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1 Short Overview of Dynamic Routing and Wavelength-Assigment in Survivable WDM Networks Carlos Simões 1,3 e Teresa Gomes 2,3 1 Escola Superior de Tecnologia de Viseu Instituto Politécnico de Viseu 2 Departamento de Engenharia Electrotécnica e Computadores FCTUC – Universidade de Coimbra 3 INESC Coimbra - Instituto de Engenharia de Sistemas e Computadores csimoes@ipv.pt, teresa@deec.uc.pt

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2 Plan Introduction The RWA problem Routing Wavelength assignment Resilient routing Conclusion

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3 Introduction The RWA Problem Optical network A connection oriented network Lightpaths The RWA Without wavelength converters: the wavelength continuity constraint. With wavelength converters. 1 2 3 A B A B Converter A-B connection blockedA-E connection successful

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4 Introduction The RWA Problem There are two variations of the RWA problem: Static – the entire set of connections is known beforehand: static lightpath establishment (SLE) problem. Dynamic - the connection requests arrive based on some stochastic process, and the lightpath is released after some amount of time: dynamic lightpath establishment (DLE) problem.

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5 Introduction The RWA Problem SLE can be formulated as a mixed-integer linear program (ILP), which is NP-complete. Because of the real-time nature of the problem, DLE problem is more difficult to solve. Strategy – The RWA problem can be partitioned into two sub-problems: (1) Routing and (2) Wavelength Assignment and each sub-problem is solved separately

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6 Introduction Routing Static Routing: Fixed routing Fixed alternative routing Table of alternative (link disjoint) paths Dynamic routing Paths are chosen based on network state An adequate use of node costs can reduce the need for wavelength conversion

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7 Introduction Wavelength Assignment Static Lightpath Establishment (SLE) Objective: Minimizing the number of used λs and satisfying the wavelength continuity constraint Graph colouring: NP-Complete problem There are efficient sequential algorithms Heuristics for Dynamic Lightpath Establishment (DLE) The most common objective is the minimisation of blocking probability.

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8 Introduction Wavelength Assignment R (Random) FF (First Fit) LU (Least Used, spread) UM (Most Used, pack) MP (Min-Product) LL (Least-Loaded) M∑ (Max-Sum) RCL (Relative Capacity Loss) Rsv (Wavelength Reservation)... Heuristics for WA in DLE:

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9 Resilient Routing Advantages of recovery mechanisms in the optical layer: Fast recovery of course grain traffic flows Protects higher layers protocols without its own recovery mechanisms. Recovery mechanisms classification: Fault Recovery Schemes ProtectionRestorationLinkSubpathPathLinkSubpathPath

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10 Resilient Routing Dedicated versus shared protection fiber Active Path A-B 1 Backup Path A-B 2 Active Path C-D 3 Backup Path C-D 4 B DC A Dedicated Protection 1 2 3 2 Shared Protection

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11 Dedicated path protection Two Step Approach (TSA) Difficulty: Trap topology problem Disjoint Shortest Path Pair (Suurballe & Tarjan, 84), Min-Sum problem 1 1 1 Resilient Routing E DFAB C 2 2 3 2 E DFAB C

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12 Resilient Routing Path protection The active path cost is made higher than the protection path: The Min-Sum with ordered dual link costs problem (MSOD) – NP-Complete Suurballe & Tarjan algorithm is no longer applicable Shared protection results in MSOD, with the additional difficulty that the cost of the protection path depends on the choice of the active path: C(AP)+C’(BP).

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13 Resilient Routing Complexity of underlying problems ProblemDedicated Protection Shared Protection Min-MinNP-Complete [1] Min-SumPolinomial [2] NP-Complete [1] Min-MaxNP-Complete [3] [4] [1] Dahai Xu, et al., “On Finding Disjoint Paths in Single and Dual Link Cost Networks,” INFOCOM’04, March 2004. [2] J. W. Surballe, et al., “A Quick Method for Finding Shortest Pairs of Disjoint Paths,” Networks, 14:325–336, 1984. [3] Arunabha Sen, et al., “Survivability of Lightwave Networks - Path Lengths in WDM Protection Scheme,” Journal of High Speed Networks, 10(4):303-315, 2001. [4] Li, et al., “The Complexity of Finding Two Disjoint Paths with Min-Max Objective Function,” Discrete Applied Mathematics, 26(1):105–115, Jan. 1990.

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14 Resilient Routing Shared Risk Link Group (SRLG) Finding a SRLG disjoint path pair: NP-Complete Therefore any optimisation problem… Routing with the λ-continuity constraint is also NP-Complete! fiber span Active Path A-B Backup Path A-B B DC A B DC A B DC A Link TopologySRLG Topology

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15 Resilient Routing BasicLink Method [Li02] Basic Link: A link that transverses only one fiber span. A link that traverses multiple fiber spans but it is the only link in those spans. Construct a topology with only basic links. Find a pair of link disjoint paths (Suurballe). Select first path as the AP. [Li02] Guangzhi Li, et al., “Fiber Span Failure Protection in Mesh Optical Networks,” Optical Networks Magazine, 3(3):21-31, 2002.

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16 Resilient Routing BasicLink Method cont. Second path is SRLG disjoint and can be the Backup Path, but a better path can be found easily: Delete links along the first path in the original graph, find the shortest path use it as backup path. Problems Uses only basic links for the AP selection. May fail too (like TSA), although two SRLG disjoint paths exists.

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17 Resilient Routing Bypass Method [Li02] The basic idea is to construct a single layer sub- network over the original optical network and find two Link disjoint paths on the constructed sub-network. Compute shortest path p from s to d: p = (s=a 1, a 2,..., a k =d) If second path fail, construct a directed auxiliary graph H with k nodes, (labeled 1,..., k). Delete all links along path p in the original graph, and the links that belong to the same SRLGs. [Li02] Guangzhi Li, et al., “Fiber Span Failure Protection in Mesh Optical Networks,” Optical Networks Magazine, 3(3):21-31, 2002.

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18 Resilient Routing Bypass Method cont. If there is a path from a i to a j - add a direct edge from i to j in H Add back edges from i to i -1 (i=2,..., k) Run Dijkstra’s algorithm on H. If we find a path in H from 1 to K then its possible to find two link disjoint paths on H, without considering the arc direction.

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19 Resilient Routing Bypass Method cont. Better than BasicLink Method – allows both paths to use non basic links. Problems The two paths may not be SRLG disjoint (links 1-4 and 3-6 may belong to the same SRLG). 123456 123456

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20 Resilient Routing Graph Transformation Technique Add dummy nodes for each SRLG and new edges (graph H) Apply Edge Disjoint Shortest Cycle Algorithm (Bhandari) to H. The two paths derived from shortest cycle on H gives two SRLG disjoint routes. d1 d2 d3 3 6 4 5 1 2 3 6 4 5 1 2 [Datta04] Pallab Datta et al., “Diverse Routing for Shared Risk Resource Groups (SRRG) Failures in WDM Optical Networks,” First International Conference on Broadband Networks, BROADNETS’04, 2004. [Datta04]

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21 Resilient Routing Graph Transformation Technique Problems Only applies if: Each SRLG size is smaller than the degree of the node on which the group is incident. A link can be shared between almost two SRLG.

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22 Resilient Routing KSP - K Shortest Paths Natural extension of TSA (Two Step Approach). Compute K shortest paths as candidate APs. Test them one by one in increasing order of their costs, until an SRLG disjoint path is found (or all of them have been tested). Problems: If current candidate AP fails the test, the next candidate is selected only based in cost, without considering which link(s) in current AP caused the trap. Many candidate APs have to be tested. The path pair is not optimal.

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23 Resilient Routing JPS-Joint Path Selection [Xin02] Compute k shortest paths as candidate APs (AP i, i=1,…, k, with cost C AP i ). For each AP i compute the shortest SRLG disjoint path BP i (with cost C BP i ). Find h such that C AP h + C BP h =min( C AP i + C BP i ), 1 i k. Select AP h as service path and BP h as Backup Path. [Xin02] Chunsheng Xin, et al., “A Joint Lightpath Routing Approach in Survivable Optical Networks,” Optical Networks Magazine, 3(3):13-20, 2002. Link Cost Function Integrated link cost function (additive) based in hop-count and available ’s:

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24 Resilient Routing JPS-Joint Path Selection cont. Path Cost Function Active Path Cost: Backup Path Cost: Dedicated Protection: Shared Protection: - sharing control weight

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25 Resilient Routing ITSA-Iterative Two-Step Approach [Ho03] Pin-Han Ho, et al., “Diverse routing for shared protection in survivable optical networks,” IEEE Global Telecommunications Conference, GLOBECOM'03, Vol. 5, pp. 2519-2523, 2003. Enhancement of the TSA. Repeats TSA iteratively, in which each k-shortest path is taken as a working path in each iteration. Start with shortest path as the AP in the first iteration. Repeat until stop condition is met. Find spare link state capacity in each link, according to AP. Compute BP, according spare link state capacity. Update the best path pair. Compute next AP (next shortest path) and repeat [Ho03]

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26 Resilient Routing ITSA-Iterative Two-Step Approach The stop condition uses more than one criteria: Optimal Path Pair found Predefined number of iterations Optimality check If the cost of candidate AP is greater than the cost of the current best path pair Advantage: guarantees the derivation of the best working and protection path-pair under the current link-state provided a sufficient amount of time. Disadvantage: Number of APs that need to be explored grows exponentially with network size.

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27 Conclusion The RWA in survivable networks is a difficult problem Many heuristics have been proposed We intend to develop a multiobjective model, exploring the trade-offs between: Blocking Probability Fairness Impact of accepting a connection in future requests (future cost/shadow price)

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