Transient analysis of non-Markovian models using stochastic state classes

Abstract

a b s t r a c tThe method of stochastic state classes approaches the analysis of Generalised Semi Markov Processes (GSMPs) through the symbolic derivation of probability density functions over supports described by Difference Bounds Matrix (DBM) zones. This makes steady state analysis viable, provided that at least one regeneration point is visited by every cyclic behaviour of the model.We extend the approach providing a way to derive transient probabilities. To this end, stochastic state classes are extended with a supplementary timer that enables the symbolic derivation of the distribution of time at which a class can be entered. The approach is amenable to efficient implementation when model timings are given by expolynomial distributions, and it can be applied to perform transient analysis of GSMPs within any given time bound. In the special case of models underlying a Markov Regenerative Process (MRGP), the method can also be applied to the symbolic derivation of local and global kernels, which in turn provide transient probabilities through numerical integration of generalised renewal equations. Since much of the complexity of this analysis is due to the local kernel, we propose a selective derivation of its entries depending on the specific transient measure targeted by the analysis.

A Retrieval Optimized Surveillance Video Storage System for Campus Application Scenarios

“…How to evaluate the performance in long-time runs if the workload is increasing? To do the performance evaluation, a transient stochastic state classes method is proposed [19]. The authors provide an approach to continuous time transient analysis.…”

Transient Analysis of Networks of Stochastic Timed Automata Using Stochastic State Classes

“…If regeneration points are guaranteed to appear infinitely often, the process is Markov regenerative (MRP); otherwise, we have a generalized semi-Markov process (GSMP). Regeneration points can be exploited in the analysis of the process [21]; if regeneration is not guaranteed, two general analysis techniques can be adopted: the so-called supplementary variable approach [16] and the method of stochastic state classes [20].…”

“…The classification cannot be based on the analysis of the automata in isolation because their interplay can be decisive. The transient analysis we propose in this paper can be easily modified to provide information on the underlying process and compute the kernels of the MRP required in calculations exploiting regeneration points (see [20]). …”

“…To support transient analysis, we include an additional clock x age to encode the absolute time of the last transition [20]. Let us formalize the concept of stochastic state class.…”

“…This was first proposed for steady state analysis [12,26], and then extended to transient analysis [20] and probabilistic model checking [19]. A similar approach was developed for the analysis of Duration Probabilistic Automata (DPA) [25], which compose a set of acyclic semi-Markov processes under control of a non-deterministic scheduler.…”