A binary (0-1) linear program formulation for the placement of limited-range wavelength converters in wavelength-routed WDM networks

We investigate the problem of optimally placing limited-range wavelength converters at a subset of nodes in wavelength-routed wavelength-division-multiplexing (WDM) networks. We consider two different aspects of the converter-placement problem: 1) the placement minimizing the network-wide blocking probability; and 2) the placement minimizing the number of wavelength-convertible nodes to meet the performance constraints. We present a binary (0-1) linear program (BLP) formulation in which the end-to-end blocking probability is expressed as a linear function of converter locations so that standard linear program (LP) optimization packages can be employed to obtain the optimal solution of the problems. We also present a new analytical model for estimating the end-to-end blocking probabilities. Experiments have been conducted over four network topologies, including 19-node European optical network (EON), 24-node USA backbone network (UBN), 32-node HYPERCUBE, and 36-node MESH-TORUS. We demonstrate that the optimal solutions of the converter-placement problems can be obtained within a reasonable computation time.