Aggregated Stochastic State Classes in Quantitative Evaluation of non-Markovian Stochastic Petri Nets

The method of stochastic state classes provides a new approach for the analysis of non-Markovian stochastic Petri Nets, which relies on the stochastic expansion of the graph of non-deterministic state classes based on Difference Bounds Matrix (DBM) which is usually employed in qualitative verification. In so doing, the method is able to manage multiple concurrent non-exponential (GEN) transitions and largely extends the class of models that are amenable to quantitative evaluation. However, its application requires that every cycle in the graph of non-deterministic state classes visits at least a regeneration point where all GEN transitions are newly enabled. In particular, this rules out models whose non-deterministic class graph includes cycles within a Continuous Time Markov Chain (CTMC) subordinated to the activity period of one or more GEN transitions. In this paper, we propose an extension that overcomes this limitation by aggregating together classes that are reached through firings that do not change the enabling status of GEN transitions. This enlarges the class of models that can be analysed through the method of stochastic state classes and makes it become a proper extension of the class of models that satisfies the so called enabling restriction.