Efficient estimation of overflow probabilities in queues with breakdowns

Efficient importance sampling methods are proposed for the simulation of a single server queue with server breakdowns. The server is assumed to altern ate between the operational and failure states according to a continuous ti me Markov chain. Both, continuous (fluid flow) and discrete (single arrival s) sources are considered. In the fluid flow model, we consider Markov-modu lated fluid sources and a constant output rate when the server is operation al. In the discrete arrivals model, we consider Markov-modulated Poisson so urces and generally distributed service time when the server is operational . We show how known results on Markov additive processes may be applied to determine the optimal (exponentially tilted) change of measure for both mod els. The concept of effective bandwidth is used in models with multiple ind ependent sources. Empirical studies demonstrate the effectiveness of the pr oposed change of measures when used in importance sampling simulations. (C) 1999 Elsevier Science B.V. All rights reserved.