Skip to main content
SpringerLink
Log in
Book cover

Modeling Time in Computing pp 209–247Cite as

Asynchronous Abstract Machines: Petri Nets

  • Chapter
  • First Online:

  • 1242 Accesses

Abstract

In this chapter, we present Petri nets, a typical asynchronous operational formalism. First, we introduce the basic formalism. Then, among the many extensions that have been proposed in the literature, we focus on those that have a major impact on timing analysis. In particular, we introduce timed Petri nets, which allow one to deal with metric time domains; nets with inhibitor arcs, which reach the full computational power of Turing machines; and stochastic Petri nets. We also discuss the composition of timed Petri nets. The chapter concludes with a brief review of the tools supporting the analysis techniques associated with the formalism.

This is a preview of subscription content, 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
Hardcover Book
USD   54.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Notes

  1. 1.

    The philosophers’ pictures are courtesy of Benjamin D. Esham/Wikimedia Commons.

  2. 2.

    As has been repeatedly observed, the setup does not perfectly fit normal eating habits, at least Italian ones, where spaghetti are eaten using only one fork. A more realistic version may assume bowls of rice eaten with chopsticks. However, we liked it better to present the “historical” version of the problem.

References

  1. Ajmone Marsan, M.: Stochastic Petri nets: an elementary introduction. In: Rozenberg, G. (ed.) Advances in Petri Nets. Lecture Notes in Computer Science, vol. 424, pp. 1–29. Springer, Berlin/New York (1989)

    Google Scholar 

  2. Ajmone Marsan, M., Balbo, G., Chiola, G., Conte, G.: Generalized stochastic Petri nets revisited: random switches and priorities. In: Proceedings of the International Workshop on Petri Nets and Performance Models, pp. 44–53. IEEE-CS Press, Los Alamitos (1987)

    Google Scholar 

  3. Ajmone Marsan, M., Balbo, G., Conte, G.: A class of generalized stochastic Petri nets for the performance analysis of multiprocessor systems. ACM Trans. Comput. Syst. 2(1), 93–122 (1984)

    Google Scholar 

  4. Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. Wiley (1995). Available online at http://www.di.unito.it/~greatspn/GSPN-Wiley/

  5. Baarir, S., Beccuti, M., Cerotti, D., De Pierro, M., Donatelli, S., Franceschinis, G.: The GreatSPN tool: recent enhancements. SIGMETRICS Perform. Eval. Rev. 36(4), 4–9 (2009)

    Google Scholar 

  6. Bérard, B., Cassez, F., Haddad, S., Lime, D., Roux, O.H.: Comparison of the expressiveness of timed automata and time Petri nets. In: Pettersson, P., Yi, W. (eds.) FORMATS. Lecture Notes in Computer Science, vol. 3829, pp. 211–225. Springer, Heidelberg (2005)

    Google Scholar 

  7. Berthomieu, B., Diaz, M.: Modeling and verification of time dependent systems using time Petri nets. IEEE Trans. Softw. Eng. 17(3), 259–273 (1991)

    Google Scholar 

  8. Berthomieu, B., Vernadat, F.: Time Petri nets analysis with TINA. In: QEST, pp. 123–124. IEEE Computer Society, Los Alamitos (2006)

    Google Scholar 

  9. Bouyer, P., Haddad, S., Reynier, P.A.: Timed Petri nets and timed automata: On the discriminating power of Zeno sequences. Inf. Comput. 206(1), 73–107 (2008)

    Google Scholar 

  10. Boyer, M., Roux, O.H.: On the compared expressiveness of arc, place and transition time Petri nets. Fundam. Inform. 88(3), 225–249 (2008)

    Google Scholar 

  11. Buchs, D., Guelfi, N.: A formal specification framework for object-oriented distributed systems. IEEE Trans. Softw. Eng. 26(7), 635–652 (2000)

    Google Scholar 

  12. Busi, N.: Analysis issues in Petri nets with inhibitor arcs. Theor. Comput. Sci. 275(1–2), 127–177 (2002)

    Google Scholar 

  13. Cassandras, C.G., Lafortune, S.: Introduction to Discrete Event Systems. Springer, Boston (2007)

    Google Scholar 

  14. Cassez, F., Roux, O.H.: Structural translation from time Petri nets to timed automata. J. Syst. Softw. 79(10), 1456–1468 (2006)

    Google Scholar 

  15. Cerone, A.: A net-based approach for specifying real-time systems. Ph.D. thesis, Università degli Studi di Pisa, Dipartimento di Informatica (1993). TD-16/93

    Google Scholar 

  16. Cerone, A., Maggiolo-Schettini, A.: Time-based expressivity of time Petri nets for system specification. Theor. Comput. Sci. 216(1–2), 1–53 (1999)

    Google Scholar 

  17. David, R., Alla, H.: Discrete, Continuous, and Hybrid Petri Nets. Springer, Berlin/London (2010)

    Google Scholar 

  18. Di Marzo Serugendo, G., Mandrioli, D., Buchs, D., Guelfi, N.: Real-time synchronised Petri nets. In: Proceedings of the 23rd International Conference on Application and Theory of Petri Nets (ICATPN’02), Adelaide. Lecture Notes in Computer Science, vol. 2360, pp. 142–162. Springer, Berlin (2002)

    Google Scholar 

  19. Diaz, M.: Petri Nets: Fundamental Models, Verification and Applications. Wiley, Hoboken (2009)

    Google Scholar 

  20. Dijkstra, E.W.: Hierarchical ordering of sequential processes. Acta Inf. 1(2), 115–138 (1971)

    Google Scholar 

  21. Esparza, J.: Decidability and complexity of Petri net problems–an introduction. In: Rozenberg, G., Reisig, W. (eds.) Advances in Petri Nets. Lecture Notes in Computer Science, vol. 1491, pp. 374–428. Springer, Berlin (1998)

    Google Scholar 

  22. Esparza, J., Nielsen, M.: Decidability issues for Petri nets–a survey. Bull. Eur. Assoc. Theor. Comput. Sci. 52, 245–262 (1994)

    Google Scholar 

  23. Felder, M., Mandrioli, D., Morzenti, A.: Proving properties of real-time systems through logical specifications and Petri net models. IEEE Trans. Softw. Eng. 20(2), 127–141 (1994)

    Google Scholar 

  24. Gardey, G., Lime, D., Magnin, M., Roux, O.H.: Romeo: a tool for analyzing time Petri nets. In: Etessami, K., Rajamani, S.K. (eds.) CAV. Lecture Notes in Computer Science, vol. 3576, pp. 418–423. Springer, Heidelberg (2005)

    Google Scholar 

  25. Gargantini, A., Mandrioli, D., Morzenti, A.: Dealing with zero-time transitions in axiom systems. Inf. Comput. 150(2), 119–131 (1999)

    Google Scholar 

  26. Ghezzi, C., Mandrioli, D., Morasca, S., Pezzè, M.: A unified high-level Petri net formalism for time-critical systems. IEEE Trans. Softw. Eng. 17(2), 160–172 (1991)

    Google Scholar 

  27. Haas, P.J.: Stochastic Petri Nets: Modelling, Stability, Simulation. Springer, New York (2010)

    Google Scholar 

  28. Heitmeyer, C.L., Mandrioli, D. (eds.): Formal Methods for Real-Time Computing. Wiley, Chichester/New York (1996)

    Google Scholar 

  29. Jensen, K., Kristensen, L.M.: Coloured Petri Nets: Modelling and Validation of Concurrent Systems. Springer, Dordrecht/New York (2009)

    Google Scholar 

  30. Khansa, W., Denat, J.P., Collart-Dutilleul, S.: P-time Petri nets for manufacturing systems. In: Proceedings of the International Workshop on Discrete Event Systems (WODES’96), Edinburgh, pp. 94–102 (1996)

    Google Scholar 

  31. Krepska, E., Bonzanni, N., Feenstra, K.A., Fokkink, W., Kielmann, T., Bal, H.E., Heringa, J.: Design issues for qualitative modelling of biological cells with Petri nets. In: Proceedings of Formal Methods in System Biology (FMSB’08), Cambridge, pp. 48–62 (2008)

    Google Scholar 

  32. Merlin, P.M., Farber, D.J.: Recoverability and communication protocols: implications of a theoretical study. IEEE Trans. Commun. 24(9), 1036–1043 (1976)

    Google Scholar 

  33. Misa, T.J.: An interview with Edsger W. Dijkstra. Commun. ACM 53(1), 41–47 (2010)

    Google Scholar 

  34. Molloy, M.K.: On the integration of delay and throughput measures in distributed processing models. Ph.D. thesis, University of California, Los Angeles (1981)

    Google Scholar 

  35. Moody, J., Antsaklis, P.J.: Supervisory Control of Discrete Event Systems Using Petri Nets. Kluwer, Boston (1998)

    Google Scholar 

  36. Natkin, S.: Les reseaux de Petri stochastiques et leur application a l’evaluation des systèmes informatiques. Thèse de Docteur Ingénieur, CNAM, Paris, France (1980)

    Google Scholar 

  37. Penczek, W., Polrola, A.: Advances in Verification of Time Petri Nets and Timed Automata: A Temporal Logic Approach. Springer, Berlin/New York (2006)

    Google Scholar 

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

    Google Scholar 

  39. Petri, C.A.: Fundamentals of a theory of asynchronous information flow. In: Proceedings of IFIP Congress, pp. 386–390. North Holland Publishing Company, Amsterdam (1963)

    Google Scholar 

  40. Ramchandani, C.: Analysis of asynchronous concurrent systems by timed Petri nets. Ph.D. thesis, Massachussets Institute of Technology (1974)

    Google Scholar 

  41. Reisig, W.: Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science. Springer, Berlin/New York (1985)

    Google Scholar 

  42. Rohr, C., Marwan, W., Heiner, M.: Snoopy–a unifying Petri net framework to investigate biomolecular networks. Bioinformatics 26(7), 974–975 (2010)

    Google Scholar 

  43. Petri nets world. http://www.informatik.uni-hamburg.de/TGI/PetriNets/

  44. UML 2.0 superstructure specification. Tech. Rep. formal/05-07-04, Object Management Group (2005)

    Google Scholar 

  45. Wang, J.: Timed Petri Nets, Theory and Application. Kluwer, Boston (1998)

    Google Scholar 

  46. Wang, J., Deng, Y.: Incremental modeling and verification of flexible manufacturing systems. J. Intell. Manuf. 10(6), 485–502 (1999)

    Google Scholar 

  47. Zhou, M., Venkatesh, K.: Modeling, Simulation, and Control of Flexible Manufacturing Systems: A Petri Net Approach. World Scientific, Singapore/River Edge (1999)

    Google Scholar 

  48. Zimmermann, A., Knoke, M.: TimeNET 4.0 user manual. Tech. Rep. 2007–13, Technische Universität Berlin, Faculty of EE&CS (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, Zürich, Switzerland

    Carlo A. Furia

  2. Dipartimento di Elettronica e Informazione, Politecnico di Milano, Milan, Italy

    Dino Mandrioli, Angelo Morzenti & Matteo Rossi

Authors
  1. Carlo A. Furia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Dino Mandrioli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Angelo Morzenti
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Matteo Rossi
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Furia, C.A., Mandrioli, D., Morzenti, A., Rossi, M. (2012). Asynchronous Abstract Machines: Petri Nets. In: Modeling Time in Computing. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32332-4_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-32332-4_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-32331-7

  • Online ISBN: 978-3-642-32332-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation