Stochastic Continuous Petri Nets: An Approximation of Markovian Net Models

Fluidization constitutes a relaxation technique to study discrete event systems through a continuous approximated model, thus overcoming the state explosion problem. In this paper, the approximation of the average marking of Markovian Petri nets by the marking of the corresponding timed continuous Petri nets, under infinite-server semantics, is studied. This represents a sort of legitimization for the use of a continuous Petri net as a relaxation of a discrete Petri net. The main contribution is the addition of Gaussian noise in order to improve the approximation when the number of active servers (enabling degree) is large. The improvement is more evident when the system evolves "close" to the boundary of regions. In such a case, not only the expected value but also the probability distribution function of the marking may be approximated.