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Über Produkt-Form-Lösungen für stochastische Petri-Netze.

Frosch-Wilke, D.

In: PH.D. Dissertation, Verlag Shaker, Aachen. 1994.

Abstract: In the first two parts of this thesis an introductionto stochastic Petri nets (SPNs) is given and an overview of results regarding product form solutions for SPNs and queueing networks is presented. After this the product form solution for a class of Markovian SPNs, which is called closed synchronized systems of stochastic sequential processes, is proved. For this reason structural properties of the SPNs are used to verify properties of the stochastic marking processes. Therefore there is no separation between qualitative and quantitative analysis of SPN models. The existence of product form solutions for Non-Markovan SPNs is verified by using results of the theory of insensitivity of generalized semi-Markov-processes. These results are used to verify the product form solution for some class of circuit-switching networks with adaptive routing.

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