Planning queueing simulations.

Simple heuristic formulas are developed to estimate the data required to achieve desired statistical precision in queueing simulations. The formulas are intended to help in the early planning stages before any data have been collected. The queueing simulations considered are single replications (one long run) conducted to estimate steady-state characteristics such as expected equilibrium queue lengths. The formulas can be applied to design simulation experiments to develop and evaluate queueing approximations. In fact, this work was motivated by efforts to develop approximations for packet communication networks with multiple classes of traffic having different service characteristics and bursty arrival processes. In addition to indicating the approximate sample size required in each case of a designed experiment, the formulas can help determine what cases to consider, what statistical precision to aim for, and even whether to conduct the experiment at all. The formulas are based on heavy- traffic limits for queues (the limiting behavior as the traffic intensity approaches its upper limit) and associated diffusion approximation.