Regenerative simulation for multiclass open queueing networks

Abstract

Conceptually, under restrictions, multiclass open queueing networks are positive Harris recurrent Markov processes, making them amenable to regenerative simulation for estimating the steady-state performance measures. However, regenerations in such networks are difficult to identify when the interarrival times are generally distributed. We assume that the interarrival times have exponential or heavier tails and show that such distributions can be decomposed into mixture of sums of independent random variables such that at least one of the components is exponentially distributed. This allows an implementable regenerative simulation for these networks. We show that the regenerative mean and standard deviation estimators are consistent and satisfy a joint central limit theorem. We also show that amongst all such interarrival decompositions, the one with largest mean exponential component minimizes the asymptotic variance of the standard deviation estimator. We also propose a regenerative simulation method that is applicable even when the interarrival times have superexponential tails.