Extending the Steady State Analysis of Hierarchical Semi-Markov Processes with Parallel Regions

Analysis of hierarchical semi-Markov processes with parallel regions is a technique that evaluates steady-state probabilities of mod- els with multiple concurrent non-Markovian timers in a compositional way without the need of full state space generation. In this paper we ex- tend the technique by removing some of its limitations and increasing its modelling power. By applying the time advancement mechanism known from stochastic state classes, exits in parallel regions with different time origins can be taken into account. Furthermore, exits can be put on state borders such that the model evolution depends on the exited region and a concept for history states is also presented. This significantly increases modeling power, such that the gap between semi-Markov processes with restricted modeling power and non-Markovian models without modeling restrictions but also with less efficient analysis is filled. Experimentations in order to validate the approach and to compare it with another tech- nique were performed in order to better characterise the advantages of the compositional approach.