Composition and equivalence of Markovian and non-Markovian models

Peter Buchholz, Miklós Telek

Research output: Conference contribution

4 Citations (Scopus)

Abstract

Compositional modeling and the aggregation of components according to equivalence relations based on stochastic bisimulation are often used to handle the problem of state space explosion in Markov models. The paper presents a general class of equivalence relations between Markov models that include stochastic bisimulation or lumpability as specific cases and proves the congruence property of the new equivalence with respect to the composition of components. It is shown that the equivalence relates Markovian and non-Markovian representations but requires some restrictions for the composition which are automatically observed if stochastic bisimulation is used as equivalence relation. Nevertheless, the approach offers the possibility of state space reduction beyond stochastic bisimulation without loosing the possibility of analyzing the resulting stochastic process by means of numerical methods.

Original languageEnglish
Title of host publicationProceedings of the 2011 8th International Conference on Quantitative Evaluation of Systems, QEST 2011
Pages213-222
Number of pages10
DOIs
Publication statusPublished - nov. 2 2011
Event2011 8th International Conference on Quantitative Evaluation of Systems, QEST 2011 - Aachen, Germany
Duration: szept. 5 2011szept. 8 2011

Publication series

NameProceedings of the 2011 8th International Conference on Quantitative Evaluation of Systems, QEST 2011

Other

Other2011 8th International Conference on Quantitative Evaluation of Systems, QEST 2011
CountryGermany
CityAachen
Period9/5/119/8/11

ASJC Scopus subject areas

  • Computer Science Applications
  • Control and Systems Engineering

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  • Cite this

    Buchholz, P., & Telek, M. (2011). Composition and equivalence of Markovian and non-Markovian models. In Proceedings of the 2011 8th International Conference on Quantitative Evaluation of Systems, QEST 2011 (pp. 213-222). [6042048] (Proceedings of the 2011 8th International Conference on Quantitative Evaluation of Systems, QEST 2011). https://doi.org/10.1109/QEST.2011.36