Regenerative generalized semi-markov processes

Abstract

A generalized semi-Markov process (GSMP) is the usual model for a discrete event simulation. The standard formulation assumes that the current state of the process uniquely determines the set of events that are scheduled to occur and that the state transition probabilities depend only on the current state, the next state, and the trigger event. We provide a formulation of a GSMP that avoids these restrictions, thus permitting formal specification of many non-Markovian simulation models. Using a monotone replacement property of “new better than used” distributions and sample path properties of the GSMP, we provide a criterion for recurrence in this setting and conditions under which a GSMP is a regenerative process and the time between regeneration points has finite moments. Steady state estimation methods for non-Markovian stochastic network simulations follow.