An optimization model for placement of wavelength converters to minimize blocking probability in WDM networks

The introduction of wavelength converters in wavelength division multiplexing (WDM) networks can reduce the blocking probabilities of calls. In this paper, we study the problem of placing a given number of converters in a general topology WDM network such that the overall system blocking probability is minimized. The original contributions of this work are the following: 1) formulation of success probability in a network as a polynomial function of the locations of converters; 2) proposal of an optimization model of the converter placement problem as the minimization of a polynomial function of 0-1 variables under a linear constraint, so that standard optimization tools can be employed to solve the problem; and 3) design of a search algorithm that can efficiently find the optimal solution to the converter placement problem. Experiments have been conducted to demonstrate the effectiveness of the proposed model and the efficiency of the algorithm.