Optical switch dimensioning and the classical occupancy problem

Results for optical switch dimensioning are obtained by analysing an urn occupancy problem in which a random number of bails is used. This analysis is applied to a high speed bufferless optical switch which uses tuneable wavelength converters to resolve contention between packets at the output fibres. Under symmetric packet routing the urn problem reduces to the classical occupancy problem. Since the problem is large scale and the loss probabilities are small, exact analysis by combinatorial methods is problematic. As an alternative, we outline a large deviations approximation which may be generalised in various ways.