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Non-Markovian Analysis.

German, Reinhard

In: LNCS 2090: Lectures on Formal Methods and Performance Analysis, pages 156-pp. First EEF/Euro Summer School on Trends in Computer Science, Berg en Dal, The Netherlands, July 3-7, 2000, Revised Lectures / E. Brinksma, H. Hermanns, J.P. Katoen (Eds.) --- Springer Verlag, September 2001.

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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