Stochastic and continuous Petri nets approximation of Markovian model

Abstract

Stochastic Petri nets (SPN) or Markov models (MC) are often more effective in the reliability analysis of discrete event systems. However, they present a problem of combinatorial explosion of the number of states when the systems present several interdependent components. This problem limits the use of the MC. The SPN is considered a Markov estimator, but it has a slow convergence in the calculations of stationary state probabilities. The continuous Petri nets (CPN) are developed to accelerate this convergence by capturing the SPN behaviour. This study considers three different Petri nets (PN) types. Simulations with the MC, SPN, and CPN, are presented and compared in different PN types. The obtained results show that the MC and the SPN have identical behaviour in the general case. Furthermore, the CPN exhibits identical behaviour in the first type, which is not the case in the other two types.