Stochastic Petri nets with matrix exponentially distributed firing times

There are widely used analysis techniques for stochastic Petri nets with phase type (PH) distributed firing times. These techniques are based on the generation of an expanded Markov chain that describes the behaviour of the marking process and additionally the phase processes of the involved PH distributions. In this paper we investigate the use of a similar approach when the firing time distribution does not allow a stochastic interpretation. We show that the same expansion based technique is applicable in case of matrix exponentially (ME) distributed firing times, but in this case the system does not allow any stochastic interpretation and the applied solution methods should not be restricted to non-negative numbers. Nevertheless, by defining an equivalence between PH and ME distributions it can be shown that marking probabilities remain the same when PH distributions are substituted by equivalent ME distributions.