Tolerance intervals for stochastic processes with timed continuous Petri nets

Abstract

Reliability analysis is often based on stochastic discrete event models like stochastic Petri nets. For complex dynamical systems with numerous components, analytical expressions of the stochastic process are tedious or even impossible to work out because of the combinatorial explosion with discrete models. For this reason, fluidification is an interesting alternative to approximate the asymptotic behavior of stochastic processes with timed continuous Petri nets. Unfortunately, these approximations only concern the average behavior and does not give any information about the dispersion of the behaviors. Moreover, the approximation errors are difficult to evaluate. In order to overcome these limitations, tolerance intervals for the firing rates and marking vector are computed with timed continuous Petri nets and binomial models in order to determine the domains of high probability of the stochastic process.