Simulating Stable Stochastic Systems, II: Markov Chains

Abstract

A technique for simulating GI/G/s queues is shown to apply to simulations of discrete and continuous-time Markov chains. It is possible to address questions of simulation run duration and of starting and stopping simulations because of the existence of a random grouping of observations which produces independent identically distributed blocks from the start of the simulation. This grouping allows confidence intervals to be obtained for a general function of the steady-state distribution of the Markov chain. The technique is illustrated with simulation of an (s, S) inventory model in discrete time and the classical repairman problem in continuous time. Consideration is also given to determining system sensitivity to errors and uncertainty in the input parameters. © 1974, ACM. All rights reserved.