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Non-Markovian Analysis

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Abstract

If in stochastic modeling the idealized assumption of exponential distributions is removed, the resulting stochastic process is non-Markovian. In this tutorial paper we give an overview of possible analytic approaches for such non-Markovian models. The modeling framework of stochastic Petri nets is used, but the ideas are applicable to other frameworks as well, if a state space can be constructed. We give a detailed presentation of one analysis approach which is based on the method of supplementary variables and give a brief review of another analysis approach which is based on embedding. A model of a timer for holding a connection is used as a tutorial example and a model for a medium access mechanism in wireless networks is used as a more complex example.

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Authors and Affiliations

  1. Computer Science 7 (Computer Networks and Communication Systems), Friedrich-Alexander Universität Erlangen-Nürnberg, Martensstr. 3, 91058, Erlangen, Germany

    Reinhard German

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  1. Reinhard German
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Editors and Affiliations

  1. Faculty of Computer Science, Formal Methods and Tools Group, University of Twente, 217, 7500, AE, Enschede, The Netherlands

    Ed Brinksma , Holger Hermanns  & Joost-Pieter Katoen ,  & 

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German, R. (2001). Non-Markovian Analysis. In: Brinksma, E., Hermanns, H., Katoen, JP. (eds) Lectures on Formal Methods and PerformanceAnalysis. EEF School 2000. Lecture Notes in Computer Science, vol 2090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44667-2_4

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  • DOI: https://doi.org/10.1007/3-540-44667-2_4

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  • Online ISBN: 978-3-540-44667-5

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