Control of initialization bias in queueing simulations using queueing approximations

Investigates the use of analytical queueing approximations to assist in mitigating the effects of the initial transient period in steady-state GI/G/m queueing simulations. We investigate using queueing approximations to stochastically set the initial conditions of the simulation and we develop a new set of truncation heuristics based on GI/G/m queueing approximations. The new truncation heuristics are based on finding the truncation point in the simulation sample path which minimizes the mean squared error of the point estimator. Given that an approximation can be found, our methodology reduces the need for pilot runs and can easily be incorporated into a simulation, with significant results. We present the performance of the heuristics for replication deletion. The adaption to batch means is discussed. The result of our methodology is a less biased and less variable estimator of the expected wait time in the queue. We used the Extend simulation package for this research on a Macintosh Quadra 840AV.