Planning Queueing Simulations

Simple heuristic formulas are developed to estimate the simulation run lengths 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 simulation run length 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 for stability) and associated diffusion approximations. In particular, the formulas apply to stochastic processes that can be approximated by reflected Brownian motion, such as the queue-length process in the standard GI/G/1 model.