Regenerative rare events simulation via likelihood ratios

Abstract

In this paper we obtain some new theoretical and numerial results on estimation of small steady-state probabilities in regenerative queueing models by using the likelihood ratio (score function) method, which is based on a change of the probability measure. For simple GI/G/1 queues, this amounts to simulating the regenerative cycles by a suitable change of the interarrival and service time distribution, typically corresponding to a reference traffic intensity ρ0 which is < 1 but larger than the given one ρ. For the M/M/1 queue, the resulting gain of efficiency is calculated explicitly and shown to be considerable. Simulation results are presented indicating that similar conclusions hold for gradient estimates and in more general queueing models like queueing networks.