Monte Carlo Estimation of the Mean Queue Size in a Stationary GI/M/1 Queue

The serial correlation coefficients of queue sizes in a stationary GI/M/1 queue are studied. It is shown in particular that when the traffic intensity τ is near 1, estimation of the mean queue size from a simulation run of length N requires that N ≈ K(l − τ)⁻² for some constant K in order that the sample means over a range of τ should have approximately the same coefficient of variation.