Concurrency and Composition in a Stochastic World

Eisentraut, Christian; Hermanns, Holger; Zhang, Lijun

doi:10.1007/978-3-642-15375-4_3

“…Additionally, our definition of strong bisimulation then reduces to the definition of strong bisimulation for MAs. Since it was already shown in [14] that strong bisimulation for MAs coincides with the corresponding notions for all subclasses of MAs, this also holds for our definition. Hence, it safely generalises the existing notions of strong bisimulation.…”

Section: Definition 5 (Strong Bisimulation)supporting

confidence: 67%

Modelling and Analysis of Markov Reward Automata

Guck

¹

,

Timmer

²

,

Hatefi

³

et al. 2014

Automated Technology for Verification and Analysis

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Abstract. Costs and rewards are important ingredients for many types of systems, modelling critical aspects like energy consumption, task completion, repair costs, and memory usage. This paper introduces Markov reward automata, an extension of Markov automata that allows the modelling of systems incorporating rewards (or costs) in addition to nondeterminism, discrete probabilistic choice and continuous stochastic timing. Rewards come in two flavours: action rewards, acquired instantaneously when taking a transition; and state rewards, acquired while residing in a state. We present algorithms to optimise three reward functions: the expected cumulative reward until a goal is reached, the expected cumulative reward until a certain time bound, and the long-run average reward. We have implemented these algorithms in the SCOOP/IMCA tool chain and show their feasibility via several case studies.

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“…This now allows us to verify probabilistic as well as hard and soft real-time systems, modelled by timed automata, Markov decision processes, probabilistic automata, continuous-time Markov chains, interactive Markov chains, and Markov automata. Except for timed automatawhich incorporate real-time deadlines-all other models are subsumed by the Markov automaton (MA) [14,13,12]. MAs can therefore be used as a semantic model for a wide range of formalisms, such as generalised stochastic Petri nets (GSPNs) [2], dynamic fault trees [9], Arcade [8] and the domain-specific language AADL [10].…”

Section: Introductionmentioning

confidence: 99%

“…As argued in [20], it is often much more natural to omit most of these weights, retaining rates and probability as well as nondeterminism, and thus obtaining an MA. For example, consider the GSPN in Figure 1(a), taken from [13]. Immediate This research has been partially funded by NWO under grants 612.063.817 (SYRUP), 12238 (ArRangeer) and Dn 63-257 (ROCKS), and EU under 318490 (SENSATION).…”

Section: Introductionmentioning

confidence: 99%

Confluence reduction for Markov automata

Timmer

¹

,

Katoen

²

,

Pol

³

et al. 2016

Theoretical Computer Science

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Abstract. Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models generated by such specifications. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep these models small. We define the notion of confluence directly on Markov automata, and discuss how to syntactically detect confluence on the MAPA language as well. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude.

show abstract

“…This now allows us to verify probabilistic as well as hard and soft real-time systems, modelled by timed automata, Markov decision processes, probabilistic automata, continuous-time Markov chains, interactive Markov chains, and Markov automata. Except for timed automatawhich incorporate real-time deadlines-all other models are subsumed by the Markov automaton (MA) [14,13,12]. MAs can therefore be used as a semantic model for a wide range of formalisms, such as generalised stochastic Petri nets (GSPNs) [2], dynamic fault trees [9], Arcade [8] and the domain-specific language AADL [10].…”

Section: Introductionmentioning

confidence: 99%

Confluence Reduction for Markov Automata

Timmer

¹

,

Pol

²

,

Stoelinga

³

2013

Lecture Notes in Computer Science

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Abstract. Markov automata are a novel formalism for specifying systems exhibiting nondeterminism, probabilistic choices and Markovian rates. Recently, the process algebra MAPA was introduced to efficiently model such systems. As always, the state space explosion threatens the analysability of the models generated by such specifications. We therefore introduce confluence reduction for Markov automata, a powerful reduction technique to keep these models small. We define the notion of confluence directly on Markov automata, and discuss how to syntactically detect confluence on the MAPA language as well. That way, Markov automata generated by MAPA specifications can be reduced on-the-fly while preserving divergence-sensitive branching bisimulation. Three case studies demonstrate the significance of our approach, with reductions in analysis time up to an order of magnitude.

show abstract

Concurrency and Composition in a Stochastic World

Cited by 35 publications

References 47 publications

Modelling and Analysis of Markov Reward Automata

Modelling and Analysis of Markov Reward Automata

Confluence reduction for Markov automata

Confluence Reduction for Markov Automata

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