Interval coverage in multiclass queues using batch mean estimates

We investigate the fixed, sample-size, batch-mean procedure for creating confidence intervals from simulated data obtained from a stochastic queueing system with multiple customer classes. We show that, for a multiclass M/M/1 queue, serial correlation between customers of the same class decreases to zero as the number of customer classes increases. We also derive a closed-form expression for the asymptotic variance of waiting time by customer type. We then empirically examine batch-mean estimator coverage for a simple queue with multiple customer classes. We find that batch-mean estimators perform better in terms of coverage and interval half width in multiclass queues, with a fixed number of observations per class, than in the traditionally studied single-class systems. We also examine the effect of multiple classes where the total computational effort remains fixed.