Dedicated path protection for waveband switching in WDM networks (Invited Paper)

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1 Dedicated path protection for waveband switching in DM networs (Invited Paper) Menge Li and Byrav Ramamurthy Department of Computer Science and Engineering, University of Nebrasa-Lincoln, USA. {mli, Tel: (0)7-779, Fax: (0) Abstract This paper considers the problem of dedicated path-protection in a wavelength-division multiplexing (DM) mesh networ with waveband switching (BS) functionality under shared ris lin group (SRLG) constraints. Two protection schemes are proposed, namely the Protecting-waveBand- At-waveBand-Level-only (PBABL) and the Mixed-Protection-AtwaveBand-and-avelength-Level (MPABL). The PBABL protects each woring waveband-path by a bacup wavebandpath. hile the MPABL protects each woring wavebandpath by either a bacup waveband-path or multiple bacup lightpaths. The performances of the two protection schemes in terms of gained revenue and cost saving are studied and compared. Integer linear programming (ILP) formulations are presented to solve the problems for each protection scheme. Numerical results of the ILPs and the experimental results of previously proposed heuristics are presented, which show that both heuristics can obtain optimum solutions. According to the results, under heavy load traffic the MPABL scheme provides solutions with higher revenues than the PBABL scheme does. Under light load traffic, where networ resources are sufficient to accommodate all the traffics, the PBABL scheme leads to less switching and transmission costs than the MPABL scheme does. Keywords avelength-division Multiplexing, aveband Switching, Path-Protection, Integer Linear Programming. I. INTRODUCTION avelength division multiplexing (DM) is a multiplexing technique that transports several high-speed data channels simultaneously through a single fiber. Each data channel, which is also referred to as a wavelength, transmits data at a very high speed ranging from OC- (.Gbps) to OC-9 (0Gbps) [] []. By accommodating increasing number of wavelengths in a fiber, DM can resolve the discrepancy between the maret needs and the traditional networ provisioning. Thus, DM establishes itself as one of the fundamental communication technologies for the next generation networs. There are up to hundreds and even thousands of wavelengths in a single fiber, each of which requires to be switched and transmitted independently by the switching components. To reduce the switching and transmission cost in the optical domain of a DM networ, waveband-switching (BS) technique was introduced in [], [],and []. Through waveband switching, multiple specific wavelengths are grouped into a waveband at one optical cross-connect (OC) and disaggregated bac into wavelengths at another OC. The waveband is transmitted as a whole along the path called a waveband-path. The potential cost saving of waveband switching by aggregating wavelengths into waveband is illustrated and analyed in [], [6], and [7]. Protection is an important technique for a DM networ to survive from networ failures and is addressed by many [8][9][0]. There are many protection schemes for wavelengthrouted DM networs, classified as path-protection, linprotection, and segment-protection, as discussed in [], [] and []. Path-protection or lin-protection protects a connection from the failures using a bacup path for its woring path or failed lin separately. Segment-protection divides the woring path for a connection into segments and protects each segment using a bacup segment. One Limitation of both linprotection and segment-protection is that the bacup path may be very long, which consumes more networ resources. Thus, path-protection is more efficient than both lin-protection and segment-protection. There are two types of path-protections: dedicated path-protection and shared path-protection. hile dedicated path-protection guarantees the protection of a connection from a single point of failure by allocating an exclusive bacup path, shared path-protection tries to utilie the networ more efficiently by sharing one bacup path among multiple connections. However, shared path-protection cannot survive from simultaneous failures of those connections. A DM networ with the functionality of BS is a waveband switching networ (BS networ). In such a networ, a networ component failure can cause the failure of several waveband-paths and lightpaths, leading to the loss of large amounts of data and revenue. Thus, fault management in a BS networ is of paramount importance. However, survivable BS is a relatively unexplored topic, only gaining attention recently. The only related study is [], which addresses the problem without considering the routing problem and the shared-ris lin group (SRLG) constraints. To the best of our nowledge, the study of survivable BS problem considering different protection schemes and including the routing problem has never been carried out before. To survive from a single point of networ failure, dedicated path-protection technique is adopted here in a BS networ under the SRLG constraints. Although dedicated path-protection may not be the most efficient technique, it guarantees that the networ will survive from any single-point of failure. In a BS networ, a connection request may be transmitted in a woring waveband-path. Different protection schemes may have different polices for protecting a wavebandpath. Two protection schemes are proposed here, which are the Protecting-waveBand-At-waveBand-Level-only (PBABL) and the Mixed-Protection-At-waveBand-and-avelength-Level

2 (MPABL). In the PBABL, a woring waveband-path is protected only by a bacup waveband-path. In the MPABL, a woring waveband-path can be protected either by a bacup waveband-path or by multiple bacup lightpaths. hile the PBABL scheme saves the computational time in finding the SRLG-diverse bacup waveband-path and simplifies the control and management on OCs, it may be inefficient because of the low utiliation of a waveband. On the other hand, the MPABL scheme is efficient and more cost effective by using more computational time in search of the possible bacup paths and requiring complex control on OCs. This paper is organied as follows. Section II discusses the research bacground. Section III describes the networ model and the two protection schemes. Section IV presents the ILP formulations for both schemes. Section VI demonstrates the effectiveness of the ILPs and the previously proposed heuristics using numerical examples. Finally, Section VII summaries the major contributions of this paper. II. RELATED ORK Previous studies on waveband switching, survivable DM networ under SRLG constraints, and global optimiation are valuable in the survivable BS study here. A. Bacground Knowledge aveband switching (BS) is an important and practical technique. An OC with the functionality of BS is called a multi-granular optical cross-connect (MG-OC). Besides the traditional functionalities of an OC, an MG-OC can transmit wavebands, multiplex specific wavelengths into a waveband, and demultiplex a waveband into wavelengths. In [], two types of MG-OCs are proposed and compared: single-layer MG-OCs and multi-layer MG-OCs. For a single-layer MG-OC, the BS function is added into the switching fabric of a traditional OC. For a multi-layer MG- OC, the BS function is supported by adding additional switching fabrics into a traditional OC. The study in [] shows that different types of MG-OCs have different benefits in different networ conditions. In waveband switching, waveband granularity is defined as the maximum number of wavelengths that can be grouped into a waveband. It is determined beforehand by the utilied optical components, such as the MG-OCs. The MG-OC may support two types of waveband switching, namely the uniform waveband switching (UBS) and the non-uniform waveband switching (NUBS). Compared with UBS where all wavebands have the same fixed granularities, NUBS is more flexible in that the wavebands may have various granularities [6]. However, the implementation of NUBS and the control of NUBS on an MG-OC are difficult. Moreover, UBS can mimic NUBS by allowing idle (free) wavelengths to be grouped into an active (used) waveband. Thus, in this study, we adopt such UBS. A waveband-path along the MG-OCs can reduce the total number of ports used compared to the lightpaths using only OCs. Generally, if all the ports in the MG-OCs have the same cost, the number of used ports can represent the routing cost in the optical domain. Thus, in the study of the survivable BS problem, an important objective is to minimie the total ports used, given the amount of provisioned traffic. Protection is an effective method for a BS networ to survive networ failures, which should protect each woring waveband-path and lightpath through bacup paths in a BS networ. In additional, each lin in the BS networ could belong to a failure ris group. A shared-ris lin group (SRLG) is a group of lins with a shared vulnerability, such as a shared fiber cable or a shared right-of-way (RO). In later discussion, an SRLG ris represents a general ris. Each lin may belong to many SRLGs and each SRLG constraint could include many lins. For the networ to be survivable under any single-point of failure, the bacup path must be SRLG-diverse from the woring path. This paper proposes two dedicated path-protection schemes, the PBABL scheme and the MPABL scheme. In both schemes, the connection requests are provisioned with maximum gained revenue. If all connection requests can be accommodated, the connection requests are provisioned with minimum cost represented by the number of utilied ports. In doing so, integer linear programming (ILP) formulations are developed for each scheme. The impacts of different protection schemes on revenue generation and networ capacity utiliation are also studied. The survivable BS problem under SRLG constraints can be formulated as a maximiation problem maximiing the gained revenue and a minimiation problem minimiing the total number of used switching and transmission ports. To find the optimum solution, the mixed integer linear programming (ILP) is used for small networs. For large networs, as the variables and constraints increase exponentially, it is difficult for the mixed integer linear programming to find the the optimum solution given limited computational resources. Thus, heuristic algorithms were proposed for the minmax problems utiliing simulated annealing (SA) techniques in search of the optimum [6]. ILP and SA are both powerful global optimiation techniques for a wide range of applications. ILP is so important that many tools and methods are developed to solve its formulations. SA is also a widely utilied technique, especially in large-sied applications. SA exploits the analogy between the annealing process and the search of the minimum in a general system. It was proposed as an optimiation technique for combinatorial (and other) problems in [7]. The SA algorithm is based on [8] by Metropolis et al., which simulates a collection of atoms in equilibrium at a given temperature. The major advantages of SA are its ability of avoiding trapped at local minima and its ability of quic approach to the optimal value. The implementation of SA is simple and shows many successes in the study of networ problems. B. Our Contributions Survivable waveband switching under SRLG constraints in DM networ provisioning is being comprehensively ad-

3 Input Fiber Figure. B avelength to aveband Mutliplexer aveband to avelength Demultiplexer Policy Control Plane C avelength Switch Fabric BC aveband Switch Fabric B... B B aveband to Fiber Multiplexer Fiber to aveband Demultiplexer Output Fiber Multi-granular Optical Cross-Connect (MG-OC). dressed in this paper. As networs under heavy load traffic and light load traffic may perform differently, two dedicated pathprotection schemes are proposed separately for the two types of networs, namely the Protecting-waveBand-At-waveBand- Level-only (PBABL) and the Mixed-Protection-At-waveBandand-avelength-Level (MPABL). e refer to a networ under light load traffic as the networ with sufficient resources. As there is no bloced traffic request in such a networ, our ultimate objective is to save maximum switching and transmission costs in terms of utilied ports. In a networ under heavy load traffic, some traffic request has to be bloced because of the limited resources. Thus, the ultimate objective is to gain as much revenue as possible. e proposed the MPABL to gain maximum revenues and the PBABL to save maximum switching and transmission cost. The PBABL and the MPABL are classified by the protections on the woring waveband-paths. Various constraints in survivable BS networ provisioning are considered and various problems are addressed to simulate the real world as close as possible. hen designing the two schemes, physical constraints such as the utilied MG-OCs, the fiber capacity, the limited number of wavebands in a fiber, the various cost and gained revenues for provisioning the traffics, the shared riss for each lin, and the distance between a node pair are considered. Each protection scheme considers the problems of wavelength assignment, routing, waveband assignment, aggregating of wavelengths, and disaggregating of wavelengths. The performances in terms of the gained revenue and the cost saving in the optical domain are studied and compared for the two schemes. To provide waveband switching, a two-layered MG-OC has been proposed shown in Fig., including a wavelengthcrossconnect (C) layer and a waveband-corssconnect (BC) layer. avelengths and wavebands are terminated or switched transparently through the switching fabrics at the C layer and the BC layer separately. The terminated waveband is demultiplexed into wavelengths, which are sent to the C layer as inputs. The output wavelengths at the C layer can be multiplexing selectively into a waveband, which is sent to the BC layer as an input. The output wavelengths from the C layer and the output wavebands from the BC layer are grouped and transmitted along the output fiber lin. Although the architecture of the MG-OC specifies UBS, NUBS can be simulated by allowing idle (free) wavelengths to be grouped into an active (used) waveband. For each scheme, ILP formulations are provided to obtain optimal revenues and optimal cost saving. To obtain the optimal solution for large networs, simulated annealing-based heuristics are utilied to solve the minmax problems. III. NETORK MODEL AND PROBLEM DEFINITION A. Networ Model The networ consists of MG-OC nodes, where each MG- OC has the same fiber capacity and waveband capacity. Such a networ is a homogeneous BS networ. Remember that although the waveband capacities are the same among the networ, NUBS can be simulated by allowing idle (free) wavelengths to be grouped into an active (used) waveband. In this paper, we do not consider wavelength conversions in the networs because of two reasons. One is that using wavelength converters increases the provisioning costs. Another reason is that wavelength conversion is a complex problem and will bring many other issues, such as the placement of wavelength converters. Thus, without wavelength conversion a lightpath/waveband-path is subjected to the wavelength/waveband continuity constraint. The nodes are interconnected by optical fiber lins. Each fiber lin may support up to wavelengths and B wavebands. The policy control plane of an MG-OC selects at most θ = B specific wavelengths to be grouped into a waveband. The grouping of wavelengths in a waveband is restricted to those from the same source and destined to the same destination. ithout loss of generality, the wavelengths in a waveband are assumed to be contiguous. Thus, the networ can be expressed as a directed graph G(V,E,,B,θ,L,R), where V is the vertex set, E is the edge set, is the wavelength set, B is the waveband set, θ is the waveband granularity, L is the set of lin length constraints, and R is the ris set. The directed graph contains the following information: (a) Each vertex of the graph represents an MG-OC node; (b) Each lin supports a fixed number of wavelengths and wavebands; (c) Each lin is associated with a number, representing the length; (d) Each lin is associated with a set of numbers, representing a set of SRLG riss. The SRLG ris set of a lin contains the riss that the lin is vulnerable to. Two lins are SRLG-diverse if they have no common riss. The SRLG ris set of a path contains all the riss that the lins along the path are vulnerable to. Two paths are SRLG-diverse if they have no common riss. A lin is SRLG-diverse to a path if their ris sets have no common elements. The number of connection requests between each node pair in the networ is given by the traffic matrix. A connection request has the following attributes: (a) It starts from a source

4 :8 B: :8 B: :6 B: :6 B: :8 B: :8 B: :8 B: : Bf :6 B: : Bb (a) Networ Topology (=8,B=, θ=) (b) PBABL and MPABL with requests from to b : B: : B: f Bb : : f : Bf : B: : (c) PBABL with another request from to Bb : Bf : : (d) MPABL with another request from to Bb Fiber Lin f oring lightpath Bf oring waveband path Bb Bacup waveband path b Bacup Lightpath : avelengths # B: avebands # Figure. Example of the PBABL and the MPABL schemes MG-OC node and terminates at a destination MG-OC node; (b) It requires a whole wavelength capacity; (c) It constrains the maximum path length allowed; (d) It generates a fixed revenue value. Different connection requests may have different revenue values. Each connection request is transmitted in a lightpath or in a waveband-path and protected by a bacup path. Given a homogeneous BS networ and a set of connection requests with the above attributes, the objective of the revenue maximiation problem is to maximie the total revenue value generated by successfully provisioning connection requests and the objective of the cost minimiation problem is to minimie the total cost incurred by successfully provisioned connection requests. The cost is represented by the total number of BC ports and C ports used in provisioning the connection requests. B. Protection-waveBand-At-waveBand-Level-only (PBABL) For the PBABL scheme, each connection request is assigned a woring and bacup path which are SRLG-disjoint. A wavelength is assigned to each of the paths. If the waveband grouping requirement is satisfied, the PBABL scheme tries to set up a woring waveband-path and a bacup waveband-path for those requests under the condition that there is a common free waveband along both paths. For example, Fig. (a) shows a node networ with 7 lins, where each lin represents two unidirectional fibers in opposite directions belonging to a single SRLG. Besides that, all fibers covered by a dashed circle are in the same SRLG. hen two connection requests from to arrive as shown in Fig. (b), the PBABL scheme finds two free wavebands along both SRLG-disjoint routes (- --) and (--). Thus, a woring waveband-path along the route (--) and a bacup waveband-path along the route (- --) are set up. A woring waveband-path will not be set up if there are no free resources for a bacup waveband-path. For example, in Fig. (c), the waveband-path is not set up for the two connection requests from node to node because that there is no free waveband along the bacup path (--), even though there is a free waveband along the woring path (--). The constraints on setting up woring and bacup paths in the PBABL scheme are summaried as: (a) For each connection request, the woring path is SRLG-diverse from the bacup path; (b) A woring waveband-path is set up with a bacup waveband-path; (c) The bacup wavelength cannot be shared with other connections; (d) The bacup waveband cannot be shared with other connections as a woring waveband; (e) The waveband-paths cannot group the connections from different sources or those destined to different destinations. C. Mixed-Protection-At-waveBand-And-avelength-Level (MPABL) The MPABL scheme is similar to the PBABL scheme. The only difference between them is that the MPABL scheme allows the woring waveband-path to be protected by multiple lightpaths. For example, in Fig. (d), there are two connection requests from node to node. There is a free waveband along the route (--). However, there is no free waveband along the route (--). The MPABL scheme sets up a woring waveband-path for the two requests along the route (--) and sets up two bacup lightpaths along the route (--). The constraints on setting up woring and

5 bacup paths for the MPABL scheme are summaried as: (a) For each connection request, a woring path is SRLG-disjoint from the bacup path; (b) A woring waveband-path can be protected either by a waveband-path or by multiple lightpaths; (c) The bacup wavelength cannot be shared with other connections; (d) The bacup waveband cannot be shared with other connections as a woring waveband; (e) The wavebandpaths cannot group the connections from different sources or those destined to different destinations. The above descriptions illustrate that the PBABL and the MPABL schemes are different only in their waveband switching policies. In both the schemes, the woring path and the bacup path carry traffic at the same time. hen a failure occurs in the woring path, the end nodes of the affected lightpaths and waveband-paths just receive and process the traffic in the bacup paths. IV. ILP FORMULATION Four integer linear programming (ILP) formulations are presented for the revenue maximiation problem and the cost minimiation problem using both the PBABL and the MPABL schemes. The networ topology G(V,E,,B,θ,L,R) is as defined in Section III. A. Notations : The maximum number of connections between each pair of nodes. (i,j) : The lin (i,j) is vulnerable to ris, where (i,j) E and R. l i,j : The length of lin (i,j). L s,d,x : The length constraint for connection request (s,d,x), where s is the source node, d is the destination node, and x is the connection call number to distinguish different connections between the same node-pair ( x ). µ s,d,x : The revenue value generated by provisioning connection request (s, d, x). : The woring path and bacup path identifier., a woring path., a bacup path. :, if the path for connection request (s,d,x) uses wavelength w on lin (i,j); 0, otherwise. :, if the path for connection request (s,d,x) uses waveband b on lin (i,j); 0, otherwise. B s,d, :, if the paths for connection requests from s to d use waveband b on lin (i,j); 0, otherwise. D s,d,x, :, if the lightpath for connection request (s,d,x) is vulnerable to ris ; 0, otherwise. K s,d,x, :, if the waveband-path for connection request (s,d,x) is vulnerable to ris ; 0, otherwise. i,j,w :, if wavelength w for a path is in waveband b on lin (i,j); 0, otherwise. G w, i,j :, if wavelength w on lin (i,j) is used for a request on its path and is not in a waveband; 0, otherwise. m b, i,j :, if waveband b on lin (i,j) is utilied by some paths for some connections; 0, otherwise. λ w, s,d,x :, if wavelength w is assigned to the path for connection request (s, d, x); 0, otherwise. i,j,w :, if waveband b is assigned to the path for connection request (s, d, x); 0, otherwise. dem s,d,x : The traffic demand., if there is a connection request (s, d, x); 0, otherwise. f i,j : The total number of utilied lins on lin (i,j) including the number of utilied waveband-lins and wavelengthlins that are not in wavebands. s,d,x B. ILP Formulation I: The Revenue Maximiation Problem for the PBABL Scheme Objective: Maximie = i:(s,i) E ( s,i,w µ s,d,x). Subject to: Constraints on the utiliation of wavelength w on lin (i,j): i,j,w, () (i,j) E, w. Constraints on the SRLG-disjointedness of the woring lightpath and the bacup lightpath: E D s,d,x, i,j,w, () (i,j) {,}, s,d V, x, R. D s,d,x, i,j,w, () (i,j) {,}, s,d V, x, R. D s,d,x,, () s,d V, x, R. Flow-conservation constraints: 8 i,j,w < λ w, s,d,x if d=j j,e,w = λ w, : s,d,x if s=j i:(i,j) E e:(j,e) E 0 otherwise () {, }, s, d V, x, w F s,d,x, i,s,w + =, i:(i,s) E =, s, d V, x, w. i:(d,j) E F s,d,x, d,j,w = 0, (6) The number of provisioned connections is equal to the number of protected connections. λ w, s,d,x = λ w, s,d,x, (7) = = s,d V, x. The number of provisioned connections should not exceed those requested. dem s,d,x λ w, s,d,x, (8) = s,d V, x.,

6 Constraints on the path length for each connection request (s,d,x): (i,j) E ( i,j,w l i,j) L ( s,d,x), (9) {,}, s,d V, x. Constraints on the utiliation of waveband b on lin (i,j): B s,d, (i,j) E, b B., (0) Constraints on the SRLG-disjointedness of the woring waveband-path and the bacup waveband-path: E K s,d,x, (i,j) b B, () {,}, s,d V, x, R. K s,d,x,, () (i,j) b B {,}, s,d V, x, R. K s,d,x,, () s,d V, x, R. Flow-conservation constraints on waveband utiliation: i:(i,j) E 8 >< j,e,b = e:(j,e) E >: {, }, s, d V, x, b B. s,d,x if d=j s,d,x if s=j 0 otherwise () B s,d,x, i,s,b + B s,d,x, d,j,b = 0, () =, i:(i,s) E =, i:(d,j) E s, d V, x, b B. A woring waveband should be protected by a bacup waveband in the PBABL scheme. s,d,x = s,d,x, (6) = b B = b B s, d V, x. Some connection requests may not be transmitted in a waveband. b B s,d,x λ w, s,d,x, (7) {,}, s,d V, x, R. K s,d,x, D s,d,x,, (8) {,}, s,d V, x, R. Constraints indicating whether a waveband b is used by some connection requests on lin (i, j): m b, i,j i,j,w, (9), {,}, (i,j) E, b B. m b, i,j i,j,w, (0) {,}, (i,j) E, b B., () m b, i,j (i,j) E, b B. Constraints indicating whether a waveband b is used on lin (i,j) in the woring paths from s to d: B s,d,, () {,}, (i,j) E, s,d V, b B. B s,d,, () {,}, (i,j) E, s,d V, b B. Constraints indicating whether a wavelength w is in a woring or a bacup waveband b on lin (i,j): B s,d, + i,j,w i,j,w, () {,}, (i,j) E, b B, w. B s,d, + i,j,w i,j,w, () {,}, (i,j) E, b B, w. Constraints indicating that each wavelength belongs to at most one waveband on a lin (i,j): i,j,w i,j,w, (6) b B {,}, (i,j) E, w. i,j,w, (7) {,}, (i,j) E, w, b B. i,j,w, (8) (i,j) E, w. Constraints indicating whether a wavelength w on lin (i, j) is to be grouped in a waveband: G w, i,j + i,j,w i,j,w = 0, (9) b B {,}, (i,j) E, w. 6

7 Constraints indicating the utiliation of a waveband b on lin (i,j) is limited by its capacity θ: i,j,w θ, (0) {,}, (i,j) E, b B. Constraints indicating that the number of wavelengths (connections) in a waveband should not exceed the waveband capacity θ: s,d,x θ, () {,}, s,d V, b B. Constraints indicating that if there is a waveband b from source s to destination d, the capacity of waveband b should be greater than or equal to and less than or equal to its capacity θ: i,j,w mb, i,j, () {,}, (i,j) E, b B. i,j,w θ mb, i,j, () {,}, (i,j) E, b B. B s,d,, () {,}, s,d V, (i,j) E, b B. θ B s,d,, () {,}, s,d V, (i,j) E, b B. The total number of used wavebands and used wavelengths that are not part of a waveband on lin (i,j). f i,j = (i, j) E. (G w, i,j ) + b B (m b, i,j ), (6) C. ILP Formulation II: The Cost Minimiation Problem for the PBABL Scheme The ILP formulation II is identical to the ILP formulation I except for the following changes. First, the objective is to minimie the total number of occupied C ports and BC ports, which is equal to two times of the occupied lins. Thus, the objective is expressed as follows. Minimie f i,j. (7) (i,j) E Second, in ILP formulation I, constraint (8) guarantees that the number of successfully provisioned connection requests is not greater than the demands. Thus, for the cost minimiation problem, constraint (8) should be replaced by constraint (8) to guarantee that the every connection request is successfully provisioned. dem s,d,x = λ w, s,d,x, (8) = s,d V, x. D. ILP Formulation III: The Revenue Maximiation Problem for the MPABL Scheme The ILP formulation III is identical to the ILP formulation I except that the constraint (6) should be replaced by (9) to allow a woring waveband-path be protected by either a bacup waveband-path or multiple bacup lightpaths. s,d,x s,d,x, (9) = b B = b B s, d V, x. E. ILP Formulation IV: The Cost Minimiation Problem for the MPABL Scheme The objective is the same as the one in ILP Formulation II. The constraints are the same as those in ILP Formulation III. F. Heuristics: The ILP formulations presented above yield optimal solutions. However, the formulations are very complex and the computational time increases exponentially as the problem sie increases. Solving the ILP is not practical for a large sied real world networs. As described in Section I, heuristic algorithms were proposed for the minmax problems utiliing simulated annealing (SA) in [6] to solve the revenue maximiation problem and the cost minimiation problem. The inputs of the heuristics are the networ topology G(V,E,,B,θ) described in Section III and a set of connection requests Φ = {φ i (s i,d i,x i,r i,l i )}, where φ i is the identifier of the group of connection requests, s i is the source node, d i is the destination node, x i is the number of connections in the group, r i is the average revenue for each connection in the group, and l i is the length constraint for each connection in the group. ithout loss of generality, we let x i θ, where θ is the waveband capacity. The outputs of the heuristics are the woring and protection wavelengthpaths or waveband-paths for the requests φ i. V. NUMERICAL RESULTS In this section, numerical results for the ILP formulations and the heuristic algorithms of the two schemes are presented and compared. The heuristic algorithms provision the connection requests group by group according to the non-increasing order of the revenue values. The connection requests which start from the same source node and destine to the same destination node can be grouped together into a waveband. The revenues for provisioning the connection request in the same group are different from each other. Each connection request requires a whole wavelength capacity. Two example networs are considered. One is a small-sied networ with 7 nodes and 9 bi-directional lins. The other is a large networ with 7

8 nodes and bi-directional lins. The topologies of the two networs are given in Fig., where each line represents two unidirectional fibers in opposite directions and are subject to a common SRLG ris. In addition, a dashed circle represents a common SRLG ris and all the lins covered by the circle are subject to the ris. The number on each lin represents the lin length in ilometers. The demands are generated randomly with length constraint ranging from 00m to 600m for the small networ and from 900m to 00m for the large networ. The revenue value for each connection request ranges from 6. to 0.. A. Comparison of the ILPs, the PBABL heuristic, and the MPBAL heuristic in a small-sied networ e use CPLE approach [9] to solve the above ILPs on a SUN Ultra60-worstation with a MH UltraSparc II processor. The running time is limited to hours. CPLE stops when it finds the optimal solution. If CPLE cannot find the optimal solution in the given time or runs out of RAM space, it will stop and report the best solution it has found. For both heuristics (see [6]) for the revenue maximiation problem, the initial value of T is T 0 =0, the final value of T is T f =, x f = 0.00, and α=0.9. For both heuristics for the cost minimiation problem, the initial value of T is T 0 =8, the finial value of T is T f =0., x f = , and α=0.9. Table I shows the results of the revenue maximiation problem in the 7-node networ. In the table, column,, and describe the number of wavelengths on each lin, the number of wavebands on each lin, and the number of connection requests separately. The results mared with asteriss are the best solutions reported by CPLE in 700 seconds. The question mar illustrates that the CPLE cannot find a solution given the time. The results obtained from the ILPs for the PBABL (ILP I) and the MPABL schemes (ILP III) are the same and the running times are almost the same. This verifies that the successful provisioning connections is only determined by the number of wavelengths/wavebands and routing results. As can be observed, the performances of the heuristic PBABL and the heuristic MPABL are the same as those of the ILPs. And the performance of the two schemes for the revenue maximiation problem are almost the same. Table II compares the results of the cost minimiation problem obtained from the ILPs and the heuristics in the 7- node networ. As can be observed, CPLE cannot find the optimum solutions as the fiber capacity increases to 6 and reports the best solutions it found in hours. On the other hand, the heuristics (described in [6]) are quic in finding the solutions which are better than those reported by CPLE. The running time of the heuristics are much shorter than these of the ILPs, which is around 0 seconds. In addition, the MPABL scheme can obtain better results than the PBABL scheme illustrated by both the ILP results and the heuristic results. It can be concluded that solving the ILP formulation is very time consuming and cannot guarantee finding the optima. For example, the ILPs cannot find the optimum for the revenue maximiation problem in the small networ with 8 or more wavelengths and 8 or more connection requests. The benefits of utiliing the heuristics are the time savings and the guarantee in finding solutions compared to using the ILPs. B. Comparison of the PBABL and the MPABL in a largesie networ This subsection compares the performance of the PBABL and the MPABL schemes in the -node networ. The number of connection requests ranges from to 60 and the connection requests are represented as {φ i (s i,d i,x i,r i,l i )} defined in IV. The connection requests are generated randomly and are uniformly distributed across the networ. The number of wavelengths in a fiber lin ranges from to 6 and the number of wavebands in a fiber lin ranges from to, which is the maximum value of x i. For both heuristics, each results can be obtained within seconds for both the problems. The results for the revenue maximiation problem are given in Fig. (a). The lines in the figure show the maximal revenue for the networ with the given number of connection requests, which may not be achievable because of the networ resource constraints. The value shown in column is the average result obtained by running the algorithms 0 times with different wavelengths and different wavebands on each fiber lin. For both the heuristics for the revenue maximiation problem, the initial value of T is T 0 =, the final value of T is T f =, x f = 0.00, and α = 0.9. As can be observed, the MPABL heuristic can obtain slight higher revenues comparing with the PBABL. The final results of the PBABL heuristic and the MPABL heuristic are compared with its initial ones INS P and INS M separately. For both heuristics, the initial solutions are almost maximum for 8 or less connection requests, resulting in small improvements of the heuristics. The improvement increases as the number of connection requests increases. Fig. (a) compares the improvements of the two heuristics in terms of the gained revenue. The results are shown as a ratio of the improvement to the maximal revenue under different number of connection requests. The MPABL heuristic almost always shows better performance than the PBABL heuristic does. The average ratio of revenue gaining is 8% for the MPABL heuristic comparing to the initial solution. For the PBABL heuristic, the average ratio of revenue gained is 6.%. The results for the cost minimiation problem are given in Fig. (b), where the minimum costs obtained by the initial solutions are normalied to the values obtained by the heuristics. Each value is the average result and is compared with the normalied initial results. For both the heuristics for the cost minimiation problem, the initial value of T is T 0 = 8, the final value of T is T f = 0., x f = , and α = 0.9. As can be observed, the PBABL heuristic results in slightly lower cost than the MPABL does. The improvement for each heuristic increases as the number of connection requests increases. The improvements of the heuristics are compared in Fig. (b) in terms of the normalied ratio of reduced cost, which is equal to normal(ins). The 8

9 0 0 Ris Ris Ris Ris Ris Ris Ris7 8 Ris Ris (a) Figure. The example networs: (a). The 7-node networ. (b). The -node networ. (b) TABLE I RESULTS FOR SOLVING THE REVENUE MAIMIZATION PROBLEM IN THE 7-NODE NETORK. Case B C Maximied Revenue Running Time (s) ILP(I&III) PBABL MPABL ILP(I&III) PBABL MPABL / / / / ? TABLE II RESULTS FOR SOLVING THE COST MINIMIZATION PROBLEM IN THE 7-NODE NETORK. Case B C Minimum Cost Running Time (s) ILP(II) ILP(IV) PBABL MPABL ILP(II) ILP(IV) PBABL MPABL * * * 7* Revenue (a) PBABL vs. MPABL for Revenue Maximiation Problem INS_P PBABL INS_M MPABL MA c Number of Demands Normalied Cost (b) PBABL vs. MPABL for Cost Minimiation Problem NOR PBABL MPABL Number of Demands Figure. Comparisons of the PBABL heuristic and the MPABL heuristic in the -node networ. (a). The revenue maximiation results comparing with the initial solutions (INS P and INS M) and the maximum values. (b). The cost minimiation results comparing with the normalied value of the initial solutions (NOR). 9

10 Gained Revenue (%) (a) Gained Revenue Comparison MPABL PBABL Number of Demands Normalied Ratio of Reduced cost (%) (b) Reduced Cost Comparison MPABL PBABL Number of Demands Figure. The performance comparison of the improvement of the PBABL heuristic and the MPABL heuristic in terms of the gained revenue and the reduced cost by adopting optimiation process in the -node networ comparing with the initial solutions. (a). The performance comparison of the gained revenue for the PBABL heuristic and the MPABL heuristic (%). (b). The performance comparison of the reduced cost for the PABL heuristic and the MPABL heuristic (%). normal(in S) is the normalied valued of the initial solution shown in Fig. (b). The normalied ratio of the reduced cost increases as the number of connection requests increases for both the heuristics, where the MPABL heuristic slightly outperforms the PBABL heuristic. VI. CONCLUSIONS e addressed the survivable waveband switching problem in a homogeneous BS networ. Two dedicated path protection schemes which accommodate any single-point of failure are proposed, namely the PBABL and the MPABL schemes. The objectives are to maximie the revenue first and to minimie the cost of provisioned connections next. ILP formulations and heuristics utiliing the simulated annealing technique are proposed. Both heuristics (the PBABL heuristic and the MPABL heuristic) can obtain very high quality solutions in a short time and the solutions are equal to the optimum results of the ILPs. Moreover, the experiments show that the MPABL is better for a heavy-loaded networ and the PBABL is better for a light-loaded networ. REFERENCES [] I. P. Kaminow, T. L. Koch, and Eds., Optical Fiber Telecommunications IIIA. Academic Press, 997. [] R. Ramaswami and K. N. Sivarajan, Optical Networs: A Practical Perspective. The Morgan Kaufmann Series in Networing, Feb [] Y. Suemura, I. Nishioa, Y. Maeno, S. Arai, R. Imailov, and S. Ganguly, Hierarchical routing in layered ring and mesh optical networs, Proc. IEEE ICC 0, vol., pp. 77 7, Apr. 00. [] L. Noirie, M. Vigoureux, and E. Dotaro, Impact of intermediate grouping on the dimensioning of multi-granularity optical networs, Pro. of Optical Fiber Communication [OFC 0], pp. TuG/, Mar. 00. [] L. Rao and V. Praveen, Effect of wavelength and waveband grooming on all-optical networs with single layer photons switching, Pro. of Optical Fiber Communication [OFC 0], pp. ThP/, Mar. 00. [6] I. Rauf, G. Samrar, K. Vitor, and C. Aiaterini, Non-uniform waveband hierarchy in hybrid optical networs, Proc. IEEE INFO- COM 00, vol., pp., Apr. 00. [7] M. Li,. Yao, and B. Ramamurthy, Same-destination-intermediategrouping vs. end-to-end grouping for waveband switching in wdm mesh networs, Proc. IEEE ICC 0, (to appear) 00. [8] D. Zhou and S. Subramaniam, Survivability in optical networs, IEEE Networ, pp. 6, Nov.-Dec [9] G. Mohan and C. S. R. Murthy, Lightpath restoration in DM optical networs, IEEE Networ, pp., Nov.-Dec [0] H. Zang, C. Ou, and B. Muherjee, Path-protection routing and wavelength assignment RA in DM mesh networs under duct-layer constraints, IEEE/ACM Transaction on Networing, vol., no., pp. 8 8, Apr. 00. [] S. Ramamurthy, L. Sahasrabuddhe, and B. Muherjee, Survivable DM mesh networs, Journal of Lightwave Technology, vol., no., Apr. 00. [] A. Fumagalli and L. Valcarenghi, IP restoration vs. DM protection: Is there an optimal choice? IEEE Networ, vol., pp., Nov [] A. Todimala and B. Ramamurthy, A dynamic partitioning protection routing technique in wdm networs, Cluster Computing: The Journal of Networs Software Tools and Applications, to be appear 00. [] A. C. Varsou, S. Ganguly, and R. Imailov, aveband protection mechanisms in hierarchical optical networs, High Performance Switching and Routing, HPSR. orshop, pp. 7, June 00. []. Cao, V. Anand, and C. Qiao, Multi-layer versus single-layer optical cross-connect architectures for waveband switching, Proc. of INFO- COM 0, Mar. 00. [6] M. Li and B. Ramamurthy, Survivable waveband switching in DM mesh networs under dedicated-path protection in Proc. IEEE GLOBE- COM 0, St. Louis, MO, USA, Nov.-Dec. 00. [7] S.Kirpatric, C.D.Gelatt, and M. Jr, Optimiation by simulated annealing, Science, vol. 0, May 98. [8] N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, and E.Teller, Equations of state calculations by fast computing machines, J. Chem. Phys., vol., 9. [9] CPLE. ILOG. Mantain View, CA. [Online]. Available: 0