The method of stochastic state classes provides a new approach for theanalysis of non-Markovian stochastic Petri Nets, which relies on thestochastic expansion of the graph of non-deterministic state classes basedon Difference Bounds Matrix (DBM) which is usually employed in qualitativeverification.In so doing, the method is able to manage multiple concurrentnon-exponential (GEN) transitions and largely extends the class of modelsthat are amenable to quantitative evaluation.However, its application requires that every cycle in the graph ofnon-deterministic state classes visits at least a regeneration point whereall GEN transitions are newly enabled.In particular, this rules out models whose non-deterministic class graphincludes cycles within a Continuous Time Markov Chain (CTMC) subordinatedto the activity period of one or more GEN transitions.In this paper, we propose an extension that overcomes thislimitation by aggregating together classes that are reachedthrough firings that do not change the enabling status of GENtransitions.This enlarges the class of models that can be analysed through themethod of stochastic state classes and makes it become a properextension of the class of models that satisfies the so calledenabling restriction.
['András Horváth', 'Enrico Vicario']
Aggregated Stochastic State Classes in Quantitative Evaluation of non-Markovian Stochastic Petri Nets