Reliability analysis of discrete model by continuous model: fluidisation approaches

Abstract

This article addresses challenges in the reliability analysis of complex systems using stochastic models. Discrete models like stochastic Petri nets face difficulties in obtaining steady state analytical expressions due to the complexity of dynamic systems. To overcome this, the paper introduces fluidisation, employing continuous Petri nets for predicting stochastic processes' asymptotic behaviour. However, disparities arise in the asymptotic average markings between stochastic and continuous Petri nets with identical structures. The paper proposes two methods to approximate the steady state of similar stochastic Petri nets using continuous Petri nets. The adaptive approach dynamically adjusts firing speeds over time, while the geometric method delineates regions for a partial homothetic approximation of the stochastic steady state. These contributions enhance reliability analysis in complex systems by reconciling discrepancies between stochastic and continuous modelling.