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Regular stochastic petri nets

  • C. Dutheillet
  • S. Haddad
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 483)

Abstract

An extension of regular nets, a class of colored nets, to a stochastic model is proposed. We show that the symmetries in this class of nets make it possible to develop a performance evaluation by constructing only a graph of symbolic markings, which vertices are classes of states, instead of the whole reachability graph. Using algebraic techniques, we prove that all the states in a class have the same probability, and that the coefficients of the linear system describing the lumped Markov process can be calculated directly from the graph of symbolic markings.

Keywords

Higher-level net models stochastic nets 

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References

  1. [Ajm 85]
    M. Ajmone Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte, and A. Cumani, "On Petri Nets with Stochastic Timing", in proc. International Workshop on Timed Petri Nets, pp 80–87, IEEE-CS Press, Torino, Italy (July 1985).Google Scholar
  2. [Ajm 87]
    M. Ajmone Marsan, G. Balbo, G. Chiola, and G. Conte, "Generalized Stochastic Petri Nets Revisited: Random Switches and Priorities", in proc. International Workshop on Petri Nets and Performance Models, pp 44–53, IEEE-CS Press, Madison, WI, USA (August 1987).Google Scholar
  3. [Chi 87]
    G. Chiola, "A Graphical Petri Net Tool for Performance Analysis", 3rd International Workshop on Modeling Techniques and Performance Evaluation, AFCET, Paris (March 1987).Google Scholar
  4. [Chi 88]
    G. Chiola, G. Bruno, and T. Demaria, "Introducing a Color Formalism into Generalized Stochastic Petri Nets", in proc. 9th European Workshop on Application and Theory of Petri Nets, pp 202–215, Venezia, Italy (June 1988).Google Scholar
  5. [Dut 89]
    C. Dutheillet, S. Haddad, "Aggregation of States in Colored Stochastic Petri Nets. Application to a Multiprocessor Architecture", in proc. PNPM 89, pp 40–49, IEEE-CS Press, Kyoto, Japan (December 1989).Google Scholar
  6. [Flo 85]
    G. Florin, S. Natkin, "Les Réseaux de Petri Stochastiques", AFCET TSI, vol. 4, no. 1, pp 143–160 (January 1985).Google Scholar
  7. [Flo 86]
    G. Florin, "RDPS, a Software Package for the Validation and the Evaluation of Dependable Computer Systems", 3rd Proc. IFAC SAFECOMP Workshop, Sarlat, France (October 1986).Google Scholar
  8. [Had 87]
    S. Haddad, "Une Catégorie Régulière de Réseaux de Petri de Haut Niveau: Définition, Propriétés et Réductions", Thèse de Doctorat, RR87/197, Laboratoire MASI, Université Paris VI, Paris, France (October 1987).Google Scholar
  9. [Had 88]
    S. Haddad and J.M. Couvreur, "Towards a General and Powerful Computation of Flows for Parametrized Coloured Nets", in proc. 9th European Workshop on Application and Theory of Petri Nets, pp 202–215, Venezia, Italy (June 1988).Google Scholar
  10. [Hub 84]
    P. Huber, A.M. Jensen, L.O. Jepsen, and K. Jensen, "Towards Reachability Trees for High Level Petri Nets", 5th European Workshop on Application and Theory of Petri Nets, Aarhus, Denmark (1984).Google Scholar
  11. [Jen 81a]
    K. Jensen, "Coloured Petri Nets and the Invariant Method", Theoretical Computer Science 14, pp 317–336 (1981).Google Scholar
  12. [Jen 81b]
    K. Jensen, “How to Find Invariants for Coloured Petri Nets”, Mathematical Foundations of Computer Science, LNCS 118, Springer-Verlag (1981).Google Scholar
  13. [Kem 60]
    J. G. Kemeny and J. L. Snell, "Finite Markov Chains", Van Nostrand, Princeton, NJ (1960).Google Scholar
  14. [Lan 77]
    S. Lang, “Algebra”, Addison-Wesley (1977).Google Scholar
  15. [Lin 87]
    Chuang Lin and D. Marinescu, "On Stochastic High Level Petri Nets", in proc. International Workshop on Petri Nets and Performance Models, pp 44–53, IEEE-CS Press, Madison, WI, USA (August 1987).Google Scholar
  16. [Mol 81]
    M. K. Molloy, "On the Integration of Delay and Throughput Measures in Distributed in Distributed Processing Models", Ph.D. Dissertation, University of California, Los Angeles, CA, USA (September 1981).Google Scholar
  17. [Zen 85]
    A. Zenie, "Colored Stochastic Petri Nets", in proc. International Workshop on Timed Petri Nets, pp 262–271, IEEE-CS Press, Torino, Italy (July 1985).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • C. Dutheillet
    • 1
  • S. Haddad
    • 1
  1. 1.Laboratoire MASI — CNRS UA 818Université Pierre & Marie CurieParis Cedex 05

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