Abstract
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).
Highlights
Reliability analysis is a major challenge to improve the safety of industrial processes
Concerning stochastic Petri nets (SPNs), the approximation of the steady state by Continuous Peti nets (CPNs) is of particular interest as long as the estimation of the asymptotic mean markings can be used to work out the availability, the mean time between failures, and other indicators for reliability
This paper has pointed out that the asymptotic behaviour of SPNs cannot be trivially approximated with CPNs
Summary
Reliability analysis is a major challenge to improve the safety of industrial processes. For complex dynamical systems with numerous interdependent components, such studies are mainly based on stochastic discrete event models like Markov models or stochastic Petri nets (SPNs) [8]. Such models are mathematically well founded and can be investigated in order to work out either analytical results or numerical simulations. In case of large systems, the combinatory explosion limits their use In this context, fluidification can be discussed as a relaxation method. The aim of this paper is to discuss the estimation of the SPNs asymptotic mean markings by using fluid models and to introduce new semantics of Continuous Peti nets (CPNs) for that issue.
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