Stochastic Petri nets simplification with singular perturbations

In this paper, we introduce a new simplification of stochastic Petri net models. This simplification uses the singular perturbation method for discrete event systems in continuous time. We adapt this method for stochastic Petri net models. The model studied should have the double time scale property in order to apply this method of simplification. The decoupling method gives us two sub-systems, a fast and a slow evolution. These evolutions are the probabilities to be in a certain marking of the stochastic Petri net. For these two sub-systems, we only preserve the slow evolution of the marking probabilities, which yields the most precision given by the singular perturbation in continuous time. The main advantage of this method is to reduce the number of places and/or transitions of the stochastic Petri net. The calculation of the performance rates is then simplified. For complex stochastic Petri net models, this method allows one to draw the sub-system with a slow evolution.