Exact and approximate analysis of ATM cell loss correlation

Cell loss behavior is analyzed for an ATM switch with homogeneous Markov sources. While prior work in this regard has focused mainly on measures such as the steady-state loss probability and conditional loss probability, we consider a more refined measure, namely the probability distribution of a cell loss period. Evaluation is based on a discrete-time, finite-state Markov process where cell arrivals at each input port are represented by an (M+1)-state source model (M ON states and one OFF state). Although we are able to formulate the loss period distribution exactly, for switches with realistic dimensions, the associated computational cost is high. As an alternative, we find that the loss period distribution is essentially insensitive to the buffer capacity K and, more importantly, its companion tail distribution can be accurately approximated by a relatively simple expression. As evidenced by numerical results, the errors of approximation are small and indeed, in many instances, the results obtained are effectively the same as those of an exact analysis.