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Analyzing Non-Markovian Systems by Using a Stochastic Process Calculus and a Probabilistic Model Checker

Author

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  • Gabriel Ciobanu

    (Faculty of Computer Science, Alexandru Ioan Cuza University, 700506 Iaşi, Romania)

Abstract

The non-Markovian systems represent almost all stochastic processes, except of a small class having the Markov property; it is a real challenge to analyze these systems. In this article, we present a general method of analyzing non-Markovian systems. The novel viewpoint is given by the use of a compact stochastic process calculus developed in the formal framework of computer science for describing concurrent systems. Since phase-type distributions can approximate non-Markovian systems with arbitrary precision, we approximate a non-Markovian system by describing it easily in our stochastic process calculus, which employs phase-type distributions. The obtained process (in our calculus) are then translated into the probabilistic model checker PRISM; by using this free software tool, we can analyze several quantitative properties of the Markovian approximation of the initial non-Markovian system.

Suggested Citation

  • Gabriel Ciobanu, 2023. "Analyzing Non-Markovian Systems by Using a Stochastic Process Calculus and a Probabilistic Model Checker," Mathematics, MDPI, vol. 11(2), pages 1-17, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:302-:d:1027669
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    References listed on IDEAS

    as
    1. Juan E. Ruiz-Castro & Christian Acal & Ana M. Aguilera & Juan B. Roldán, 2021. "A Complex Model via Phase-Type Distributions to Study Random Telegraph Noise in Resistive Memories," Mathematics, MDPI, vol. 9(4), pages 1-16, February.
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