Skip to main content
SpringerLink
Log in

Introduction to Generalized Stochastic Petri Nets

  • Chapter
Formal Methods for Performance Evaluation (SFM 2007)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 4486))

Abstract

Generalized Stochastic Petri Nets are a modelling formalism that can be conveniently used for the analysis of complex models of Discrete Event Dynamic Systems and for their performance and reliability evaluation. The automatic construction of the probabilistic models that underly the dynamic behaviours of these nets rely on a set of results that derive from the theory of untimed Petri nets. The paper briefly surveys some results of net theory together with the different approaches used to introduce the concept of time in these models that are useful for the definition of Stochastic Petri Nets and Generalized Stochastic Petri Nets. Details on the solution techniques and on their computational aspects are provided. A brief overview of advanced material is included at the end of the paper to highlight the state of the art in this field and to give pointers to relevant results published in the literature.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Agerwala, T.: Putting Petri nets to work. IEEE Computer, 85–94 (December 1979)

    Google Scholar 

  2. Ajmone Marsan, M., Balbo, G., Bobbio, A., Chiola, G., Conte, G., Cumani, A.: The effect of execution policies on the semantics and analysis of stochastic Petri nets. IEEE Transactions on Software Engineering 15(7), 832–846 (1989)

    Article  MathSciNet  Google Scholar 

  3. Ajmone Marsan, M., Balbo, G., Chiola, G., Conte, G.: Generalized stochastic Petri nets revisited: Random switches and priorities. In. In: Proc. Intern. Workshop on Petri Nets and Performance Models, Madison, WI, USA, August 1987, pp. 44–53. IEEE Computer Society Press, Los Alamitos (1987)

    Google Scholar 

  4. Ajmone Marsan, M., Balbo, G., Conte, G.: A class of generalized stochastic Petri nets for the performance analysis of multiprocessor systems. ACM Transactions on Computer Systems 1 (1984)

    Google Scholar 

  5. Ajmone Marsan, M., Balbo, G., Conte, G.: Performance Models of Multiprocessor Systems. MIT Press, Cambridge (1986)

    Google Scholar 

  6. Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. J. Wiley, Chichester (1995)

    MATH  Google Scholar 

  7. Ajmone Marsan, M., Balbo, G., Trivedi, K.S. (eds.): Proc. Intern. Workshop on Timed Petri Nets, Torino, Italy, July 1985. IEEE-CS Press, Los Alamitos (1985)

    Google Scholar 

  8. Ajmone Marsan, M., Chiola, G.: On Petri nets with deterministic and exponential transition firing times. In: Proc. 7th European Workshop on Application and Theory of Petri Nets, Oxford, England, June 1986, pp. 151–165 (1986)

    Google Scholar 

  9. Alaiwan, H., Memmi, G.: Algorithmes de recherche des solutions entieres positives d’un systeme d’equations lineaires homogeneus en nombres entieres. Revue Technique Thomson-CSF 14(1), 125–135 (1982)

    Google Scholar 

  10. Alaiwan, H., Toudic, J.M.: Research des semiflots, des verrous et des trappes dans le reseaux de Petri. Technique et Science Informatiques 4(1) (1985)

    Google Scholar 

  11. Balbo, G.: Exponential stochastic petri nets. In: Balbo, G., Silva, M. (eds.) Performance Models for Discrete Event Systems with Synchronisations: Formalisms and Analysis Techniques, pp. 307–344. KRONOS, Zaragoza (1998)

    Google Scholar 

  12. Balbo, G.: Non-exponential stochastic petri nets. In: Balbo, G., Silva, M. (eds.) Performance Models for Discrete Event Systems with Synchronisations: Formalisms and Analysis Techniques, pp. 345–385. KRONOS, Zaragoza (1998)

    Google Scholar 

  13. Balbo, G.: Introduction to stochastic petri nets. In: Brinksma, E., Hermanns, H., Katoen, J.-P. (eds.) Lectures on Formal Methods and Performance Analysis. LNCS, vol. 2090, pp. 84–155. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  14. Balbo, G., Silva, M. (eds.): Performance Models for Discrete Event Systems with Synchronizations: Formalisms and Analysis Techniques. KRONOS, Zaragoza (1998)

    Google Scholar 

  15. Blakemore, A.: The cost of eliminating vanishing markings from generalized stochastic Petri nets. In: Proc. 3rd Intern. Workshop on Petri Nets and Performance Models, Kyoto, Japan, December 1989, IEEE Computer Society Press, Los Alamitos (1989)

    Google Scholar 

  16. Buchholz, P.: Hierarchical high level Petri nets for complex system analysis. In: Valette, R. (ed.) ICATPN 1994. LNCS, vol. 815, pp. 119–138. Springer, Heidelberg (1994)

    Google Scholar 

  17. Chen, P., Bruell, S.C., Balbo, G.: Alternative methods for incorporating non-exponential distributions into stochastic Petri nets. In: Proc. 3rd Intern. Workshop on Petri Nets and Performance Models, Kyoto, Japan, December 1989, pp. 187–197. IEEE Computer Society Press, Los Alamitos (1989)

    Google Scholar 

  18. Chiola, G., Ajmone Marsan, M., Balbo, G., Conte, G.: Generalized stochastic Petri nets: A definition at the net level and its implications. IEEE Transactions on Software Engineering 19(2), 89–107 (1993)

    Article  Google Scholar 

  19. Chiola, G., Dutheillet, C., Franceschinis, G., Haddad, S.: Stochastic Well-Formed coloured nets for symmetric modelling applications. IEEE Transactions on Computers 42(11) (1993)

    Google Scholar 

  20. Chiola, G., Franceschinis, G.: Colored GSPN models and automatic symmetry detection. In: Proc. 3rd Intern. Workshop on Petri Nets and Performance Models, Kyoto, Japan, December 1989, IEEE Computer Society Press, Los Alamitos (1989)

    Google Scholar 

  21. Chiola, G., Franceschinis, G., Gaeta, R., Ribaudo, M.: GreatSPN1.7: GRaphical Editor and Analyzer for Timed and Stochastic Petri Nets. Performance Evaluation (Special Issues on Performance Modelling Tools) 24 (1995)

    Google Scholar 

  22. Choi, H., Kulkarni, G., Trivedi, K.S.: Transient analysis of deterministic and stochastic petri nets. In: Ajmone Marsan, M. (ed.) ICATPN 1993. LNCS, vol. 691, Springer, Heidelberg (1993)

    Google Scholar 

  23. Choi, H., Kulkarni, V.S., Trivedi, K.S.: Markov regenerative stochastic Petri nets. In: Proc. of Performance 93, Rome, Italy (September 1993)

    Google Scholar 

  24. Ciardo, G.: Analysis of large Petri net models. PhD thesis, Department of Computer Science, Duke University, Durham, NC, USA (1989)

    Google Scholar 

  25. Ciardo, G., German, R., Lindemann, C.: A characterization of the stochastic process underlying a stochastic Petri net. In: Proc. 5th Intern. Workshop on Petri Nets and Performance Models, Toulouse, France, Oct. 1993, pp. 170–179. IEEE Computer Society Press, Los Alamitos (1993)

    Chapter  Google Scholar 

  26. Ciardo, G., Lindemann, C.: Analysis of deterministic and stochastic Petri nets. In: Proc. 5th Intern. Workshop on Petri Nets and Performance Models, Toulouse, France, Oct. 1993, pp. 160–169. IEEE Computer Society Press, Los Alamitos (1993)

    Chapter  Google Scholar 

  27. Ciardo, G., Muppala, J., Trivedi, K.S.: On the solution of GSPN reward models. Performance Evaluation 12(4), 237–253 (1991)

    Article  MATH  Google Scholar 

  28. Cumani, A.: On the canonical representation of homogeneousMarkov processes modelling failure time distributions. Microelectron Reliability 22, 583–602 (1982)

    Article  Google Scholar 

  29. Dugan, J.B., Trivedi, K.S., Geist, R.M., Nicola, V.F.: Extended stochastic Petri nets: Applications and analysis. In: Proc. PERFORMANCE ’84, Paris, France (December 1984)

    Google Scholar 

  30. Dutheillet, C., Haddad, S.: Aggregation and disaggregation of states in colored stochastic Petri nets: Application to a multiprocessor architecture. In: Proc. 3rd Intern. Workshop on Petri Nets and Performance Models, Kyoto, Japan, December 1989, IEEE Computer Society Press, Los Alamitos (1989)

    Google Scholar 

  31. Florin, G., Natkin, S.: Les reseaux de Petri stochastiques. Technique et Science Informatiques 4(1) (1985)

    Google Scholar 

  32. Florin, G., Natkin, S.: Matrix product form solution for closed synchronized queueing networks. In: Proc. 3rd Intern. Workshop on Petri Nets and Performance Models, Kyoto, Japan, December 1989, pp. 29–39. IEEE Computer Society Press, Los Alamitos (1989)

    Google Scholar 

  33. German, R., Lindemann, C.: Analysis of stochastic Petri nets by the method of supplementary variables. In: Proc. of Performance 93, Rome, Italy (September 1993)

    Google Scholar 

  34. Lautenbach, K.: Linear algebraic technique for place/transition nets. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 254, pp. 142–167. Springer, Heidelberg (1987)

    Google Scholar 

  35. Lin, C., Marinescu, D.C.: On stochastic high level Petri nets. In: Proc. Intern. Workshop on Petri Nets and Performance Models, Madison, WI, USA, August 1987, IEEE Computer Society Press, Los Alamitos (1987)

    Google Scholar 

  36. Mainkar, V., Choi, H., Trivedi, K.: Sensitivity analysis of Markov regenerative stochastic Petri nets. In: Proc. 5th Intern. Workshop on Petri Nets and Performance Models, Toulouse, France, Oct. 1993, IEEE Computer Society Press, Los Alamitos (1993)

    Google Scholar 

  37. Martinez, J., Silva, M.: A simple and fast algorithm to obtain all invariants of a generalized Petri net. In: Proc. 2nd European Workshop on Application and Theory of Petri Nets, Bad Honnef, West Germany, September 1981. Informatik-Fachberichte, vol. 52, Springer, Heidelberg (1981)

    Google Scholar 

  38. Merlin, P.M., Farber, D.J.: Recoverability of communication protocols: Implications of a theoretical study. IEEE Transactions on Communications 24(9), 1036–1043 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  39. Meyer, J.F., Movaghar, A., Sanders, W.H.: Stochastic activity networks: Structure, behavior, and application. In: Proc. Intern. Workshop on Timed Petri Nets, Torino,Italy, July 1985, pp. 106–115 (1985)

    Google Scholar 

  40. Molloy, M.K.: On the Integration of Delay and Throughput Measures in Distributed Processing Models. PhD thesis, UCLA, Los Angeles, CA (1981)

    Google Scholar 

  41. Molloy, M.K., Murata, T., Vernon, M.K. (eds.): Proc. Intern. Workshop on Petri Nets and Performance Models, Madison, Wisconsin, August 1987. IEEE-CS Press, Los Alamitos (1987)

    Google Scholar 

  42. Murata, T.: Petri nets: properties, analysis, and applications. Proceedings of the IEEE 77(4), 541–580 (1989)

    Article  Google Scholar 

  43. Natkin, S.: Les Reseaux de Petri Stochastiques et leur Application a l’Evaluation des Systemes Informatiques. These de Docteur Ingegneur, CNAM, Paris, France (1980)

    Google Scholar 

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

    MATH  Google Scholar 

  45. Noe, J.D., Nutt, G.J.: Macro e-nets representation of parallel systems. IEEE Transactions on Computers 31(9), 718–727 (1973)

    Article  Google Scholar 

  46. Peterson, J.L.: Petri Net Theory and the Modeling of Systems. Prentice-Hall, Englewood Cliffs (1981)

    Google Scholar 

  47. Petri, C.A.: Communication with automata. Technical Report RADC-TR-65-377, Rome Air Dev. Center, New York, NY (1966)

    Google Scholar 

  48. Reisig, W.: Petri Nets: an Introduction. Springer, Heidelberg (1985)

    MATH  Google Scholar 

  49. Symons, F.J.W.: Introduction to numerical Petri nets, a general graphical model of concurrent processing systems. Australian Telecommunications Research 14(1), 28–33 (1980)

    Google Scholar 

  50. Telek, M., Bobbio, A.: Markov regenerative stochastic petri nets with age type general transitions. In: DeMichelis, G., Díaz, M. (eds.) ICATPN 1995. LNCS, vol. 935, Springer, Heidelberg (1995)

    Google Scholar 

  51. Varga, R.S.: Matrix Iterative Analysis. Prentice-Hall, Englewood Cliffs (1962)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Università di Torino, Dipartimento di Informatica, Corso Svizzera, 185, 10149 Torino, Italy

    Gianfranco Balbo

Authors
  1. Gianfranco Balbo
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Marco Bernardo Jane Hillston

Rights and permissions

Reprints and permissions

Copyright information

© 2007 Springer Berlin Heidelberg

About this chapter

Cite this chapter

Balbo, G. (2007). Introduction to Generalized Stochastic Petri Nets. In: Bernardo, M., Hillston, J. (eds) Formal Methods for Performance Evaluation. SFM 2007. Lecture Notes in Computer Science, vol 4486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72522-0_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-72522-0_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-72482-7

  • Online ISBN: 978-3-540-72522-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation