Transient Evaluation of Non-Markovian Models by Stochastic State Classes and Simulation

TL;DR

This paper presents a hybrid approach combining Stochastic State Classes and simulation to efficiently analyze transient properties of complex non-Markovian models, especially for rare event estimation.

Contribution

It introduces a method that integrates SSCs with simulation to improve transient analysis and rare event probability estimation in non-Markovian models.

Findings

Reduced computational time compared to pure simulation.

Improved variance reduction in rare event probability estimates.

Effective analysis of models where SSCs alone are infeasible.

Abstract

Non-Markovian models have great expressive power, at the cost of complex analysis of the stochastic process. The method of Stochastic State Classes (SSCs) derives closed-form analytical expressions for the joint Probability Density Functions (PDFs) of the active timers with marginal expolynomial PDF, though being hindered by the number of concurrent non-exponential timers and of discrete events between regenerations. Simulation is an alternative capable of handling the large class of PDFs samplable via inverse transform, which however suffers from rare events. We combine these approaches to analyze time-bounded transient properties of non-Markovian models. We enumerate SSCs near the root of the state-space tree and then rely on simulation to reach the target, affording transient evaluation of models for which the method of SSCs is not viable while reducing computational time and variance of the estimator of transient probabilities with respect to simulation. Promising results are observed in the estimation of rare event probabilities.