Determine: route for each connection and protect them if necessary to minimize total network cost (say wavelength-links).

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1 Service Provisioning to Provide Per-Connection-Based Availability Guarantee in WDM Mesh Networks Jing Zhang, Keyao Zhu, Hui Zang, and Biswanath Mukherjee Abstract We present availability analysis for WDM-mesh-network protection schemes. We propose cost-effective provisioning approaches to provide differentiated per-connection-based services to carry connections by appropriate routes and to protect them according to their availability requirements. 1. Introduction Protection schemes for WDM mesh networks (dedicated-path, shared-path, etc.) are typically based on the single-failure scenario. When fiber-cut rate and network maintenance frequency are high, the network operator needs novel methods to handle multiple, near-simultaneous failures where different network components (including fiber spans) may have different failure rates. Service reliability determines (a) whether protection is needed, and (b) its effectiveness. In a wavelength-routed optical network, service reliability is represented by connection availability, which is the probability that the connection will be in operating state at a random time in future [1,2]. Connection availability is defined in Service-Level Agreement (SLA) along with revenue and penalty. How to provision customers' requests to satisfy their availability requirements so as to avoid penalty and minimize cost is a major concern to a service provider. We propose a new provisioning framework to provide availability-guaranteed service to each traffic demand. The framework contains two parts: (a) WDM mesh network service-availability analysis; and (b) connection-provisioning approaches based on the analysis. Using our approaches, each connection is routed and protected (if necessary) according to its SLA and network component failure characteristics. 2. Connection Availability Analysis in WDM Mesh Networks Availability of a system (network component, path, connection, etc.) is the fraction of time the system is "up" during its entire service time. It can be computed as follows: Network component: Availability of a network component is calculated based on the component's failure rate and average time to fix a failure. Path: Availability of path i can be computed as multiplication of availabilities of network components along path i since path i is available only when all network components along path i are available. Connection: If connection t is carried by a single path, its availability (A t ) is equal to the path availability. If t is dedicated-path protected, A t is shown in Eqn. (1) (where A p and A b denote availabilities of primary (p) and backup (b) paths, respectively) since t is "down" only when both p and b are unavailable. If t is sharedpath protected, let S p denote a set that contains all primary paths (except p) whose backup paths are sharing some resources with b; n is size of S p ; p i is probability that exactly i primary paths in S p are unavailable; and δ i is probability that p can get backup resource when both p and other i primary paths in S p failed. A t can be computed by Eqn. (2) since t will be available if p is available; or p is unavailable, b is available, and failure on p happens before failures to other primary paths in S p. We assume p and all other primary paths in S p fail independently; hence, δ i = 1/(i+1). (Note that two primary paths in S p might traverse the same fiber link so their path failures may not be independent. In this case, 1/(i+1) δ i 1/2 when i 1. δ i = 1/(i+1) will give the lower bound of A t.) A t = 1 - (1 - A p ) (1 - A b ) = A p + (1 A p ) A b (1) A t = A p + Σ i=0,n δ i (1 - A p ) A b p i (2) 3. Proposed Provisioning Approaches

2 3.1 General Problem Statement Given: physical network topology, availability for each link, number of free wavelengths on each link, and set of connection requests (source, destination, and availability requirement). Determine: route for each connection and protect them if necessary to minimize total network cost (say wavelength-links). 3.2 ILP-Based Approaches Suppose path p traverses links l 1, l 2,..., l n. Then, p is a reliable path for connection t only if: A p = A 1 A 2... A n A ' t (3) where A i is availability of link l i, and A ' t is availability requirement of connection t. Computing logarithm of both sides, noting that availabilities are between 0 and 1, and multiplying both sides by -1, we get: -loga p = -loga 1 - loga loga n -loga ' t (4) Now, if cost of link l i (C i ) is defined as a function of its availability (i.e., C i = - loga i ), the cost is additive and the path with minimum cost will be the path with maximum availability (such a path is called mostreliable path (MRP)). This Multiplication-to-Summation (MS) technique can be used to compute the MRP. If availability of a MRP is lower than A ' t, then protection is needed for connection t. Therefore, we classify connections into two groups: one-path-satisfiable connections (T 1 ), whose availability can be satisfied without any backup path, and protection-sensitive connections (T 2 ), otherwise. Our MS technique enables us to formulate the problem of provisioning connections in T 1 into an integer linear program (ILP) since (nonlinear) multiplication is converted into (linear) summation. For connections in T 2, due to nonlinearity of availability calculation for dedicated-path protection (Eqn. (1)), the problem is nonlinear; hence, we develop two approximation approaches [3]. 3.3 Heuristic Approaches We investigate several heuristics for instances where the ILP may have difficulty due to large network size and high volume of connection requests. Fixed-alternate routing is used, i.e., for each node pair, K candidate routes or link-disjoint route-pairs are pre-computed, and availability of each route is calculated. Therefore, a request t = <s, d> can pick routes (or route-pairs) which satisfy its requirement from K candidate routes from s to d. Let S t denote a set containing all routes (or route-pairs) that can satisfy availability requirement of request t. R best (RP best ) denotes route (route-pair) with highest availability in S t. Each request t can select its route using following approaches: Randomly pick one request t, and randomly pick one route (or route-pair) r from S t. Use r to carry t if replacing current route of t by r could reduce total cost (wavelength-links) without introducing additional wavelengths into the network, or Iteratively-select could reduce wavelength channels needed; otherwise, keep current route. Repeat above steps until no route replacement happens in a large number of continuous iterations (10 5 in our numerical simulations). Most-reliable Use R best for request t if there is a R best in S t ; use RP best otherwise. Just-above-threshold Route (or route-pairs) with minimal availability in S t is used to carry request t. Minimal-cost Route (or route-pairs) with minimal cost in S t is used to carry request t. After route selection, a connection can be either unprotected or dedicated-protected. In order to further improve network resource efficiency without scarifying service reliability, we can offer shared protection to connections so that availability requirement can still be met, as follows:

3 Examine sharing possibility among all connections, and assume they are shared protected if possible. Evaluate each connection's availability. Upgrade protection scheme of a connection from sharedprotection to dedicated-protection if required availability is not satisfied. Other more-intelligent optimization algorithms can also be developed based on reliability analysis, network configuration, and customers' requirements, and they may achieve better network performance. 4. Illustrative Numerical Examples Figure 1 shows the sample network used in our study. Let the network have full wavelength-conversion capability. For illustration purposes, availability of each link is a pre-assigned value (99%, 99.9%, or 99.99%); and cost of any link is unity. There are 1000 requests, randomly generated and uniformly distributed among all node pairs. Availability requirements of connection requests are uniformly distributed among five classes: 98%, 99%, 99.5%, 99.7%, and 99.9% (Class I to Class V). Table 1 compares performance of different provisioning schemes in terms of number of wavelength channels needed (W), connection availability satisfaction rate (ASR), and total wavelength-links (W-Links). W is equal to minimal number of wavelength channels through which the network can carry all connection requests. ASR represents fraction of connections whose availability requirements have been satisfied. W- Links denotes total number of consumed wavelength fiber links, which is optimized according to value of W in each ILP scheme. Schemes I, II, and III in Table 1 are ILP-based approaches. In Scheme I, all connections are provisioned without any protection; in Scheme II, all connections are provisioned with 1+1 protection; and network resources are optimized without any connection-availability consideration in both schemes. In Scheme III, connections are first classified into T 1 and T 2 groups. Connections of T 1 are provisioned using ILP approach in Section 3.2. Connections of T 2 are provisioned using an approximation approach [3]. We observe from Table 1 that Scheme I consumes least amount of resource but only provides 30.2% ASR. Scheme II can significantly improve ASR by providing 1+1 protection to all connections; however, it also consumes a large amount of resources. Through connection classification and traffic optimization, Scheme III jointly optimizes ASR and resource usage. It uses fewer wavelength-channels and around 17% less W- Links compared to Scheme II, and provides 99.9% ASR. Table 1 also shows performance of heuristics without sharing. All heuristics can provide 100% ASR because the route for request t is selected from S t, in which all routes can satisfy availability requirement of t. Note that Iteratively-select uses least amount of resources in both W and W-Links compared to other heuristics and its performance is comparable to that of Scheme III. This is because, in Iteratively-select, either W or W-Links will be reduced whenever replacing a request's current route by a new one. Figures 2 and 3 show results of heuristics without sharing for four different traffic distributions - Class I: Class II: Class III: Class IV: Class V = 2:2:2:2:2, 1:1:2:2:4, 4:2:2:1:1, and 1:2:4:2:1 (distributions 1 through 4, respectively). In both figures, observe that Iteratively-select consistently demonstrates better performance than other heuristics; and performance of Most-reliable is worst over all distributions since highly-reliable route is chosen while sacrificing resources. Notice that, in the third distribution, there are more requests with low availability requirement than those in other distributions. In this case, more requests can be provisioned by using a single route; consequently, the third traffic distribution utilizes less resource compared to other distributions (see Figs. 2 and 3). Figure 4 compares performance of heuristics with and without sharing for traffic distribution 1. Observe that resource-sharing further reduces wavelength-links used in all heuristics (number of wavelengths used is also reduced although not shown here). We find that around 45% requests are unprotected, 30% are dedicated protected, and 25% are shared protected in all heuristics. This percentage varies when traffic distribution changes. Note that resource sharing is achieved without scarifying service reliability. To conclude, our results indicate that our proposed provisioning framework can help network operators to differentiate network services, improve service reliabilities, and optimize resource efficiency.

4 References [1] M. Clouqueur and W. D. Grover, "Availability analysis of span-restorable mesh networks," IEEE J. on Selected Areas in Communications, vol. 20, no. 4, pp , May [2] K. C. Chu, M. Mezhoudi, and Y. Hu, "Comprehensive end-to-end reliability assessment of optical network transports, " Proc., OFC'2002, pp , March [3] J. Zhang, K. Zhu, H. Zang, and B. Mukherjee, "A new provisioning framework to provide availability-guaranteed service in WDM mesh networks," Technical Report No. CSE , CS Dept., UC Davis, Sept W ASR W-Links Scheme I Scheme II Scheme III Iteratively-select Most-reliable Just-above-threshold Minimal-cost Figure 1: Sample network topology. Table 1: Results from ILP formulations and heuristic algorithms.

5 Iteratively-select Most-reliable Just-above-threshold Minimal-cost Iteratively-select Most-reliable Just-above-threshold Minimal-cost Number of Wavelengths Traffic Distributions Number of Wavelength-Links Traffic Distributions Figure 2: Number of wavelength channels used by heuristic algorithms (without sharing) with different traffic distributions. Figure 3: Number of wavelength-links used by heuristic algorithms (without sharing) with different traffic distributions. without sharing with sharing Number of Wavelength-Links Heuristics Figure 4: Number of wavelength-links used by heuristics (Iteratively-select, Most-reliable, Just-above-threshold, Minimal-cost, illustrated as heuristics 1 through 4, respectively) with and without resource sharing.