Efficient estimation of overflow probabilities in queues with breakdowns

Abstract

Efficient importance sampling methods are proposed for the simulation of a single server queue with server breakdowns. The server is assumed to alternate between the operational and failure states according to a continuous time Markov chain. Both, continuous (fluid flow) and discrete (single arrivals) sources are considered. In the fluid flow model, we consider Markov-modulated fluid sources and a constant output rate when the server is operational. In the discrete arrivals model, we consider Markov-modulated Poisson sources 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 models. The concept of effective bandwidth is used in models with multiple independent sources. Empirical studies demonstrate the effectiveness of the proposed change of measures when used in importance sampling simulations.