are, b r1 : 4 2 1, b r2 : Since p and b r2 have shared inks, and so do r and b p2, the faiure of one ink on p coud cause b r2 to fai, and the faiure of one ink on r coud cause b p2 to fai. If the above scenario occurs, b p1 and b r1 wi be used to reroute the primary traffic on p and r, respectivey. Therefore they must not share backup capacity even if they have common ink (2,1). Now we summarize the backup mutipexing rues. 1) Primary p and r are ink-disjoint: Tabe I case 1-6 summarize the topoogy reationships and backup capacity sharing constraint. The foowing notations and equations are used to express the topoogy reations and backup capacity sharing constraint. 1) p r = φ: primary path p and r are ink-disjoint; otherwise, they have shared ink(s). 2) BC(b pi ): backup capacity reserved on backup path b pi. 3) BC(b pi ) BC(b r ) = φ: backup paths b pi and b r must not share backup capacity on their common ink(s). 2) Primary p and r are not ink-disjoint: In addition to the above constraint, the faiure of the shared ink of p and r wi cause both p and r to go down simutaneousy. The worst-case scenario is that one of the backup paths of p and one of the backup paths of r aso have a common ink and that ink aso fais, causing these two backup paths to fai at the same time. If the above faiure scenario occurs, the other backup paths of p and r wi be used to reroute the primary traffic on p and r, 5 respectivey. Therefore they must not share backup capacity. This scenario is summarized in case 7 of Tabe I. TABLE I THE TOPOLOGY RELATIONSHIPS, FAILURE SCENARIOS AND BACKUP CAPACITY SHARING CONSTRAINT Primary paths Backup-primary, backup-backup Backup capacity topoogy topoogy reationships sharing constraints reationships p r = φ 1. b pi r φ, b r p φ, BC(b pi) BC(b r ) i and {1, 2} = φ 2. b pi r φ, b r p = φ, BC(b pi) BC(b r ) b rm p φ, = φ i,, and m {1, 2}, m 3. b pi r = φ, b pj r φ, BC(b pi) BC(b r ) b r p = φ, b rm p φ, = φ i, j,, and m {1, 2}, i j, m 4. b pi r = φ, b r p = φ, BC(b pj) BC(b r ) b rm p φ, = φ, j = 1 or 2 i,, and m {1, 2}, m 5. b pi r = φ, b r p φ, BC(b pj) BC(b r ) i and {1, 2} = φ, j = 1 or 2 6. b pi r = φ, b r p = φ, BC(b pj) BC(b rm) i and {1, 2} = φ, j = 1 or 2, m = 1 or 2 p r φ In addition to the above BC(b pj) BC(b rm) primary- and backup cases, = φ, j and m there is one backup -backup {1,2}, j i, m reationship we need to consider 7. b pi b r = φ, i, {1, 2} III. PROBLEM FORMULATION In this section, we deveop the ILP formuation to optimize the capacity utiization for both shared- and dedicated-path protection schemes. A. Route Choices for Primary and Backup Paths For the ILP to optimize the capacity utiization, a set of aternate routes for each node pair need to be provided as given information to the ILP. Eigibe routes can be determined by using hop-imit and distance-imit[7]. The number of equations for the ILP grows rapidy as the number of eigibe routes increases, especiay in the case of existence of waveength continuity constraint. In this work, three successive shortest ink-disjoint routes for each node pair are pre-computed and this information is given to ILP. We are working to find the heuristics to reduce the compexity of ILPs caused by using more aternate routes and hope to present them in the future. B. Probem Formuations We assume the foowing information is given: (a) the network topoogy represented as a directed graph G, (b) a demand matrix, and (c) aternate routing tabes at each node. Each of the three aternate routes between a s-d pair is viewed as W (number of waveengths avaiabe on the ink) waveength continuous paths, and therefore, we do not have an expicit constraint for waveength continuity. Our objective is to minimize the tota number of waveengths used on a the inks in the network (for both the primary and backup paths), measured by number of waveength-inks. 1 waveength-ink is a waveength used on a ink. We first define the notations used in ILPs. = 1, 2..., L: Number assigned to each ink

3 = 1, 2..., W : Number assigned to each waveength i, j = 1, 2..., N(N 1): Number assigned to s-d pair K = 3: Number of aternate routes between s-d pair p, r = 1, 2,..., : Number assigned to a path (i, p) : Refers to the pth path for s-d pair i d i : Demand for node pair i δ i,p : It takes a vaue one if (i, p) is chosen as a primary path, zero otherwise (binary variabe) ν j,r : It takes a vaue one if (j, r) is chosen as a restoration path, zero otherwise (binary variabe) ɛ i,p : Link indicator, which takes a vaue one if ink is used in path (i, p), zero otherwise (data) : Waveength indicator, which takes a vaue one if is used by the path (i, p), zero otherwise (data) g, : It takes a vaue one if waveength is used by some restoration routes that traverses ink (binary variabe) s : Number of waveengths used by backup ightpaths, which pass through ink (variabe) w : Number of waveengths used by primary ightpaths, which pass through ink (variabe) I (i,p)(j,r) : It takes a vaue one if paths (i, p) and (j, r) share ink(s), zero otherwise. If i = j, then p q (data) α (i,p)(j,r) : The number of shared inks between paths (i, p) and (j, r) (data) ψ i,p 1) ILP1: Dedicated-Path Protection: Objective: Minimize Subject to w = s = L (w + s ) (1) =1 w + s W 1 L (2) δ i,p = d i 1 i N(N 1) (3) ψ i,p 1 L (4) 1 L (5) + j=1 ν j,r ɛ j,r ψ j,r 1 (6) 1 L, 1 W Demand constraint for node pair i There are two restoration routes for each primary ca. Let x, y, z { 0, 1, 2} and x y z; t, u, v {x,y,z}, t u v: (t+1)w p=tw +1 δ i,p + (u+1)w p=uw +1 δ i,p = (v+1)w r=vw +1 1 i (N 1) ν i,r (7) 2) ILP2: Shared-Path Protection: It has the same objective and constraints (2),(3),(4) and (7) in ILP 1. Equations (8)- (11) are needed to repace equations (5) and (6) to ensure that sharing of backup capacity is aowed. s = W g, 1 L (8) =1 g, (N 1) g, ψ i,p + g, 1 (9) kw 1 L, 1 W ψ i,r (10) ψ i,r (11) For the foowing equations, et m, n {0, 1, 2}; s, s {(m+ 1) mod 3, (m + 2) mod 3}, s s ; t, t {(n + 1) mod 3, (n + 2) mod 3}, t t. X i,m = ν i,mw + i,mw + ψ (12) Constraint for backup mutipexing rues 1, 2 and 3 in Section II-B: if I (i,s)(j,n) = 1, I (i,m)(j,t) = 1 and I (i,s )(j,t ) = 1, then X i,s 1 1 i < j N(N 1), 1 W (13) Constraint for backup mutipexing rues 4 and 5 in Section II-B: if I (i,s)(j,n) = 0, I (i,s )(j,n) = 0, I (i,m)(j,t) = 1, I (i,s)(j,t ) = 1 and I (i,s )(j,t ) = 1. α (i,smin)(j,t) = MIN(α (i,s)(j,t ), α (i,s )(j,t )), then X i,smin 1 1 i, j N(N 1), 1 W(14) Constraint for backup mutipexing rue 6 in Section II- B: if I (i,s)(j,n) = 0, I (i,s )(j,n) = 0, I (i,m)(j,t) = 0, I (i,m)(j,t ) = 0, I (i,s)(j,t ) = 1, I (i,s)(j,t) = 1, I (i,s)(j,t ) = 1, I (i,s )(j,t) = 1 and I (i,s )(j,t ) = 1, α (i,smin)(j,tmin) = MIN(α (i,s)(j,t), α (i,s)(j,t ), α (i,s )(j,t), α (i,s )(j,t )), then X i,smin + X j,tmin 1 1 i < j N(N 1), 1 W(15) For foowing constraint, et m, n {0, 1, 2}; s, s {m + 1, m + 2}, s s ; t, t {n + 1, n + 2}, t t. Constraint for rue 7: if I (i,m)(j,n) = 1, I (i,s)(j,t) = 1 and I (i,s )(j,t ) = 1, then X i,s 1 1 i, j N(N 1), 1 W (16) IV. RESULTS AND DISCUSSION We use CPLEX Linear Optimizer to sove the ILPs. We first demonstrate the working of the ILPs using a sma exampe. Then we present the numerica resuts for randomy generated demand matrices on a 11-node network.

4 A. An Iustration Consider the simpe 5-node network of Figure 1 again. Assume that the network has one fiber per ink and 3 waveengths per fiber. Let a node pair (i, j) be numbered sequentiay in the order of i and j, i.e. node pair (1, 2) is numbered 1, node pair (1, 3) is numbered 2, and so on. Assume that each of four node pairs 1 (1,2), 5 (2,1), 13 (4,1), 20 (5,4) have one ightpath request between them. The routes and waveengths of primary and backup ightpaths for the dedicated-path protection (as soved by ILP1), and the shared-path protection (as soved by ILP2) are given in Tabe II. TABLE II THE ROUTES AND WAVELENGTHS OF PRIMARY AND BACKUP PATHS UNDER DEDICATED- AND SHARED-PATH PROTECTION Scheme Node pair Primary ightpath Backup 1 Backup 2 Dedicated 1 (1,2) 3 (1,3,2) 2 (1,5,4,2) 2 5 (2,1) 3 (2,3,1) 1 (2,4,5,1) 3 13 (4,2,1) 1 (4,3,1) 2 (4,5,1) 2 20 (5,4) 3 (5,3,4) 3 (5,1,2,4) 1 Shared 1 (1,3,2) 3 (1,2) 3 (1,5,4,2) 1 5 (2,3,1) 3 (2,1) 3 (2,4,5,1) 3 13 (4,5,1) 2 (4,2,1) 1 (4,3,1) 1 20 (5,3,4) 3 (5,4) 1 (5,1,2,4) 3 In dedicated scheme, each reserved waveength on a backup path is dedicated to a primary path. In contrast, in shared scheme, 3 on inks (5, 1) and (2, 4) is shared by backup paths and on inks (5, 4) is shared by backup paths and on inks (4, 2) is shared by backup paths and on ink (1, 2) is shared by backup paths 1 2 and As stated in section II-B, backup paths 2 1 and can not share backup capacity on their common ink (2, 1) because of backup mutipexing constraint 3 in Tabe I. The routings for the primary paths under dedicated- and shared-path schemes are different, because the routing under the shared-path scheme yieds maximum saving for tota capacity. The shared- and dedicated-path protection schemes use a tota of 19 and 24 waveength-inks for this demand matrix, respectivey. The shared-path protection saves about 21% capacity. In ink-based protection, dedicated- and shared-ink schemes use 28 and 23 waveength-inks, respectivey[8]. B. Resuts on Modified NJ LATA Network We present our soution on a modified NJ LATA network shown in Figure 2. The modifications incude adding inks (1,4) and (4,6), so that the network becomes three connected. We assume the network has one fiber per ink for a optimizations. Three groups of demand sets were generated randomy. Each group consists of 10 sets of demand matrix. We wrote a program to generate each set of demand matrix using the foowing steps. Let T NR denotes the desired tota number of requests, and et MNR denotes the maximum number of requests for any node pair. 1) counter = 0; 2) randomy generate source and destination nodes, and the number of requests for this node pair d i, which is between 1 and MNR; Fig A 11-node 22-ink modified NJ LATA network 3) counter = counter + d i ; 4) if counter < T NR, go to step 2; The T NR for group I, II and III are 40, 60, 100, respectivey. The MNR is 4 for group I, II and III. Assume the number of waveengths per fiber is aways sufficient to obtain the feasibe soution for each scheme. The optimization resuts for group I, II and III are shown in Tabe III, IV and V, respectivey. To study the effect of distribution of connection requests, we generated group IV by setting T NR and MNR to be 60 and 8, respectivey. The optimization resuts for group IV are shown in Tabe VI. In a tabes, we denote waveengthinks by WLS, dedicated-path protection scheme by DPS, and shared-path protection scheme by SPS. TABLE III THE OPTIMIZATION RESULTS FOR REQUEST GROUP I set number Tota WLS WLS Saving Primary Primary of node requests used by used by by SPS by DPS pairs average 27.0 Tabe III shows that for a tota of about 40 requests the shared-path scheme requires between % smaer tota capacity than dedicated-path scheme. For a tota of about 60 connection requests, Tabe IV shows that the shared-path scheme saves between % of the tota capacity. For a tota of about 100 requests, shared-path scheme saves between % of the tota capacity, as shown in Tabe V. We cacuated the capacity used by primary paths for group II, shown in coumns 7 and 8 of Tabe III. Resuts show that the average primary capacity for shared-path scheme is 14% higher than the average primary capacity for the dedicated-path scheme.this is due to the factor that in order to yied more 8 6 4

5 saving by sharing backup capacity, sometimes the shared-path scheme uses a onger primary path than the dedicated-path scheme. TABLE IV THE OPTIMIZATION RESULTS FOR REQUEST GROUP II set number of Tota WLS WLS Saving node pairs requests used by used by average TABLE V THE OPTIMIZATION RESULTS FOR REQUEST GROUP III set number of Tota WLS WLS Saving node pairs requests used by used by average 32.3 TABLE VI THE OPTIMIZATION RESULTS FOR REQUEST GROUP IV request number of Tota WLS WLS Saving set node pairs requests used by used by average 23.0 Among groups I to III, The group III obtains the most average saving and group I gets the east average saving in the tota capacity. This is due to the fact that the number of node pairs in the demand matrix increases from group I to III as T N R increases from group I to III. This eads to more sharing in backup capacity. The group II gets more average saving than group IV, which has same number of T NR, but smaer number of node pairs compared to group II. This suggests that the demand matrix with connection requests distributed more eveny (as in the case in group III) wi have more chances to share backup capacity, thus saves more in tota capacity. We conducted optimization for group I, with both dedicatedand shared-ink methods presented in [8]. The resuts are summarized in Tabe VII (SLS:shared-ink scheme; DLS:dedicated-ink scheme). Comparison between the resuts in Tabe III and Tabe VII shows that the path-based methods are more efficient in the tota capacity utiization than the inkbased methods, and on average, the dedicated-path scheme yieds better performance than share-ink scheme. There are no feasibe soutions for some of the demand matrices in dedicated-ink scheme. It is due to the fact that in the inkbased methods, the backup paths have to use the same waveength as the primary paths and in the dedicated-ink scheme, it is easy for conficts to occur between the two backup paths for the two inks on the same primary path. TABLE VII THE OPTIMIZATION RESULTS FOR REQUEST GROUP I request number of Tota WLS WLS Saving set node pairs requests used by used by SLS DLS infeasibe NA infeasibe NA infeasibe NA infeasibe NA infeasibe NA infeasibe NA infeasibe NA V. CONCLUSION We presented a path-based doube-ink faiure recovery mode, in which two backup paths are provided for each node pair and resources are reserved for each connection. We deveoped the rues for identifying the scenarios when backup paths can share their backup capacity without vioating 100% restoration guarantee. The shared-path scheme provides significant tota capacity saving (up to 37.5%). We aso found that the backup mutipexing provides more saving for the demand sets that distribute the connection requests more eveny. For the doube-ink faiure recovery methods, path-based methods are more efficient in tota capacity utiization than ink-based methods. Dedicated-path scheme performs better than sharedink scheme in tota capacity utiization on average. REFERENCES [1] T.H. Wu, Fiber Network Service Survivabiity, Norwood, MA: Artech House, [2] S. Ramamurthy and B. Mukherjee, Survivabe wdm mesh networks, part i:protection, IEEE INFOCOM, vo. 2, pp , March [3] B.T. Doshi, S. Dravida, P. Harshavardhana, O. Hauser, and Y. Wang optica network design and restoration, Be Labs Technica Journa, pp , January-March [4] H. Sakauchi, Y. Okanoue, and S. Hasegawa, Spare-channe design schemes for sef-heaing networks, IEICE Trans. Comm., Vo. E75-B, no.7, PP , Juy [5] M. Couqueur, and W.D.Grove, Computationa and design studies on the unavaiabiity of mesh-restorabe networks, Proc. IEEE/VDE Design of Reiabe Communication Networks 2000, pp , Apri [6] H. Choi, S. Subramaniam, and H.A. Choi, On doube-ink faiure recovery in wdm optica networks, IEEE INFOCOM, pp , June [7] M. Couqueur and Wayne D. Grove, Mesh-restorabe networks with compete dua faiure restorabiity and with seectivey enhanced duafaiure restorabiity properties, Proc. SPIE vo.4874, pp. 1-12, Juy [8] W. He, M. Sridharan and A. K. Somani, Capacity optimization for toerating doube ink faiures in WDM mesh optica networks, Proc. SPIE vo. 4874, pp , Juy 2002.