Blocking in wavelength routing networks .I. The single path case

We study a class of circuit-switched wavelength routing networks with and without wavelength converters, and we present the first part of a new analytical framework to accurately and efficiently evaluate the blocking performance of such networks. The model allows non-uniform traffic, it accounts for the correlation among the loads at all links in a path, and it can be used when the location of converters is fixed but arbitrary. We first construct an exact Markov process that captures the behaviour of a path in terms of wavelength use. We also obtain an approximate Markov process which has a closed-form solution that can be efficiently computed for short paths. We then develop an iterative algorithm to analyze approximately arbitrarily long paths. The algorithm decomposes a path into shorter segments which are then studied in isolation using the corresponding approximate Markov process. The individual solutions are appropriately combined to obtain a solution for the original path. Finally, we demonstrate how the analytical techniques can be used to gain insight into the problem of converter placement in wavelength routing networks.