Regenerative Aspects of the Steady-State Simulation Problem for Markov Chains

P. W. Glynn

Technical Report, Department of Operations Research, Stanford University (1982)

The general discrete-event simulation can be viewed, by using the technique of supplementary variables, as a Markov chain living in a general state space. For such chains, we can define in precise terms, the notion of an associated well-posed steady-state simulation problem. We prove that the concept of well-posedness is equivalent to assuming that the Markov chain has regenerate-type structure. These two conditions are, in turn, equivalent to assuming a certain smoothness on the transition probabilities of the chain. We also consider two examples which illustrate how a chain can fail to have regenerate-type structure.