Title: Stochastic and continuous Petri nets approximation of Markovian model

Authors: Hamid El-Moumen; Nabil El Akchioui; Mohammed Hassani Zerrouk

Addresses: Faculty of Sciences and Technology Al Hoceima, University Abdelmalek Essaadi, Morocco ' Faculty of Sciences and Technology Al Hoceima, University Abdelmalek Essaadi, Morocco ' Faculty of Sciences and Technology Al Hoceima, University Abdelmalek Essaadi, Morocco

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.

Keywords: reliability analysis; Markov model; reachability graph; RG; combinatorial explosion; stationary state; stochastic Petri nets; SPN; fluidification; continuous Petri nets; CPN.

DOI: 10.1504/IJMIC.2024.135571

International Journal of Modelling, Identification and Control, 2024 Vol.44 No.1, pp.97 - 106

Received: 07 Nov 2022
Accepted: 21 Apr 2023
Published online: 18 Dec 2023 *

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