Fluidification of Stochastic Petri Net by Non Linear Timed Continuous Petri Net

Reliability analysis is often based on stochastic discrete event models like Markov models or 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. Moreover, the convergence of stochastic estimators is slow. For these reasons, fluidification can be investigated to estimate the asymptotic behaviour of stochastic processes with timed continuous Petri nets. The contributions of this paper are to sum up some properties of the asymptotic mean marking and average throughputs of stochastic and timed continuous Petri nets, then to point out the limits of the fluidification in the context of the stochastic steady state approximation. To overcome these limitations, the new semantic and the condition for convergence is proposed: fluid Petri nets with Non Linear Timed Continuous Petri Net (NL-CPN).