ANALYSIS OF TIMED AND LONG-RUN OBJECTIVES FOR MARKOV AUTOMATA

作者：Guck Dennis^*; Hatefi Hassan; Hermanns Holger; Katoen Joost Pieter; Timmer Mark

来源：Logical Methods in Computer Science, 2014, 10(3): 17.

DOI：10.2168/LMCS-10(3:17)2014

• Quantitative analysis
• Markov automata
• continuous time
• expected time
• long-run average
• timed reachability

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 %26 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.

• 出版日期2014