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International Conference on Analytical and Stochastic Modeling Techniques and Applications

ASMTA 2017: Analytical and Stochastic Modelling Techniques and Applications pp 16–31Cite as

Equivalence and Lumpability of FSPNs

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 10378)

Abstract

We consider equivalence relations for Fluid Stochastic Petri Nets (FSPNs). Based on equivalence relations for Stochastic Petri Nets (SPNs), which are derived from lumpability for Markov Chains, and from lumpability for certain classes of differential equations, we define an equivalence relation for FSPNs. Lumpability for the differential equations is based on a finite discretization approach and permutations of the fluid part of the FSPN.

As for other modeling formalisms, the availability of an appropriate equivalence relation allows one to aggregate sets of equivalent states into single states. This state space reduction can be exploited for a more efficient analysis of FSPNs using a discretization approach. Lumpable equivalence relations can be computed from an appropriately discretized state space of the stochastic process or directly from the FSPN.

Keywords

  • Fluid Stochastic Petri Nets
  • Lumpability
  • Equivalence

The work of F. Bause, P. Buchholz and I. Tarasyuk has been partially supported by DFG under grant BE 1267/14-1.

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Authors and Affiliations

  1. Informatik 4, TU Dortmund, 44221, Dortmund, Germany

    Falko Bause & Peter Buchholz

  2. A.P. Ershov Institute of Informatics Systems, Siberian Branch of the Russian Academy of Sciences, Acad. Lavrentiev pr. 6, 630090, Novosibirsk, Russian Federation

    Igor V. Tarasyuk

  3. MTA-BME Information Systems Research Group, Department of Networked Systems and Services, Technical University of Budapest, 1521, Budapest, Hungary

    Miklós Telek

Authors
  1. Falko Bause
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  2. Peter Buchholz
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  3. Igor V. Tarasyuk
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  4. Miklós Telek
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Corresponding author

Correspondence to Peter Buchholz .

Editor information

Editors and Affiliations

  1. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Nigel Thomas

  2. School of Computing Science, Newcastle University, Newcastle upon Tyne, UK

    Matthew Forshaw

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Bause, F., Buchholz, P., Tarasyuk, I.V., Telek, M. (2017). Equivalence and Lumpability of FSPNs. In: Thomas, N., Forshaw, M. (eds) Analytical and Stochastic Modelling Techniques and Applications. ASMTA 2017. Lecture Notes in Computer Science(), vol 10378. Springer, Cham. https://doi.org/10.1007/978-3-319-61428-1_2

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  • DOI: https://doi.org/10.1007/978-3-319-61428-1_2

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