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On Petri nets with deterministic and exponentially distributed firing times

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 266))

Abstract

A class of Petri nets (DSPN) in which transitions can fire after either a deterministic or a random, exponentially distributed, firing delay is defined, and a solution technique is presented to obtain the steady-state probability distribution over markings, introducing restrictions on the use of deterministic firing delays. An example of application of this modeling technique is presented to demonstrate the impact that the use of a mix of deterministic and exponentially distributed firing delays (instead of all exponentially distributed firing delays) can have on performance and reliability estimates.

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References

  1. Proceedings of the International Workshop on Timed Petri Nets, IEEE CS press, Torino, Italy (July 1985).

    Google Scholar 

  2. M.K. Molloy, “Discrete Time Stochastic Petri Nets,” IEEE Transactions on Software Engineering SE-11(2) pp. 417–423 (April 1985).

    Google Scholar 

  3. M.A. Holliday and M.K. Vernon, “A Generalized Timed Petri Net Model for Performance Analysis,” in Proc. Int. Workshop on Timed Petri Nets, IEEE, Torino, Italy (July 1985).

    Google Scholar 

  4. M.K. Molloy, “On the Integration of Delay and Throughput Measures in Distributed Processing Models,” Ph.D. Thesis, UCLA, Los Angeles, CA (1981).

    Google Scholar 

  5. S. Natkin, “Les Reseaux de Petri Stochastiques et leur Application a l'Evaluation des Systemes Informatiques,” These de Docteur Ingegneur, CNAM, Paris, France (1980).

    Google Scholar 

  6. M. Ajmone Marsan, G. Balbo, and G. Conte, “A Class of Generalized Stochastic Petri Nets for the Performance Analysis of Multiprocessor Systems,” ACM TOCS 2(2), pp. 93–122 (May 1984).

    Google Scholar 

  7. J.B. Dugan, K.S. Trivedi, R.M. Geist, and V.F. Nicola, “Extended Stochastic Petri Nets: Applications and Analysis,” in proc. PERFORMANCE 84, Paris, France (December 1984).

    Google Scholar 

  8. M. Ajmone Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte, and A. Cumani, “On Petri Nets with Stochastic Timing,” in proc. Int. Workshop on Timed Petri Nets, IEEE, Torino, Italy (July 1985).

    Google Scholar 

  9. M.F. Neuts, Matrix Geometric Solutions in Stochastic Models, Johns Hopkins University Press, Baltimore, MD (1981).

    Google Scholar 

  10. A. Cumani, “ESP — A Package for the Evaluation of Stochastic Petri Nets with Phase-Type Distributed Transition Times,” in proc. Int. Workshop on Timed Petri Nets, IEEE, Torino, Italy (July 1985).

    Google Scholar 

  11. R.A. Howard, Dynamic Probabilistic Systems, John Wiley, New York, NY (1971).

    Google Scholar 

  12. L. Kleinrock, Queueing Systems; vol.1: Theory, John Wiley, New York, NY (1975).

    Google Scholar 

  13. G. Chiola, “A Graphical Petri Net Tool for Performance Analysis,” in proc. 3 rd Int. Workshop on Modeling Techniques and Performance Evaluation, AFCET, Paris, France (March 1987).

    Google Scholar 

  14. J.F. Meyer, “On Evaluating the Performability of Degradable Computing Systems,” IEEE Transactions on Computers C-29(8) pp. 720–731 (August 1980).

    Google Scholar 

  15. M. Ajmone Marsan, G. Chiola, and A. Fumagalli, “An Accurate Performance Model of CSMA/CD bus LAN,” in this volume

    Google Scholar 

  16. M. Ajmone Marsan, G. Chiola, and G. Conte, “Generalized Stochastic Petri Net Models of Multiprocessors with Cache Memories,” in proc. 1 st Int. Conf. on Supercomputing Systems, IEEE, St. Petersburg, FL (December 1985).

    Google Scholar 

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Grzegorz Rozenberg

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© 1987 Springer-Verlag Berlin Heidelberg

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Marsan, M.A., Chiola, G. (1987). On Petri nets with deterministic and exponentially distributed firing times. In: Rozenberg, G. (eds) Advances in Petri Nets 1987. APN 1986. Lecture Notes in Computer Science, vol 266. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18086-9_23

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  • DOI: https://doi.org/10.1007/3-540-18086-9_23

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18086-9

  • Online ISBN: 978-3-540-47743-3

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