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A computation method for scenario studies in WDM network planning

James Yiming Zhang (School of Information Technology and Engineering, University of Ottawa, Ottawa, Canada)
Jing Wu (Communications Research Centre (CRC) Canada, Ottawa, Canada)
Gregor v. Bochmann (School of Information Technology and Engineering, University of Ottawa, Ottawa, Canada)
Michel Savoie (Communications Research Centre (CRC) Canada, Ottawa, Canada)



The purpose of this paper is to present the benefits of using the Lagrangian relaxation (LR) and subgradient methods in scenario studies for wavelength division multiplexing (WDM) network planning. The problem of WDM network planning for a given set of lightpath demands in a mesh topology network is to select lightpath routes and then allocate wavelength channels to the lightpaths. In WDM network planning, a scenario study is to find out the network performance under different lightpath demands and/or different network resource configurations.


A scenario study must solve a series of related static WDM network planning problems. Each static WDM network planning problem is an optimization problem, and may be formulated as an integer linear programming problem, which can be solved by the proposed Lagrangian relaxation and subgradient methods. This paper uses the Lagrange multipliers that are obtained from previous scenarios as initial Lagrange multiplier values for other related scenarios.


This approach dramatically reduces the computation time for related scenarios. For small to medium variations of scenarios, the method reduces the computation time by several folds. The proposed method is the first method that effectively considers the relations between related scenarios, and uses such relations to improve the computation efficiency of scenario studies in WDM network planning.

Practical implications

The method improves the efficiency of a scenario study in WDM network planning. By using it, many “what‐if” type of scenario study questions can be answered quickly.


Unlike other existing methods that treat each scenario individually, this method effectively uses the information of the relation between different scenarios to improve the overall computation efficiency.



Yiming Zhang, J., Wu, J., v. Bochmann, G. and Savoie, M. (2009), "A computation method for scenario studies in WDM network planning", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 28 No. 6, pp. 1632-1646.



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Copyright © 2009, Emerald Group Publishing Limited

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