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2019 | OriginalPaper | Buchkapitel

A Modest Markov Automata Tutorial

verfasst von : Arnd Hartmanns, Holger Hermanns

Erschienen in: Reasoning Web. Explainable Artificial Intelligence

Verlag: Springer International Publishing

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Abstract

Distributed computing systems provide many important services. To explain and understand why and how well they work, it is common practice to build, maintain, and analyse models of the systems’ behaviours. Markov models are frequently used to study operational phenomena of such systems. They are often represented with discrete state spaces, and come in various flavours, overarched by Markov automata. As such, Markov automata provide the ingredients that enable the study of a wide range of quantitative properties related to risk, cost, performance, and strategy. This tutorial paper gives an introduction to the formalism of Markov automata, to practical modelling of Markov automata in the Modest language, and to their analysis with the Modest Toolset. As case studies, we optimise an attack on Bitcoin, and evaluate the performance of a small but complex resource-sharing computing system.

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Fußnoten
1
Actually, the semantics of Modest  [30] is defined in terms of stochastic hybrid automata (SHA), of which MA are a special case; we restrict to that case in this paper.
 
2
MA model checking requires finite state spaces; thus all variables must be bounded. Indicating the bounds in the types is good practice to avoid accidentally creating infinite-state models and may improve performance, but it is not a requirement for the mcsta model checker (see Sect. 3.2) as long as only finitely many distinct values are ever assigned to the variables occurring in the model.
 
3
moconv can also export CTMDP to Jani, but due to their lack of a natural parallel composition operator, the analysis of CTMDP is not supported in the other tools.
 
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Metadaten
Titel
A Modest Markov Automata Tutorial
verfasst von
Arnd Hartmanns
Holger Hermanns
Copyright-Jahr
2019
DOI
https://doi.org/10.1007/978-3-030-31423-1_8

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