Letter to the Editor—Stopping Rules for Queuing Simulations

In queuing simulations when service times and/or inter-arrival times are exponentially distributed it is possible to obtain independent estimates of the quantities of interest, such as the probability of a request being served immediately or the proportion of requests that are delayed more than say t time units. It is shown that a weighted average of estimates of the probability of being served immediately is asymptotically unbiased for two simple queuing systems; it is also shown that an unweighted average is biased for one of these systems. Because the estimates are independent, the calculation of the variance of the weighted average is simplified. Expressions are presented for the calculation of the mean and variance of the estimate of interest. This paper presents only the nucleus of an idea and indicates several areas where research should prove useful.