Exploiting Non-deterministic Analysis in the Integration of Transient Solution Techniques for Markov Regenerative Processes

Abstract

Transient analysis of Markov Regenerative Processes (MRPs) can be performed through the solution of Markov renewal equations defined by global and local kernels, which respectively characterize the occurrence of regenerations and transient probabilities between them. To derive kernels from stochastic models (e.g., stochastic Petri nets), existing methods exclusively address the case where at most one generally-distributed timer is enabled in each state, or where regenerations occur in a bounded number of events. In this work, we analyze the state space of the underlying timed model to identify epochs between regenerations and apply distinct methods to each epoch depending on the satisfied conditions. For epochs not amenable to existing methods, we propose an adaptive approximation of kernel entries based on partial exploration of the state space, leveraging heuristics that permit to reduce the error on transient probabilities. The case study of a polling system with generally-distributed service times illustrates the effect of these heuristics and how the approach extends the class of models that can be analyzed.