A Shared Backup Path Protection Scheme for Optical Mesh Networks

Edith Cowan University Research Online

ECU Publications Pre. 2011

2005

Hoang N. Nguyen Edith Cowan University

Daryoush Habibi Edith Cowan University

Quoc Viet Phung Edith Cowan University

Kungmang Lo Edith Cowan University

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10.1109/APCC.2005.1554070 This is an Author's Accepted Manuscript of: Nguyen, H. N., Habibi, D. , Phung, Q.V. , & Lo, K. (2005). A Shared Backup Path Protection Scheme for Optical Mesh Networks. Proceedings of Asia Pacific Conference on Communications. (pp. 309-313). Perth, Western Australia. IEEE. Available here © 2005 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. This Conference Proceeding is posted at Research Online. https://ro.ecu.edu.au/ecuworks/2897 2005 Asia-Pacific Conference on Communications, Perth, Western Australia, 3 - 5 October 2005. A Shared Backup Path Protection Scheme for Optical Mesh Networks

Hoang N. Nguyen, Daryoush Habibi, Senior Member, IEEE, Quoc V. Phung, Kungmeng Lo SCHOOL OF ENGINEERING AND MATHEMATICS EDITH COWAN UNIVERSITY JOONDALUP WA 6027 AUSTRALIA

Abstract— We propose a new heuristic ILP model for share the model is very complex and has a large number of vari- backup path protection (SBPP) scheme of mesh networks, which ables/ constraints, especially, due to the wavelength continuity used the sets of disjoint-joint primary-backup path candidates requirements absence of wavelength converters, large number of using path-pair candidates. The solution of the model is near optimal and provides all the routing details of demands as of wavelength channels may have to be installed. Therefore, well as the sharing information between backup paths, and also this model can practically be applied only to networks with simplifies the wavelength assignment problem if the wavelength no more than 10 nodes [6]. continuity is a consideration. The new entities are introduced into In this paper, we propose a new alternative joint SBPP model, this model that allow to control the the resource utilization as which employs a minimum set of disjoint-joint primary- well as congestion level of the network for optimization purposes and the pre-processing of data offers more control in properties backup paths set of demands. The solution of this model of the path candidates. provides all the routing details for each connection in a given demands as well as sharing details between backup paths I. INTRODUCTION of demands. The rest of this paper is organized as follows: Protecting Networks against the failures of physical compo- in Sec. II, we describe the general ILP model for link-path nents is a crucial task in network design and development. This formulation; Sec. III, introduces the heuristic SBPP model is particularly important with networks employing wavelength based on minimum set of disjoint-joint primary-backup path division multiplexing (WDM), which offers terabit/second data pairs; simulation results are presented in Sec. IV; Sec. V channels over the fiber infrastructure. Survivable networks can summarizes some remarks and conclusion from our work. be defined as networks that can continue functioning correctly in the presence of the failures of network components [1]. II. BACKGROUND Optical mesh networks are becoming more wide spread due An optical mesh network using a large number of wave- to the facts that they use much less resource compared to lengths, usually includes Optical Cross Connects (OXCs). ring networks, and can satisfy the growth in demand of Each OXC switches the optical signal coming from the input data communication, by integrating new technologies into the fiber link on a wavelength to an output fiber link with networks that help reduce the response time gap between mesh the same wavelength (or different wavelength if the OXC and ring networks. is equipped with a wavelength-converter). Thus an optical The survivability at optical layer in mesh networks is based on channel established over the network of OXCs is the lightpath, two paradigms: path protection/restoration and link protection/ in some papers referred to as λ-channel, which may span over restoration. Protection and restoration are generally different a number of fiber links (physical hops). In the absence of in the timing of when the alternative paths are established, wavelength converters, a lightpath is associated with the same statically in design time for protection mechanism or dynam- wavelength on all hops that the light pass through (referred to ically after the failure has occurred for restoration. There as wavelength continuity constraint). If wavelength converters are basically two types of resource allocation in network are used, different wavelengths may be used on each hop to protection schemes: dedicated or shared. Studies of survivable create the lightpath. In this paper, we assume that the system mesh networks have shown that SBPP schemes offer the either has enough wavelengths or wavelength converters are highest resource efficiency compared to others [1], [2], [3], installed, hence wavelength continuity constraint is not con- [4]. However, due to the capacity sharing between backup sidered. paths, SBPP schemes generally have greater complexity in term of modeling and computation. Currently, there are three A. General mathematical model for network’s traffic routing different approaches to the capacity allocation modeling for There are two basic types of network routing models known SBPP: non-joint SBPP , joint SBPP and joint SBPP design as Link-Path formulation and Node-Link formulation [7], with wavelength assignment [5], [6]. In the first approach, the [8]. The Node-Link model usually has a larger number of Non-Joint SBPP has to admit the possibility of the infeasibility variables and constraints than the Link-Path model, thus has in finding the backup routes for the given primary routes. The a greater complexity. However, the Link-Path model requires third approach involves wavelength assignment problem, thus preprocessing of data before being implemented, such as

0-7803-9132-2/05/$20.00 ©2005 IEEE. 309 TABLE I computing sets of candidate paths for the traffic demands. NO. OF VARIABLES & CONSTRAINTS. More details about Link-Node model can be found in [8]. The new SBPP model introduced in this paper will be based on the Number of Variables Number of Constraints above Link-Path formulation due to the following advantages PN¯ (N − 1) + 1 kN¯ N (N − 1) + 1 kN¯ it provides: 2 2 • The pre-processing data allows the properties of path candidates to be controlled , eg. limited number of hops, B. Data pre-processing for SBPP path cost. Using Link-Path formulation for modeling the SBPP re- • The model can easily be extended further for dedicated quires pre-processing of data to bring them into suitable forms. protection, SBPP application. This generally includes finding disjoint paths for each demand; • The size of the model is small in terms of variables and the capacity constraint for each link; defining the cost related constraints. to a physical link; and the physical topology of the network is Typical Link-Path model is as bellows: checked for survivable before any further implementation. Fol- Model 1: General Link-Path model and Notations for ILPs. lowing are typical processes involved when modeling SBPP: • Notation 1) Survivable physical topology: A physical topology is considered to be survivable if it can cope with any single – Network notation failure of network components by allows rerouting the con- A network physical topology can be modeled as nections that are affected by the failure through an alternative ( ) an undirected graph G V,E , where V is a set of path. This requires some degree of capacity redundancy in the network nodes and E is a set of physical links. network, and the network physical topology must be in the = { } V v1,v2,...,vN , where N is the number form of a 2-connected or bi-connected graph. More details of network nodes. about this can be found in [5], [2], [9], [10]. In this paper, = { } E e1,e2,...,eM , where M is the number we assume that the given network can be presented by a 2- of network links. connected graph, thus it is survivable. – Indices 2) Finding k-disjoint paths pair: In path protection routing, =1 2 d , ,...,D demands for each connection, two disjoint paths must be provided =1 2 d b , ,...,P candidate paths pair between between the source and the destination nodes. The primary end nodes of demand d path is provisioned to serve the request under normal operation =1 2 e , ,...,M links while the backup path is reserved in case of failure of the – Constants corresponding primary path. There are various well developed δedp =1 if link e belongs to path p of demand d; 0, otherwise techniques for finding disjoint path pairs [11], [12], [13], [14]. Alg. 1 describes the technique of finding K pairs of hd volume of demand d disjoint paths adopted from [15], [16]. The outcomes form ξe unit cost of link e this will be used for generating K set of disjoint-joint path ce upper bound on the capacity of link e pairs. Alg. 2 presents the general algorithm for finding disjoint- – Variables joint primary-backup paths. This algorithm, however, won’t xdp flow variable allocated to path provide all possible candidates because there would be a large p of demand d number of them, and thus the model become impractical with ye capacity on link e the present of an enormous number of variables. Therefore, we • ILP model address the following model as an heuristic model for SBPP. – Objective The reader can refer to [15] for more details and the proof of Alg. 1. Minimize : Σeξeye (1) III. SBPP MODELING WITH K-MINIMUM SETS OF – Constraints JOINT-DISJOINT PATHS Definition 1: Let S(P, R) be the set of candidate path- Σ x = h ,d=1, 2,...,D (2) p dp d pairs, where Σ Σ σ x ≤ y ,e=1, 2,...,E (3) d p edp dp e P = {P1,...,PD} is the set of candidate primary paths. ye ≤ ce ,e=1, 2,...,E (4) R = {R1,...,RD} is the set of candidate backup paths. = { 1 2 K } Pd pd,pd,...,pd is the set of K candidate primary paths th Form the above model, the number of variables and constraints for connection d, where pd denotes the th primary path of are as in Tab. I. Where P¯ is the average of candidate paths, connection d. × ( − 1) = { 1 2 K } N N is the demand D, with N is the number of Rd rd,rd,...,rd is the set of K candidate backup paths ¯ th nodes generating demand, N is the network’s nodes and k is for connection d, where rd denotes the th backup path of th the average node degree. connection d disjoint with pd .

310 The set of Joint-Disjoint path-pairs of group demands denote xdgp flow variable allocated to set p = { l } l demand d of group g as H Hd,g,k , where Hd,g,k is the set of joint- disjoint path pairs of the kth candidate primary of demand d in group ye capacity on link e l = { ( )| ⊆ • ILP model demand g at share level l, with: Hd,g,k S P ,R S ( )} – Objective S P, R satisfying the following conditions: ) ∀ ∈ = ∅ = Minimize Σ ξ y (5) a pi,pj P ,pi pj ,i j : primary paths disjoint. e e e ) ∀ ∈ = ∅ = b ri,rj R ,ri rj ,i j : backup paths joint. – Constraints c) ∃ei ∈ E, ∈ ei = l : shared level. p P Σ = ∈ Model 2: Proposed new ILP model for Joint SBPP pxdgp hd ,d D (6) Σ Σ ≤ =1 2 • Notation d pσegpxdgp ye ,e , ,...,E (7) ≤ =1 2 – Network notation ye ce ,e , ,...,E (8) The number of variables and constraints that are introduced in Similar to Model 1. the new SBPP model are given in Tab. II. – Indices H set of disjoint-joint path-pair TABLE II candidates NO. OF VARIABLES & CONSTR. IN JOINT SBPP d =1, 2,...,D demands e =1, 2,...,M links Number of Variables Number of Constraints p =1, 2, ..., n p ∈ H PN¯ (N − 1) + 1 kN¯ N (N − 1) + 1 kN¯ – Constants 2 2 δedb =1 if link e belongs to path b of demand d; 0, otherwise. Routing cost vs. network congestion: th σegp =Σb∈pδedb if path-pair b in S uses link Optimization models for wavelength routing currently have e belongs to set p of group objective functions aimed at reducing either the network con- demand g = {di}; gestion level (referred to as CongMin) or the total wavelength 0, otherwise. channels used (referred to as CapMin) [15]. The purpose hd volume of demand. d of the CongMin scheme is balancing the network load, thus ξe unit cost of link. e lowering the number of wavelength channels needed and W upper bound on the amount reducing the blocking probability for future connections. How- of capacity of link e. ever, the total cost or capacities used by CongMin is usually – Variables higher compared to the CapMin scheme. In contrast, when the objective function has employed the CapMin scheme, the total network capacities used may be reduced, but the utilized Algorithm 1 : K disjoint-path pairs wavelength channels on some links in the network can reach Input : An indirected graph G(V,E), a pair of source and their upper limit, thus no future demands can be served via destination nodes (s, d), and the number of shortest those links. disjoint-path pairs required. By combining the above two schemes into the objective Output: A set of K-shortest disjoint-path pairs. function of the ILP model, we can control and balance the 1: Take a shortest path between the source s and destination capacity utilization and congestion level of the network. To d, using one of the shortest path algorithms, eg. modified do that, we need to introduce some new identities into the Dijkstra or BFS [13], [8]. Denote this as p. model as follows: 2: Define the direction of each link traversed in p from s • Constants toward d as positive direction. fp =Σpσegp total capacity used by set p 3: Remove all directed links on the shortest path p and • Variables replace them with reverse direction and negative weight α max congestion of the network of each such link (eg. by multiplying the original link’s • = The modified ILP model: If we define fsum p fp cost with −1). and fmax = kα, where k is the controlling factor, then: 4: Find K least cost paths from s to d in the modified graph – Objective using the algorithm in [17]. Denote these as the set of paths S = {s1,s2 ...,sK }. Minimize fsum + fmax (9) 5: For each pair of paths (p, s ), remove any link of i – Constraints the original graph traversed by both p and si. These

are called interlacing links. Identify all path segments Σpxdgp = hd ,d∈ D (10) by the link removal from path p and s . Such path- i Σ Σ σ x ≤ α (11) pairs form the K-disjoint path pairs (P pairs)= d p egp dgp α ≤ W (12) {(w1,r1), (w2,r2),...,(wK ,rK )}.

311 Algorithm 2 Finding Joint-Disjoint Primary-Backup paths contains information about the number of k shortest path- Input : An undirected graph G(V,E), T = {t1,t2,...,tD} pair candidates that the program generates and is used in the is the set of connection demands D over the network, model, and the maximum allowable sharing per physical link where ti denotes the connection between node pair {si,di} in the network. Note that the number of candidates k for each required for each demand d. A set of candidate disjoint demand are not necessarily the same; they can have different path-pairs S =(P, R) as in Deﬁnition 1 values, eg. demand 1 of connection (1-4) may have the k =3 Output: Set of Joint-Disjoint path pairs H of demand D at candidate path-pairs due to the limits of the physical network, different share levels. while demand 4 of connection (2-4) can have the k =5 1: Finding primary disjoint path of K shortest path-pair for candidate path-pairs. The details of the solution given by each demand d ∈ D: init. i ← 1 TABLE III i LINK CONFIGURATION for every pd do i ←{ i } dPd pd Link index end nodes capacity cost end for while i

the ILP solver are shown in tables VI and VII. Table VI IV. SIMULATION AND DISCUSSION contains the routing details of each demand for both primary path (indicated by letter P) and backup path (indicated by the In this section, we illustrate the performance of our pro- letter B). The last column of the table gives the indices of posed model through an example using a small randomly the corresponding demands used for cross referencing with generated network. Note that our purpose is to demonstrate

the abilities of the new ILP model, therefore a small number

of trafﬁc demands are used for the simulation. Fig. 1 shows ¿

º º

the randomly generated network which has 7 nodes and 8 º

½ º

º º

links, and has the link conﬁguration and connection demands º

as shown in tables III, IV and V. In table III, each physical ½

link of the network is assigned an index. For simplicity,

all links have the same capacity and cost. In table V, each Ë

trafﬁc is also assigned an index. By indexing the network links and demands, the implementation of the model is much easier and we can create the cross reference table for the translation of the solution from the ILP solver. Table IV Fig. 1. An arbitrary network

312 table VII, which shows the sharing details between backup model can be extended to support multi-failure scenarios by paths of demands. Assigning wavelength for paths selected, the use of k disjoint paths for the candidates. and placement of wavelength converters can simply be done V. C ONCLUSION by using the information provided in these two tables. From the routing details, the two demands with indices 4 and 5 In this paper, we have reviewed the survivability of the have the same source and destination, and also have the same optical networks with particular focus on the SBPP at the primary and backup paths assigned to them as in table VI. optical layer because of its resource efficiency due to the fact However, this is not always the case as the primary-backup that the backup paths can share wavelength channels on links paths can be different between such demands. while their corresponding primary paths are link disjoint. We presented a new heuristic ILP model for SBPP problem based TABLE VI on the general link-path formulation and compared our model ROUTING DETAILS with the conventional models. The total number of constraints in the our model is lager than the conventional one, but has less Link used Traffic Demand constraints. The new SBPP model gives near optimal solution, e1 e2 e3 e4 e5 e6 e7 e8 index P 10110000 assures 100% protection under single link failures, and gives (1 - 4) 1 B 01000101 full routing details for each connection sharing in the demand P 10101000 (1 - 5) 2 set, thus simplifying the wavelength assignment problem in B 01000011 P 00000101 the network design phase. In addition, the new model can be (6 - 4) 3 B 11110000 extended to solve SBPP with multiple link failures by using P 00110000 (2 - 4) 5 k-disjoint path candidates instead of path pair candidates. B 11000101 P 00110000 (2 - 4) 4 REFERENCES B 11000101 P 00000011 [1] D. Zhou and S. Subramanian, “Survivability in optical networks,” IEEE (6 - 5) 6 B 11101000 Networks, 2000. [2] S. Ramamurthy and B. Mukherjee, “Survivable WDM mesh networks. part i-protection,” in Proceedings of Eighteenth Annual Joint Conference of the IEEE Computer and Communications Societies. INFOCOM’99, TABLE VII vol. 2, (New York, NY, USA), pp. 744–751, 1999. SHARING DETAILS BETWEEN BACKUP PATHS OF TRAFFICS [3] S. Ramamurthy and B. Mukherjee, “Survivable WDM mesh network.ii. restoration,” in IEEE International Conference on Communications, Connection Sharing vol. 3, (Vancouver, BC Canada), pp. 2023 – 2030, 1999. [4] P. Arijs, B. V. Caenegem, P. Demeester, and P. Lagasse, “Design of ring and mesh based wdm transport networks,” , 1 0 Optical Networks Magazine vol. 1, no. 3, pp. 27–41, 2000. 2 0 [5] W. D. Grover, 3 4 Mesh-based Survivable Networks: Options and Strategies . Prentice Hall 4 3 for Optical, MPLS, SONET/SDH, and ATM networking PTR, 2004. 5 6 [6] S. Ramamurthy, L. Sahasrabuddhe, and B. 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New York: Springer-Verlag, 2000. [11] J. McHugh, Algorithmic Graph Theory. Prentice Hall PTR, 1990. objective of the optimization problem. Hence, wavelength [12] D. Xu, Y. Chen, Y. Xiong, C. Quia, and X. He, “On finding disjoint assignment will be the next task if this model is employed. In paths in single and dual link cost networks,” in Proceedings of the 23rd contrast, the proposed model although having less advantages Conference of the IEEE Communications Society, (Hong Kong), 2004. [13] R. Bhandari, Survivable Networks: Algorithms for Diverse Routing. in terms of size of variables and requires data pre-processing, Kluwer Academic Publishers, 1999. it provides all the routing details for each connection in the [14] J. Zhang, K. Zhu, L. Sahasrabuddhe, and S. B. Yoo, “On the demands such as which path is selected for the corresponding study of routing and wavlength assignment approaches for survivable wavelength-routed WDM mesh networks,” Optical Networks Magazine, connection and how the links are shared between backup vol. 4, no. 6, pp. 16–28, 2003. paths. In addition, due to the candidates in Model 2 are [15] Q. V. Phung, D. Habibi, H. N. Nguyen, and K. Lo, “Capacity utilization sets of Disjoint-Joint primary-backup paths, hence assigning versus network congestion level in wavelength routing problem in wdm network,” Submited to APCC, 2005. wavelengths for each path selected, and placing the wavelength [16] Q. V. Phung, D. Habibi, H. N. Nguyen, and K. Lo, “K-pairs of converters at suitable nodes is just the matter of translate from two-disjoint paths algorithm for protection in wdm optical networks,” the solution details and can be done via a simple program Submited to APCC, 2005. [17] Q. V. Phung, D. Habibi, H. N. Nguyen, and K.-M. 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