Analysis of Timed and Long-Run Objectives for Markov Automata
Abstract
Markov automata (MAs) extend labelled transition systems with random delays and probabilistic branching. Action-labelled transitions are instantaneous and yield a distribution over states, whereas timed transitions impose a random delay governed by an exponential distribution. MAs are thus a nondeterministic variation of continuous-time Markov chains. MAs are compositional and are used to provide a semantics for engineering frameworks such as (dynamic) fault trees, (generalised) stochastic Petri nets, and the Architecture Analysis & Design Language (AADL). This paper considers the quantitative analysis of MAs. We consider three objectives: expected time, long-run average, and timed (interval) reachability. Expected time objectives focus on determining the minimal (or maximal) expected time to reach a set of states. Long-run objectives determine the fraction of time to be in a set of states when considering an infinite time horizon. Timed reachability objectives are about computing the probability to reach a set of states within a given time interval. This paper presents the foundations and details of the algorithms and their correctness proofs. We report on several case studies conducted using a prototypical tool implementation of the algorithms, driven by the MAPA modelling language for efficiently generating MAs.
Cite
@article{arxiv.1407.7356,
title = {Analysis of Timed and Long-Run Objectives for Markov Automata},
author = {Dennis Guck and Hassan Hatefi and Holger Hermanns and Joost-Pieter Katoen and Mark Timmer},
journal= {arXiv preprint arXiv:1407.7356},
year = {2015}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1305.7050