Using importance sampling to simulate queuing networks with heavy-tailed service time distributions

Abstract

Characterization of steady-state queue length distributions using direct simulation is generally computationally prohibitive. We develop a fast simulation method by using an importance sampling approach based on a change of measure of the service time in an M/G/1 queue. In particular, we present an algorithm for dynamically finding the optimal distribution within the parametrized class of delayed hazard rate twisted distributions of the service time. We run it on a M/G/1 queue with heavy-tailed service time distributions and show simulation gains of two orders of magnitude over direct simulation for a fixed confidence interval.