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Design of Logical Topologies: A Linear Formulation for Wavelength-Routed Optical Networks with No Wavelength Changers

Krishnaswamy, Rajesh M and Sivarajan, Kumar N (2001) Design of Logical Topologies: A Linear Formulation for Wavelength-Routed Optical Networks with No Wavelength Changers. In: IEEE/ACM Transactions on Networking, 9 (2). pp. 186-198.


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We consider the problem of constructing logical topologies over a wavelength-routed optical network with no wavelength changers. We present a general linear formulation which considers routing traffic demands, and routing and assigning wavelengths to lightpaths, as a combined optimization problem. The formulation also takes into account the maximum number of hops a lightpath is permitted to take, multiple logical links in the logical topology, multiple physical links in the physical topology, and symmetry/asymmetry restrictions in designing logical topologies. The objective is to minimize congestion. We show by examples how equality and inequality logical degree constraints have a bearing on congestion. We prove that, under certain conditions, having equality degree constraints with multiple edges allowed in the design of logical topologies does not affect congestion. This helps in reducing the dimensionality of the search space and hence speeds up the search for an optimal solution of the linear formulation.We solve the linear formulation for small examples and show the tradeoff between congestion, number of wavelengths available and the maximum number of hops a lightpath is allowed to take. For large networks, we solve the linear formulation by relaxing the integer constraints. We develop topology design algorithms for large networks based on rounding the solutions obtained by solving the relaxed problem. Since the whole problem is linearizable, the solution obtained by relaxation of the integer constraints yields a lower bound on congestion. This is useful in comparing the efficiency of our heuristic algorithms. Following Bienstock and Gunluk, 1995, we introduce a cutting plane which helps in obtaining better lower bounds on congestion and also enables us to reduce the previously obtained upper bounds on congestion.

Item Type: Journal Article
Publication: IEEE/ACM Transactions on Networking
Publisher: ACM Press
Additional Information: ©2001 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Keywords: All-optical networks;linear program;network planning;topology design
Department/Centre: Division of Electrical Sciences > Electrical Communication Engineering
Date Deposited: 22 Aug 2008
Last Modified: 19 Sep 2010 04:12
URI: http://eprints.iisc.ac.in/id/eprint/269

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