Transient Analysis of Generalised Semi-Markov Processes Using Transient Stochastic State Classes

The method of stochastic state classes approaches the analysis of Generalised Semi Markov Processes (GSMP) through symbolic derivation of probability density functions over Difference Bounds Matrix (DBM) zones. This makes viable steady state analysis in both discrete and continuous time, provided that each cyclic behavior that changes the enabling status of generally distributed transitions visits at least one regeneration point. However, transient analysis is supported only in discrete time. We extend the approach providing a way to derive continuous time transient probabilities. To this end, stochastic state classes are extended with a supplementary age clock that enables symbolic derivation of the distribution of times at which the states of a zone can be reached. The approach is amenable to efficient implementation when model timings are given by expolynomial distributions, and it can in principle be applied to transient analysis with any given time bound for any GSMP. In the speci...

• Type: Journal
• Year: 2010
• Where: QEST
• Authors: András Horváth, Lorenzo Ridi, Enrico Vicario
• Keywords: Analysis, Modeling And Simulation, QEST 2010, Stochastic State, Symbolic Derivation