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Petri nets with marking-dependent arc cardinality: Properties and analysis

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Application and Theory of Petri Nets 1994 (ICATPN 1994)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 815))

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Abstract

We discuss P/T-nets where the arc cardinalities are allowed to be marking-dependent expressions of various types, resulting in a hierarchy of subclasses. Some of the language and decidability properties of these classes have been studied before, but we focus on the practical implications in systems modeling, adding some new insight to the known results about the relative expressive power of the subclasses.

We show how the p-semiflows of a P/T-net with marking-dependent arc cardinality can be obtained from the p-semiflows of a related ordinary P/T-net and how bounds on the relative throughputs of the transitions can be obtained, a weaker condition than t-semiflows.

Finally, we briefly discuss several modeling applications where these subclasses are used.

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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 Trans. Comp. Syst., 2(2):93–122, May 1984.

    Google Scholar 

  2. M. Ajmone Marsan and G. Chiola. On Petri Nets with deterministic and exponentially distributed firing times. In G. Rozenberg, editor, Adv. in Petri Nets 1987, Lecture Notes in Computer Science 266, pages 132–145. Springer-Verlag, 1987.

    Google Scholar 

  3. T. Araki and T. Kasami. Some decision problems related to the reachability problem for Petri nets. Theoretical Computer Science, 3:85–104, 1977.

    Google Scholar 

  4. G. Balbo, G. Chiola, G. Franceschinis, and G. Molinari Roet. On the efficient construction of the tangible reachability graph of generalized stochastic Petri nets. In Proc. of the Int. Workshop on Petri Nets and Performance Models, Madison, Wisconsin, Aug. 1987.

    Google Scholar 

  5. J. Bechta Dugan and G. Ciardo. Stochastic Petri net analysis of a replicated file system. IEEE Trans. Softw. Eng., 15(4):394–401, Apr. 1989.

    Google Scholar 

  6. G. Chiola. A Graphical Petri Net Tool for Performance Analysis. In Proc. 3rd Int. Conf. on Modeling Techniques and Tools for Performance Analysis, Paris, pages 323–333, 1987.

    Google Scholar 

  7. G. Chiola, S. Donatelli, and G. Franceschinis. GSPNs versus SPNs: what is the actual role of immediate transitions? In Proc. of the Fourth Int. Workshop on Petri Nets and Performance Models (PNPM91), Melbourne, Australia, Dec. 1991.

    Google Scholar 

  8. G. Ciardo. Analysis of large stochastic Petri net models. PhD thesis, Duke University, Durham, North Carolina, 1989.

    Google Scholar 

  9. G. Ciardo, A. Blakemore, P. F. J. Chimento, J. K. Muppala, and K. S. Trivedi. Automated generation and analysis of Markov reward models using Stochastic Reward Nets. In C. Meyer and R. J. Plemmons, editors, Linear Algebra, Markov Chains, and Queueing Models, volume 48 of IMA Volumes in Mathematics and its Applications, pages 145–191. Springer-Verlag, 1993.

    Google Scholar 

  10. G. Ciardo, R. German, and C. Lindemann. A characterization of the stochastic process underlying a stochastic Petri net. In Proc. of the Fifth Int. Workshop on Petri Nets and Performance Models (PNPM93), Toulouse, France, Oct. 1993.

    Google Scholar 

  11. G. Ciardo and C. Lindemann. Analysis of deterministic and stochastic Petri nets. In Proc. of the Fifth Int. Workshop on Petri Nets and Performance Models (PNPM93), Toulouse, France, Oct. 1993.

    Google Scholar 

  12. G. Ciardo and K. S. Trivedi. A decomposition approach for stochastic reward net models. Perf. Eval., 18:37–59, 1993.

    MathSciNet  Google Scholar 

  13. G. Ciardo, K. S. Trivedi, and J. Muppala. SPNP: stochastic Petri net package. In Proc. of the Third Int. Workshop on Petri Nets and Performance Models (PNPM89), pages 142–151, Kyoto, Japan, Dec. 1989. IEEE Computer Society Press.

    Google Scholar 

  14. J. M. Colom and M. Silva. Convex geometry and semiflows in P/T nets. A comparative study of algorithms for the computation of minimal p-semiflows. In 10th International Conference on Application and Theory of Petri Nets, Bonn, Germany, 1989.

    Google Scholar 

  15. M. Hack. Petri net languages. Technical Report 159, Laboratory for Computer Science, Massachusetts Institute of Technology, Cambridge, Massachussetts, Mar. 1976.

    Google Scholar 

  16. O. C. Ibe and K. S. Trivedi. Stochastic Petri net modeling of VAXCluster system availability. In Proc. of the Third Int. Workshop on Petri Nets and Performance Models (PNPM89), Kyoto, Japan, Dec. 1989.

    Google Scholar 

  17. M. Jantzen. Language theory of Petri nets. In W. Brauer, W. Reisig, and G. Rozenberg, editors, Adv. in Petri Nets 1986, Part 1, Lecture Notes in Computer Science 254, pages 397–412. Springer-Verlag, 1986.

    Google Scholar 

  18. G. Klas and R. Lepold. TOMSPIN, a tool for modeling with stochastic Petri nets. In CompEuro 92, pages 618–623, The Hague, The Netherlands, May 1992.

    Google Scholar 

  19. C. Lindemann. DSPNexpress: A software package for the efficient solution of Deterministic and Stochastic Petri Nets. In Proc. 6th Int. Conf. on Modelling Techniques and Tools for Computer Performance Evaluation, pages 15–29, Edinburgh, Great Britain, 1992.

    Google Scholar 

  20. M. Lu, D. Zhang, and T. Murata. Analysis of self-stabilizing clock synchronization by means of stochastic Petri nets. IEEE Trans. Comp., 39:597–604, 1990.

    Google Scholar 

  21. J. L. Peterson. Petri Net Theory and the Modeling of Systems. Prentice-Hall, 1981.

    Google Scholar 

  22. C. Petri. Kommunikation mit Automaten. PhD thesis, University of Bonn, Bonn, West Germany, 1962.

    Google Scholar 

  23. W. Reisig. Petri Nets, volume 4 of EATC Monographs on Theoretical Computer Science. Springer-Verlag, 1985.

    Google Scholar 

  24. R. Valk. On the computational power of extended Petri nets. In Seventh Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science 64, pages 527–535. Springer-Verlag, 1978.

    Google Scholar 

  25. R. Valk. Generalizations of Petri nets. In Mathematical foundations of computer science, Lecture Notes in Computer Science 118, pages 140–155. Springer-Verlag, 1981.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, College of William and Mary, 23187-8795, Williamsburg, VA, USA

    Gianfranco Ciardo

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  1. Gianfranco Ciardo
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Robert Valette

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© 1994 Springer-Verlag Berlin Heidelberg

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Ciardo, G. (1994). Petri nets with marking-dependent arc cardinality: Properties and analysis. In: Valette, R. (eds) Application and Theory of Petri Nets 1994. ICATPN 1994. Lecture Notes in Computer Science, vol 815. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58152-9_11

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  • DOI: https://doi.org/10.1007/3-540-58152-9_11

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58152-9

  • Online ISBN: 978-3-540-48462-2

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