p-Cycle Design in Survivable WDM Networks with - Semantic Scholar

p-Cycle Design in Survivable WDM Networks with Shared Risk Link Groups (SRLGs) Chang Liu and Lu Ruan Department of Computer Science Iowa State University, Ames, IA 50011 Email: {liuc, ruan}@cs.iastate.edu Abstract- The p-cycle survivable network design under the single link failure assumption has been studied extensively. Shared risk link group (SRLG) is a concept that better reflects the nature of network failures. An SRLG is a set of llnks that may fail simultaneously because of the common risk they share. The capability of dealing with SRLG failures is essential to network survivability. In this paper, we extend the p-cycle design from the single link failure model to the single SRLG failure model. An integer linear programming (ILP) formulation that minimizes spare capacity requirement is provided. To avoid enumerating all cycles of a network, we also provide an algorithm to generate a basic candidate p-cycle set that guarantees 100% restorability in case of a single SRLG failure given enough spare capacities. Simulation results of optimal p-cycle design under the single SRLG failure model are presented. The spare capacity efficiency performance of the basic candidate p-cycle set is also evaluated. Finally, we give a brief overview of the SRLG failure detection problem and its impact on the restoration speed which is an important consideration of p-cycle design.

Index Terms-Network survivability, p-cycle, shared risk link group (SRLG) I. INTRODUCTION

p-Cycle is a promising approach for survivable design in WDM networks because of its ability to achieve ring-link recovery speed while maintaining the capacity efficiency of a mesh-restorable network [1]. A p-cycle is a pre-configured cycle formed out of the spare capacity in the network, which occupies one unit of spare capacity on each on-cycle span. Like a self-healing ring, a p-cycle provides one restoration path for every on-cycle span; unlike a self-healing ring, a pcycle also provides two restoration paths for every straddling span-a span whose two end nodes are on the cycle but itself is not on the cycle. As shown in Fig. 1, a-b-c-d-a is a p-cycle. For the on-cycle span a - b, the p-cycle provides one restoration path a - d- c - b. For the straddling span a - c, the p-cycle provides two restoration paths: a - b - c and a - d - c. Thus, a p-cycle can protect one unit of working capacity on every on-cycle span and protect two units of working capacity on every straddling span. The problem of finding a set of p-cycles to protect given working capacities such that the total spare capacity cost is minimized under the single failure assumption has received This work is supported in part by the National Science Foundation under award #ANI-0237592.

Fig. 1. A p-cycle example

much study recently. Integer linear programming (ILP) formulation for this optimization problem was provided in [1]. In this approach, a set of candidate p-cycles is precomputed and supplied for the ILP to find the optimal set of p-cycles out of the candidate p-cycles. The ILP will give the optimal solution when the candidate p-cycle set includes all cycles in the network. However, since the number of cycles in a network grows exponentially with the network size, various methods have been proposed to reduce the size of the candidate pcycle set. One method is to limit the maximum length of the candidate p-cycles [I][2]. Another method is to select a certain amount of candidates from all cycles according to the a priori efficiency metric pre-computed for each cycle [3]. While both methods can reduce the number of candidate p-cycles, they still require the enumeration of all cycles in the network. To address this problem, an algorithm called SLA was proposed in [4]. The idea is to generate one p-cycle for each span in the network so that the span is a straddling span of the p-cycle. In [5], three algorithms (SP-Add, Expand, and Grow) were provided to find more efficient candidate p-cycles based on those generated by SLA. In [6], a weighted DFS-based cycle search heuristic was proposed to find a candidate p-cycle set of size 0(m) (m is the number of links in the network) that helps to achieve solutions close to the optimal ones derived from all cycles. To circumvent the inherent hardness of ILP, a heuristic algorithm called CIDA was proposed in [5]. In CIDA, a p-cycle is chosen from candidate p-cycles according to an efficiency score and placed in the network to reduce

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the unprotected working capacity iteratively until all working capacities are protected. Some recent works [7][8][9] explored p-cycle design for dual link failures. In this paper, we consider single-SRLG failure model, which is more general than the widely studied single-link failure model. An SRLG (Shared Risk Link Group) is a set of links that share a common resource whose failure will cause the failure of all links in it [10]. For instance, multiple fiber links laid out in a common conduit in WDM networks can be viewed as an SRLG because the conduit cut will result in the failure of all fibers in it. In general, a network contains a set of SRLGs that can be pre-detennined according to the resource sharing relationship. An example SRLG set for the network in Fig. 1 may be {{ab}, {ac, ad, ae}, {bc, ac}, {cd}, {ad, de}}. If the SRLG {ac, ad, ae} fails, the links ac, ad, and ae all fail. A well-studied protection scheme for the single-SRLG failure model is SRLG-diverse routing, which finds a pair of SRLG-disjoint paths (primary path and backup path) between the source and destination. SRLG-disjoint means that in no way does any single SRLG failure break both the primary and the backup paths simultaneously. The NP-completeness of the SRLG-diverse routing problem as well as an ILP solution are given in [Il]. Heuristic approaches to this problem are proposed in [12][13]. In this paper, we will discuss a new protection strategy for the single-SRLG failure model. That is to apply p-cycle network design onto networks with SRLGs. The rest of the paper is organized as follows. In section II, we study the protection a p-cycle can offer upon an SRLG failure. In section III, we describe the p-cycle design problem and give an ILP formulation that solves it optimally. In section IV, we provide an algorithm for generating a subset of all cycles that can protect any single SRLG failure. In section V, we present some simulation results on two networks and randomly generated SRLG sets and evaluate the efficiency performance of the candidate p-cycle sets generated by our algorithm. In section VI, we briefly discuss how the SRLG failure detection issue affects fast restoration, a notable virtue of the p-cycle design. Finally, a conclusion is given in section

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Fig. 2. Relationship between an SRLG failure and a p-cycle (Solid lines are links in the failed SRLG. Dashed-line ellipses represent p-cycles.)

SRLG failure. Two restoration paths can be provided for links respectively given enough copies of the p-cycle. However, no restoration path can be provided for link x - y since y is not on the p-cycle. In part (b), the p-cycle is broken into a path from s to t after the SRLG failure. One restoration path can be provided for links s - t, u - v, and t- x respectively given enough copies of the p-cycle. The p-cycle provides no restoration path for link y - z because y and z are not on the p-cycle. In part (c), the p-cycle is broken into two segments s ... u and v * t. No restoration path is available for links s - t, u - v, and x - z since their two end nodes are on different segments. However, the p-cycle can supply one restoration path for link x - y since both x and y are on the segment v-- t. To compute the protection a p-cycle can provide for a link upon an SRLG failure, we define a function called CYCLE1INK-SRLG. CYCLE±INKSRLG takes a cycle i, a link j, and an SRLG k as inputs, and retums the number of restoration paths that can be provided for link j by cycle i in case of the failure of SRLG k. The pseudocode of function CYCLELINK-SRLG is given below. s - t, u - v, and t - x

int CYCLELINK.SRLG(cycle i, link j, SRLG k) 1. if j i k then 2. return 0; 1/ The link does not belong to the SRLG and therefore does not fail. 3. if link j's end nodes are not both on cycle i then 4. return 0; // The link cannot be protected by the cycle. VII. 5. Remove links in SRLG k from cycle i. II. p-CYCLE PROTECTION UPON AN SRLG FAILURE 6. If cycle i remains a cycle then In the single link failure model, the protection that can be 7. return 2; provided by a p-cycle for a link depends on their relationship. 8. else l/ Cycle i is broken into one or more segments. Specifically, if the link is on-cycle, then the p-cycle can offer 9. if link j's end nodes are on the same segment then return l; one restoration path in case the link fails; if the link straddles 10. I 1. else the p-cycle, then two restoration paths are provided by the pcycle when the link is broken; otherwise the p-cycle cannot 12. return 0; protect the link. Upon an SRLG failure, all links in this SRLG are gone. To restore such a failure, every failed link must be III. AN ILP FOR OPTIMAL p-CYCLE DESIGN taken care of by some p-cycles. Meanwhile, since multiple links may fail in case of an SRLG failure, if two or more A. Problem Description failed links happen to be on the same p-cycle, then the p-cycle We consider the following p-Cycle design problem: given a is broken, which makes the situation more complicated than network represented by a graph G = (V, L), a set of SRLGs in in the single link failure model. Fig. 2 illustrates the possible G, a set of distinct candidate p-cycles in G, and the working relationships between an SRLG failure and a p-cycle. Part (a) capacity on each link in G, compute a set of p-cycles that shows the case where the p-cycle remains a cycle after the minimizes the total spare capacity cost on all links subject to

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the constraint of 100% restorability in case of a single SRLG SRLG k (i.e., b3k = 1), its working capacity should be protected in case SRLG k fails. And if link j is not affected failure. To guarantee the existence of a solution to this problem, the by SRLG k's failure (i.e., bjk = 0), this constraint can be ignored since the left hand side is 0. This enforces that when following conditions are assumed: . The network is 2-edge-connected so that each link can an SRLG fails, only the links that belong to it fail. Constraints in (3) ensure that when SRLG k fails, all links in k should be protected by at least one cycle. . The failure of any single SRLG does not disconnect the be restored. So the number of copies of cycle i needed for SRLG k's failure is the sum of the number of copies of cycle network. i needed for all links in SRLG k. Constraint (4) is equivalent this for each link in . In case of any single SRLG failure, to ni = maxkER nik. This equation holds because under the SRLG, at least one cycle exist in the candidate p-cycle SRLG failure assumption, the number of copies of cycle single set such that the cycle can provide at least one restoration needed is dominated by the maximum requirement over all i path for it. single SRLG failures. . There is enough capacity on each link in the network. IV. GENERATION OF CANDIDATE CYCLES

B. ILP Formulation Sets: (input) L: The set of all links. P: The set of candidate p-cycles. R: The set of SRLGs. Parameters: (input or pre-computed) wj: The working capacity on link j. c;: The cost of one unit of spare capacity on link j. pij: 1 if link j is on cycle i, 0 otherwise. bJk: 1 if link j is in SRLG k, 0 otherwise. xijk: The number of restoration paths for link j that can be provided by cycle i in case SRLG k fails. This value can take 0, 1, or 2, which is pre-computed by the function

CYCLElINK-SRLG(i, j, k).

Variables: (to be determined) sj: The spare capacity on link j. ni: The number of copies of cycle i needed in the p-cycle design. nik: The number of copies of cycle i needed in case SRLG k fails. nijk: The number of copies of cycle i needed for link j in case SRLG k fails.

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As in the single link failure model, enumerating all cycles of the network is necessary to achieve the optimal p-cycle design. This requirement blows up the complexity of the pcycle design since the number of cycles in a network grows exponentially with the network size. To ease this difficulty, we give an algorithm for generating a small subset of all cycles as the candidate p-cycle set such that a p-cycle design can be found to fully survive any single SRLG failure in the network given enough spare capacities. The algorithm works as follows. For each SRLG, first remove all links in it from the network graph, then for each pair of end nodes of a removed link, find its shortest path as well as two nodedisjoint shortest paths (if exist) in the remaining graph. The shortest path is combined with the removed link to form a cycle that contains the removed link as on-cycle link, and the two node-disjoint shortest paths (if exist) are combined to form a cycle on which the removed link straddles. The distinct cycles generated are collected into the candidate p-cycle set. FINDTBASIC&CYCLES is a function implementing the above algorithm and the pseudocode of it is given below. FINDABASIC-CYCLES(network G, SRLG set R) 1. P = 0; 2. for each SRLG k E R do

(4)

Given a 2-edge-connected network and an SRLG set such Constraints in (1) reflect the relationship between the spare that any single SRLG failure does not disconnect the network, capacities and the result p-cycle design. Specifically, the spare the algorithm can always find a candidate p-cycle set that can capacity on link j will be the total number of p-cycles that provide 100% restorability in case of any single SRLG failure traverse it. Constraints in (2) guarantee that if link j is in given enough spare capacities. The reason is that in case of

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TABLE I

OPTIMALp-CYCLE DESIGN RESULTS Networki 150 r-anc om 307 307

Unifortm [ # candidate

cycles Working Capacity

(a). 11-node, 23-span

96

244

Umor 139 195

Network2 300 ranaom 139 683

Spare Capacity 86 214 139* 477 (I-SRLG set) _ 122 Spare Capacity 302 278 1013 (2-SRLG set) Spare Capacity 133 315 427 1534 (3-SRLG set) 165 Spare Capacity 392 625 2188 (4-SRLG set) *: Stopped before the solver found the optimal solution. MIPGAP < 0.7%.

(b). 14-node, 21-span Fig. 3. Test networks.

any SRLG failure, for each affected link, it is always possible to find a shortest path between the two end nodes of the link Note that a network with single link failure has a I-SRLG because the network is still connected. This guarantees that when an SRLG fails, each link in the SRLG has at least one set. All simulations are run on a Sun Ultra 10 workstation cycle that can provide a restoration path for it . For each link j E L, suppose tj is the number of SRLGs that equipped with a single 440MHz CPU, 256MB RAM, and contains j. Let t = maxjEL tj. Then the number of distinct 4GB virtual memory. CPLEX8. 1 is used as the solver for ILP cycles generated by this algorithm is O(tm) where m is the formulations. number of links in the network. B. Results on Optimal p-Cycle Design V. NUMERIC RESULTS To compute the optimal p-cycle design, for both test netall cycles are used as candidate p-cycles for the ILP. works, A. Settings The minimum spare capacity results under different simulation Two networks shown in Fig. 3 are used for simulations. settings are shown in Table I. It can be seen that when a Networkl is a lI-node 23-link network taken from the website SRLG set has larger SRLGs, the total spare capacity needed of [14] and Network2 is the 14-node 21-link NSFNET. becomes larger since more working capacity are affected by For each network, two groups of demand sets are used. a single SRLG failure. On the other hand, this trend seems One is the uniform demand set that contains one demand to be more dramatic for Network2 than for Networkl. This for each unordered source-destination pair; the other is a set can be explained by two reasons. First, the average working that contains 150 random demands for Networkl and 300 capacity per link in Network2 is higher than that in Networkl, random demands for Network2 respectively. In all demand so the amount of affected working capacity grows faster in sets, each demand requests for one unit of capacity. For each Network2 than in Networkl as the size of SRLGs in the SRLG combination of a test network and a demand set, working set becomes larger. Second, Network2 is a sparser network capacities on the network links are obtained by routing each with fewer cycles compared to Networkl, so spare capacity demand over the shortest path. The cost of each unit of spare efficiency drops more rapidly in Network2 than in Networkl capacity on a link is set to one, i.e., c3 = 1 for all j E L. as the size of SRLGs in the SRLG set becomes larger. In practice, SRLG sets are known a priori. In our simulations, they are randomly generated. To facilitate this, we define C. All Cycles vs. Basic Candidate Cycle Set the tenn "r-SRLG set" where r is a positive integer. An rTo evaluate the spare capacity efficiency of the SRLG set has the property that each SRLG in the set contains basic candidate p-cycle sets generated by algorithm at most r links. For each network, we randomly generate r- FIND-BASICQCYCLES described in section IV, we SRLG sets (2 < r < 4) conforming the following rules for compare the ILP solutions resulted from them to the optimal each SRLG set: solutions derived from all cycles. Table II and III list the * Any single SRLG failure does not disconnect the net- results. The tables show the number of cycles generated work. This is necessary to guarantee a feasible p-cycle for the basic candidate cycle set, the total spare capacity design. required for ILP with all cycles, and the total spare capacity * Each link in the network belongs to at least one SRLG. required for ILP with the basic candidate cycle set for various That is, there is no risk-free link in the network. simulation settings. For ILP with basic candidate cycle set, * Each SRLG is not a subset of another SRLG. Note that we also list the percentage of extra spare capacity required as long as an SRLG failure is restorable, a failure of any over the optimal solution in the parentheses. In algorithm subset of it is also restorable without requiring more spare FINDJBASIC-CYCLES, we used the two-step algorithm to capacities. find two node-disjoint shortest paths for a pair of nodes. That

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TABLE I1 COMPARISON BETWEEN ALL CYCLES AND BASIC CYCLES FOR NETWORK 1

Spare Capacity 1 -SRLG set

(% over opt)

2-SRLG set (% over opt) 3-SRLG set (% over opt) 4-SRLG set (% over opt)

# cycles Uniform demands 150 random demands generated ALL BASIC ALL BASIC by BASIC . _ 27 86 136 214 329 . (58.1%) (53.7%) 39 122 175 302 445 (43.4%) (47.4%) 33 133 188 315 444 . (41.4%) (41.0%) 38 165 251 392 588 . _ (52.1%) .__ (50.0%)

TABLE III COMPARISON BETWEEN ALL CYCLES AND BASIC CYCLES FOR NETWORK2

Spare

# cycles generated by BASIC

Uniform demands 300 random demands ALL BASIC [[ALL BASIC

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Fig. 4. SRLG Failure Detection Problem

in order to figure out which pre-configured p-cycles should be used to restore this link, the end-nodes of this link need 23 183 477 1-SRLG set 683 to know which SRLG has failed. Unless this can be inferred (% over opt) . | (31.7%) ||___ (43.2%) directly from the knowledge of the SRLG set, a signaling if 1013 42 2-SRLG set 278 322 1186 protocol is needed to enable all involved nodes to find out . | (15.8%) || (17.1%) (% over opt) 44 if 1534 3-SRLG set 427 497 1829 which SRLG has failed. For example, in Fig. 4, when SRLG (% over opt) (16.4%) (19.2%) = {ab, ac} fails, node c can detect the failure of link ac g, 4-SRLG set 51 625 755 2188 2644 instantly; however, since ac also belongs to another SRLG 92, (% over opt) (20.8%) _____ (20.8%) c cannot tell whether the failed SRLG is 9g or 92 until it gets more failure information from the network. Developing strategies to cope with this problem so that pis, we find a shortest path first, then remove all intermediate nodes along this path and try to find a shortest path in the cycle design can regain the property of fast restoration as it possesses in single link failure model is beyond the scope of remaining graph. this paper. We will discuss some strategies in another paper As shown in Table II and III, the spare capacity obtained by ILP with basic candidate cycle set is always that is being worked on. greater than the optimal value. This is expected because FINDJBASIC&CYCLES generates a small subset of all cycles. VII. CONCLUSION AND FUTURE WORK We notice that for both test networks, with single link failure (1-SRLG set), the spare capacity over usage is relatively larger In this paper, we extended the p-cycle survivable network than with 2, 3, 4-SRLG sets. In other words, the negative design from the single link failure model to the single SRLG effect of using a small basic candidate cycle set on an r- failure model. An ILP formulation is provided to compute a SRLG set (r > 1) is less than on the single link failure minimum spare capacity p-cycle design for an input network, model. For Network2, the percentage over optimal can even its SRLG set, and its working capacities on the network go below 20%, which can be attributed to the fact that the links such that 100% restorability can be guaranteed in case loss of candidate cycles is not that much compared to that of of any single SRLG failure. To avoid the enumeration of Networkl. From the simulation results, we can see that for all cycles in a network, we proposed an algorithm called a sparser network, the spare capacity performance of using FINDJBASIC-CYCLES to generate a candidate p-cycle set the basic candidate cycle set tends to be closer to the optimal of size O(tm) (m is the number of links in the network and perfornance than for a denser network. t = maxjEL tj where tj is the number of SRLGs to which link j belongs). Such a candidate p-cycle set can accomplish a VI. IMPACT OF SINGLE SRLG FAILURE ON RESTORATION 100% restorable p-cycle design given enough spare canacity. SPEED However, it sacrifices the optimality of the ILP solution due An important feature of p-cycle survivable network de- to the reduced number of candidate cycles. Simulation results sign with the single link failure model is fast restoration. show that this negative effect is less serious in the SRLG When a link failure happens, its end nodes can detect the failure model than in the single link failure model. Also, the failure immediately and start restoration right away using negative effect is less serious in a sparser network than in a the pre-configured p-cycles. But the single SRLG failure denser network. model changes the situation. Upon an SRLG failure, for each We note that the SRLG failure detection issue undermines failed link, although its end nodes can detect this link failure fast restoration, which is a key merit of p-cycle survivable immediately as in the single link failure model, they may not network design with the single link failure model. We are be able to start restoration at that moment. The reason is that currently working on this problem in a follow-up paper. Capacity

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[8] D. A. Schupke, "Multiple failure survivability in WDM networks with pcycles", Proc. ofIEEE International Symposium on Circuits and Systems (ISCAS) 2003, pp. 866-869, May 2003. [9] D. A. Schupke, W. D. Grover, and M. Clouqueur, "Strategies for Enhanced Dual Failure Restorability with Static or Reconfi gurable p-Cycle Networks", Proc. of IEEE ICC 2004, pp. 1628-1633, June 2004. [10] D. Papadimitriou et al., "Inference of shared risk link groups", in Internet Draft, Work in Progress, November 2001. [11] J. Hu, "Diverse routing in optical mesh networks", IEEE Transactions on Communications, vol. 51, pp. 489494, 2003. [12] A. Todimala and B. Ramamurthy, "An iterative heuristic for SRLG diverse routing in WDM mesh networks", Proceedings of IEEE ICCCN 2004, pp. 199-204, October 2004. [13] D. Xu, Y. Xiong, C. Qiao, and G. Li, "Trap avoidance and protection schemes in networks with shared risk link groups", IEEE Journal of Lightwave Technology, vol. 21, no. 11, pp. 2683-2693, November 2003. [14] W. D. Grover, Mesh-based Survivable Networks: Options and Strategies for Optical, MPLS, SONET and ATM Networking, Prentice Hall PTR, Upper Saddle River, New Jersey, 2003.

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