Approximation of the asymptotic mean marking of SPNs with contPNs

Reliability analysis is based on stochastic discrete event models like stochastic Petri nets. For complex dynamical systems with numerous components, analytical expressions of the steady state are tedious to work out because of the combinatory explosion with discrete models. For this reason, fluidification is investigated to estimate the asymptotic behavior of stochastic processes and the stationary indicators used for reliability issues. Unfortunately, the asymptotic mean markings of stochastic and continuous Petri nets are mainly often different. This paper proposes approximations of the stochastic steady state according to a set of reference data and to the classification of the firing rates, based on a kk-nearest-neighbor method. This method maps the parameters of the stochastic model with the ones of the fluid model. It leads to the design of modified timed continuous Petri nets suitable to approximate the steady state of any stochastic Petri net.