Probabilistic Time Petri Nets

Abstract : We introduce a new model for the design of concurrent sto-chastic real-time systems. Probabilistic time Petri nets (PTPN) are an extension of time Petri nets in which the output of tokens is randomised. Such a design allows us to elegantly solve the hard problem of combining probabilities and concurrency. This model further benefits from the con-cision and expressive power of Petri nets. Furthermore, the usual tools for the analysis of time Petri nets can easily be adapted to our probabilistic setting. More precisely, we show how a Markov decision process (MDP) can be derived from the classic atomic state class graph construction. We then establish that the schedulers of the PTPN and the adversaries of the MDP induce the same Markov chains. As a result, this construction notably preserves the lower and upper bounds on the probability of reaching a given target marking. We also prove that the simpler original state class graph construction cannot be adapted in a similar manner for this purpose.
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Yrvann Emzivat, Benoit Delahaye, Didier Lime, Olivier Roux. Probabilistic Time Petri Nets. 37th INTERNATIONAL CONFERENCE ON APPLICATIONS AND THEORY OF PETRI NETS AND CONCURRENCY, Jun 2016, Torun, Poland. pp.261-280. ⟨hal-01590900⟩

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