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A new approach to the evaluation of non Markovian stochastic Petri nets. (English) Zbl 1234.68301
Donatelli, Susanna (ed.) et al., Petri nets and other models of concurrency – ICATPN 2006. 27th international conference on applications and theory of Petri nets and other models of concurrency, Turku, Finland, June 26–30, 2006. Proceedings. Berlin: Springer (ISBN 978-3-540-34699-9/pbk). Lecture Notes in Computer Science 4024, 221-240 (2006).
Summary: In this work, we address the problem of transient and steady-state analysis of a stochastic Petri net which includes non Markovian distributions with a finite support but without any additional constraint. Rather than computing an approximate distribution of the model (as done in previous methods), we develop an exact analysis of an approximate model. The design of this method leads to a uniform handling of the computation of the transient and steady state behaviour of the model. This method is an adaptation of a former one developed by the same authors for general stochastic processes (which was shown to be more robust than alternative techniques). Using Petri nets as the modelling formalism enables us to express the behaviour of the approximate process by tensorial expressions. Such a representation yields significant savings w.r.t. time and space complexity.
MSC:
68Q85Models and methods for concurrent and distributed computing
68Q87Probability in computer science (algorithm analysis, random structures, phase transitions, etc.)