Guck, Dennis and Hatefi, Hassan and Hermanns, Holger and Katoen, Joost-Pieter and Timmer, Mark - Analysis of Timed and Long-Run Objectives for Markov Automata

lmcs:943 - Logical Methods in Computer Science, September 10, 2014, Volume 10, Issue 3
Analysis of Timed and Long-Run Objectives for Markov Automata

Authors: Guck, Dennis and Hatefi, Hassan and Hermanns, Holger and Katoen, Joost-Pieter and Timmer, Mark

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.


Source : oai:arXiv.org:1407.7356
DOI : 10.2168/LMCS-10(3:17)2014
Volume: Volume 10, Issue 3
Published on: September 10, 2014
Submitted on: June 25, 2015
Keywords: Computer Science - Logic in Computer Science,Computer Science - Formal Languages and Automata Theory


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