Analysis of Timed and Long-Run Objectives for Markov Automata
| Autor: | Guck, Dennis, Hatefi, Hassan, Hermanns, Holger, Katoen, Joost-Pieter, Timmer, Mark |
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| Rok vydání: | 2014 |
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| Zdroj: | Logical Methods in Computer Science, Volume 10, Issue 3 (September 10, 2014) lmcs:943 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2168/LMCS-10(3:17)2014 |
| Popis: | 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. Comment: arXiv admin note: substantial text overlap with arXiv:1305.7050 |
| Databáze: | arXiv |
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