Accelerated Consistent Estimation of a High Load Probability in M/G/1 and GI/G/1 Queues*

Abstract

A special speed-up simulation technique based on a combination of splitting and regenerative approach is developed to estimate a rare event probability. A consistent estimation of the probability that the workload process in M /G/1 and GI/G/1 queues exceeds a high level within a regeneration cycle is considered. A similar problem is studied for the queue-size process in an M /G/1 queue. The key element of the approach is to consider an embedded Markov chain instead of the original non-Markovian process. A comparison with the known analytical results and with the crude Monte Carlo (CMC) simulation shows a high efficiency of the approach.