Abstract
We consider the efficient estimation, via simulation, of very low buffer overflow probabilities in certain acyclic ATM queueing networks. We apply the theory of effective bandwidths and Markov additive processes to derive an asymptotically optimal simulation scheme for estimating such probabilities for a single queue with multiple independent sources, each of which may be either a Markov modulated process or an autoregressive process. This result extends earlier work on queues with either independent arrivals or with a single Markov modulated arrival source. The results are the extended to estimating loss probabilities for intree networks of such queues. Experimental results show that the method can provide many orders of magnitude reduction in variance in complex queueing systems that are not amenable to analysis. © 1994.