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

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.