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International Conference on Application and Theory of Petri Nets

ICATPN 1995: Application and Theory of Petri Nets 1995 pp 161–180Cite as

A notion of equivalence for stochastic Petri nets

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 935))

Abstract

Equivalence is a central concept for the qualitative analysis of dynamic systems. Several different notions of equivalence preserving qualitative properties of a system appeared in the literature on Petri nets (PNs). If apart from qualitative also quantitative aspects of a systems should be analysed, then there exists the class of stochastic Petri nets (SPNs) extending PNs by associating exponentially distributed delays with transitions. However, relations to define equivalence of systems according to quantitative aspects in a systematic way have not been published. This paper proposes a first approach to define quantitative equivalence of SPNs. It is shown that one of the presented relations is an extension of bisimulation equivalence for nets without time. Furthermore, quantitative equivalence is a congruence according to the parallel composition of SPNs as introduced in this paper. For the proposed quantitative equivalence an algorithm to compute the minimal equivalent realisation of a SPN on marking space level is presented.

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Authors and Affiliations

  1. Informatik IV, Universität Dortmund, 44221, Dortmund, Germany

    Peter Buchholz

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  1. Peter Buchholz
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Giorgio De Michelis Michel Diaz

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© 1995 Springer-Verlag Berlin Heidelberg

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Buchholz, P. (1995). A notion of equivalence for stochastic Petri nets. In: De Michelis, G., Diaz, M. (eds) Application and Theory of Petri Nets 1995. ICATPN 1995. Lecture Notes in Computer Science, vol 935. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60029-9_39

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  • DOI: https://doi.org/10.1007/3-540-60029-9_39

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60029-9

  • Online ISBN: 978-3-540-49408-9

  • eBook Packages: Springer Book Archive

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