Equivalence via Stochastic and Continuous Petri Nets for Modeling of Large Systems with Availability Constraints

High availability constraints ensure a high level of operational performance that must be maintained during a contractual measurement period. Such constraints must be satisfied, particularly, for critical systems related to global security and human safety. High availability often results from material redundancies and lead to large stochastic discrete event models with numerous states. Markov processes and stochastic Petri nets can be used to model, simulate and analyse such systems but their use is limited by the so called “combinatorial explosion” problem. This paper investigates the fluidification of stochastic Petri nets to overcome the previous problem. The main contribution is to propose a modular modeling of active and passive redundancies with Petri nets. Some approaches are then proposed to obtain equivalent behaviors in the long time with stochastic and continuous Petri nets. General terms: SPN: stochastic petri net, PDF: probability density functions, contPNs: continuous Petri nets, rv: random variable KeywordsReliability analysis; Redundancies; Petri nets; Fluidification.