Simulating M/G/1 queues with heavy-tailed service

We examine the performance and accuracy of simulating M/G/1 queues when the service time is Pareto distributed with shape parameter, alpha, between one and three. Two applications of this problem are in insurance risk and telecommunications. When 2 < alpha <= 3, the theoretical distribution of the sample averages of the queue waiting times is a stable distribution. When alpha <= 2, the mean waiting time does not exist. We provide a modified quantile simulation method, which is able to solve harder problems than existing methods; in addition, it requires less memory, and allows the user to emphasize accuracy or execution time. We also give numerical examples for other heavy-tailed distributions, such as the lognormal.