Process Algebra and Markov Chains

Hendrik Brinksma, H. Hermanns

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

42 Citations (Scopus)

Abstract

This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study the interrelation of reactive processes and Markov chains in this setting, and introduce the algebra of Interactive Markov Chains as an orthogonal extension of both process and Markov chain algebra. We conclude with comparing this approach to related (Markovian) stochastic process algebras by analysing the algebraic principles that they support.
Original languageEnglish
Title of host publicationLectures on Formal Methods and Performance Analysis
EditorsHendrik Brinksma, H. Hermanns, Joost P. Katoen
Place of PublicationBerlin
PublisherSpringer
Pages183-231
Number of pages49
ISBN (Electronic)978-3-540-44667-5
ISBN (Print)978-3-540-42479-6
DOIs
Publication statusPublished - Jul 2001

Publication series

NameLecture Notes in Computer Science
PublisherSpringer Verlag
Volume2090

Fingerprint

Process Algebra
Markov chain
Algebra
Stochastic Process Algebra
Markovian Process
Continuous-time Markov Chain
Modeling

Keywords

  • FMT-PM: PROBABILISTIC METHODS
  • EWI-6419
  • FMT-PA: PROCESS ALGEBRAS
  • IR-63273
  • FMT-FMPA: FORMAL METHODS FOR PERFORMANCE ANALYSIS

Cite this

Brinksma, H., & Hermanns, H. (2001). Process Algebra and Markov Chains. In H. Brinksma, H. Hermanns, & J. P. Katoen (Eds.), Lectures on Formal Methods and Performance Analysis (pp. 183-231). (Lecture Notes in Computer Science; Vol. 2090). Berlin: Springer. https://doi.org/10.1007/3-540-44667-2_5
Brinksma, Hendrik ; Hermanns, H. / Process Algebra and Markov Chains. Lectures on Formal Methods and Performance Analysis. editor / Hendrik Brinksma ; H. Hermanns ; Joost P. Katoen. Berlin : Springer, 2001. pp. 183-231 (Lecture Notes in Computer Science).
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Brinksma, H & Hermanns, H 2001, Process Algebra and Markov Chains. in H Brinksma, H Hermanns & JP Katoen (eds), Lectures on Formal Methods and Performance Analysis. Lecture Notes in Computer Science, vol. 2090, Springer, Berlin, pp. 183-231. https://doi.org/10.1007/3-540-44667-2_5

Process Algebra and Markov Chains. / Brinksma, Hendrik ; Hermanns, H.

Lectures on Formal Methods and Performance Analysis. ed. / Hendrik Brinksma; H. Hermanns; Joost P. Katoen. Berlin : Springer, 2001. p. 183-231 (Lecture Notes in Computer Science; Vol. 2090).

Research output: Chapter in Book/Report/Conference proceedingChapterAcademic

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N2 - This paper surveys and relates the basic concepts of process algebra and the modelling of continuous time Markov chains. It provides basic introductions to both fields, where we also study the Markov chains from an algebraic perspective, viz. that of Markov chain algebra. We then proceed to study the interrelation of reactive processes and Markov chains in this setting, and introduce the algebra of Interactive Markov Chains as an orthogonal extension of both process and Markov chain algebra. We conclude with comparing this approach to related (Markovian) stochastic process algebras by analysing the algebraic principles that they support.

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KW - FMT-PM: PROBABILISTIC METHODS

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KW - FMT-PA: PROCESS ALGEBRAS

KW - IR-63273

KW - FMT-FMPA: FORMAL METHODS FOR PERFORMANCE ANALYSIS

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BT - Lectures on Formal Methods and Performance Analysis

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Brinksma H, Hermanns H. Process Algebra and Markov Chains. In Brinksma H, Hermanns H, Katoen JP, editors, Lectures on Formal Methods and Performance Analysis. Berlin: Springer. 2001. p. 183-231. (Lecture Notes in Computer Science). https://doi.org/10.1007/3-540-44667-2_5