| In this dissertation, we study the accuracy and performance of simulating M/Pareto/1 queues when the Pareto shape parameter is between one and three. This problem has wide interest, from economics to telecommunications, and has recently been the focus of attention. In economics, one instance of the problem is determining the ruin probability associated with insurance claim processes having Pareto distributed claim sizes. In telecommunications, one example is estimating the delay due to transmitting files along the same path as a number of IP packets from one source to one destination (i.e. downloads from the WWW). The Pareto distribution is appropriate for these applications because it closely reflects the empirical data associated with insurance claim amounts and the size of files retrieved from servers connected to the Internet. That is, the Pareto distribution models a preponderance of small values, with some large observations occurring with nonnegligible probability. As the Pareto distribution's shape parameter decreases, the likelihood of a large observation increases. When the shape parameter is between one and three, the problem is especially interesting.; We provide the following results. When the shape parameter is greater than two and less than or equal to three, we derive the theoretical distribution of the sample averages of the queue waiting times. Next, we quantify simulation accuracy for obtaining the mean queue waiting time. Then, when simulations to obtain the mean queue waiting time cannot achieve the desired accuracy, we establish guidelines for switching the simulation performance measure from the mean queue waiting time to simulating quantiles of the queue waiting-time distribution. Where the mean does not exist (α ≤ 2), this new performance measure is also appropriate. This change of performance measure requires a different simulation approach. Therefore, we modify a quantile simulation method. Our method solves problems where other methods cannot, requires less memory, and provides the user the choice of emphasizing accuracy or execution time in obtaining quantile estimates. Our results provide guidance to practitioners concerning simulation accuracy, processing time, and parameter selection. |
