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Computational restrictions for SPN with generally distributed transition times

  • Session 3: Evaluation
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Dependable Computing — EDCC-1 (EDCC 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 852))

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Abstract

The analysis of stochastic systems with non-exponential timing requires the development of suitable modeling tools. Recently, some effort has been devoted to generalize the concept of Stochastic Petri nets, by allowing the firing times to be generally distributed. The evolution of the PN in time becomes a stochastic process, for which in general, no analytical solution is available. The paper describes suitable restrictions of the PN model with generally distributed transition times, that have appeared in the literature, and compares these models from the point of view of the modeling power and the numerical tractability.

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References

  1. M. Ajmone Marsan, G. Balbo, and G. Conte. A class of generalized stochastic Petri nets for the performance evaluation of multiprocessor systems. ACM Transactions on Computer Systems, 2:93–122, 1984.

    Article  Google Scholar 

  2. M. Ajmone Marsan and G. Chiola. On Petri nets with deterministic and exponentially distributed firing times. In Lecture Notes in Computer Science, pages 132–145, Springer Verlag, 1987.

    Google Scholar 

  3. M. Ajmone Marsan, G. Balbo, A. Bobbio, G. Chiola, G. Conte, and A. Cumani. The effect of execution policies on the semantics and analysis of stochastic Petri nets. IEEE Transactions on Software Engineering, SE-15:832–846, 1989.

    Article  Google Scholar 

  4. D. Aldous and L. Shepp. The least variable phase type distribution is Erlang. Stochastic Models, 3:467–473, 1987.

    Google Scholar 

  5. A. Bertoni and M. Torelli. Probabilistic Petri nets and semi Markov processes. In Proceedings 2-nd European Workshop on Petri Nets, 1981.

    Google Scholar 

  6. A. Bobbio. Petri nets generating Markov reward models for performance/reliability analysis of degradable systems. In R. Puigjaner and D. Poitier, editors, Modeling Techniques and Tools for Computer Performance Evaluation, pages 353–365, Plenum Press, 1989.

    Google Scholar 

  7. A. Bobbio and M. Telek. A benchmark for PH estimation algorithms: Results for acyclic PH. Stochastic Models, 10:3, 1994.

    Google Scholar 

  8. G. Chiola. GreatSPN 1.5 Software architecture. In G. Balbo and G. Serazzi, editors, Computer Performance Evaluation, pages 121–136, Elsevier Science Publishers, 1992.

    Google Scholar 

  9. Hoon Choi, V.G. Kulkarni, and K. Trivedi. Transient analysis of deterministic and stochastic Petri nets. In Proceedings of the 14-th International Conference on Application and Theory of Petri Nets, Chicago, June 1993.

    Google Scholar 

  10. Hoon Choi, V.G. Kulkarni, and K. Trivedi. Markov regenerative stochastic Petri nets. In G. Iazeolla ans S.S. Lavenberg, editor, Proceedings International Conference PERFORMANCE'93, pages 339–352, 1993.

    Google Scholar 

  11. G. Ciardo, J. Muppala, and K.S. Trivedi. On the solution of GSPN reward models. Performance Evaluation, 12:237–253, 1991.

    Article  Google Scholar 

  12. G. Ciardo, R. German, and C. Lindemann. A characterization of the stochastic process underlying a stochastic Petri net. In Proceedings International Workshop on Petri Nets and Performance Models — PNPM93, pages 170–179. IEEE Computer Society, 1993.

    Google Scholar 

  13. G. Ciardo and C. Lindemann. Analysis of deterministic and stochastic Petri nets. In Proceedings International Workshop on Petri Nets and Performance Models — PNPM93, pages 160–169. IEEE Computer Society, 1993.

    Google Scholar 

  14. E. Cinlar. Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, 1975.

    Google Scholar 

  15. D.R. Cox. The analysis of non-Markov stochastic processes by the inclusion of supplementary variables. Proceedings of the Cambridge Philosophical Society, 51:433–441, 1955.

    Google Scholar 

  16. A. Cumani. Esp — A package for the evaluation of stochastic Petri nets with phasetype distributed transition times. In Proceedings International Workshop Timed Petri Nets, pages 144–151, IEEE Computer Society Press no. 674, Torino (Italy), 1985.

    Google Scholar 

  17. J. Bechta Dugan, K. Trivedi, R. Geist, and V.F. Nicola. Extended stochastic Petri nets: applications and analysis. In Proceedings PERFORMANCE '84, Paris, 1984.

    Google Scholar 

  18. G. Florin and S. Natkin. Les reseaux de Petri stochastiques. Technique et Science Informatique, 4:143–160, 1985.

    Google Scholar 

  19. R. German and C. Lindemann. Analysis of SPN by the method of supplementary variables. In G. Iazeolla and S.S. Lavenberg, editors, Proceedings International Conference PERFORMANCE'93, pages 320–338, 1993.

    Google Scholar 

  20. P.J. Haas and G.S. Shedler. Regenerative stochastic Petri nets. Performance Evaluation, 6:189–204, 1986.

    MathSciNet  Google Scholar 

  21. D.L. Jagerman. An inversion technique for the Laplace transform. The Bell System Technical Journal, 61:1995–2002, October 1982.

    Google Scholar 

  22. R. Lepold. PEPNET: A new approach to performability modelling using stochastic Petri nets. In Proceedings 1st International Workshop on Performability Modelling of Computer and Communication Systems, pages 3–17, University of Twente-Enschede (NL), 1991.

    Google Scholar 

  23. C. Lindemann. An improved numerical algorithm for calculating steady-state solutions of deterministic and stochastic Petri net models. Performance Evaluation, 8, 1993.

    Google Scholar 

  24. J.F. Meyer, A. Movaghar, and W.H. Sanders. Stochastic activity networks: structure, behavior and application. In Proceedings International Workshop Timed Petri Nets, pages 106–115, IEEE Computer Society Press no. 674, Torino (Italy), 1985.

    Google Scholar 

  25. M.K. Molloy. Performance analysis using stochastic Petri nets. IEEE Transactions on Computers, C-31:913–917, 1982.

    Google Scholar 

  26. S. Natkin. Les reseaux de Petri stochastiques et leur application a l'evaluation des systemes informatiques. Technical Report, These de Docteur Ingegneur, CNAM, Paris, 1980.

    Google Scholar 

  27. M.F. Neuts. Matrix Geometric Solutions in Stochastic Models. Johns Hopkins University Press, Baltimore, 1981.

    Google Scholar 

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Klaus Echtle Dieter Hammer David Powell

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© 1994 Springer-Verlag Berlin Heidelberg

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Bobbio, A., Telek, M. (1994). Computational restrictions for SPN with generally distributed transition times. In: Echtle, K., Hammer, D., Powell, D. (eds) Dependable Computing — EDCC-1. EDCC 1994. Lecture Notes in Computer Science, vol 852. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58426-9_128

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  • DOI: https://doi.org/10.1007/3-540-58426-9_128

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  • Print ISBN: 978-3-540-58426-1

  • Online ISBN: 978-3-540-48785-2

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