A path decomposition approach for computing blocking probabilities in wavelength-routing networks

We study a class of circuit-switched wavelength-routing networks with fixed or alternate routing and with random wavelength allocation. We present an iterative path decomposition algorithm to evaluate accurately and efficiently the blocking performance of such networks with and without wavelength converters. Our iterative algorithm analyzes the original network by decomposing it into single-path subsystems. These subsystems are analyzed in isolation, and the individual results are appropriately combined to obtain a solution for the overall network. To analyze individual subsystems, we first construct an exact Markov process that captures the behavior of a path in terms of wavelength use. We also obtain an approximate Markov process which has a closed-form solution that can be computed efficiently for short paths. We then develop an iterative algorithm to analyze approximately arbitrarily long paths. The path decomposition approach naturally captures the correlation of both link loads and link blocking events. Our algorithm represents a simple and computationally efficient solution to the difficult problem of computing call-blocking probabilities in wavelength-routing networks. We also demonstrate how our analytical techniques can be applied to gain insight into the problem of converter placement in wavelength-routing networks