Asynchronous Abstract Machines: Petri Nets

  • Carlo A. Furia
  • Dino Mandrioli
  • Angelo Morzenti
  • Matteo Rossi
Part of the Monographs in Theoretical Computer Science. An EATCS Series book series (EATCS)


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.


Firing Rate Firing Time Firing Sequence Dine Philosopher Time Semantic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 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. 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. 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. 4.
    Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. Wiley (1995). Available online at
  5. 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. 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. 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. 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. 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. 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. 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. 12.
    Busi, N.: Analysis issues in Petri nets with inhibitor arcs. Theor. Comput. Sci. 275(1–2), 127–177 (2002)Google Scholar
  13. 13.
    Cassandras, C.G., Lafortune, S.: Introduction to Discrete Event Systems. Springer, Boston (2007)Google Scholar
  14. 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. 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-16/93Google Scholar
  16. 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. 17.
    David, R., Alla, H.: Discrete, Continuous, and Hybrid Petri Nets. Springer, Berlin/London (2010)Google Scholar
  18. 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. 19.
    Diaz, M.: Petri Nets: Fundamental Models, Verification and Applications. Wiley, Hoboken (2009)Google Scholar
  20. 20.
    Dijkstra, E.W.: Hierarchical ordering of sequential processes. Acta Inf. 1(2), 115–138 (1971)Google Scholar
  21. 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. 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. 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. 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. 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. 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. 27.
    Haas, P.J.: Stochastic Petri Nets: Modelling, Stability, Simulation. Springer, New York (2010)Google Scholar
  28. 28.
    Heitmeyer, C.L., Mandrioli, D. (eds.): Formal Methods for Real-Time Computing. Wiley, Chichester/New York (1996)Google Scholar
  29. 29.
    Jensen, K., Kristensen, L.M.: Coloured Petri Nets: Modelling and Validation of Concurrent Systems. Springer, Dordrecht/New York (2009)Google Scholar
  30. 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. 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. 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. 33.
    Misa, T.J.: An interview with Edsger W. Dijkstra. Commun. ACM 53(1), 41–47 (2010)Google Scholar
  34. 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. 35.
    Moody, J., Antsaklis, P.J.: Supervisory Control of Discrete Event Systems Using Petri Nets. Kluwer, Boston (1998)Google Scholar
  36. 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. 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. 38.
    Peterson, J.L.: Petri Net Theory and the Modelling of Systems. Prentice-Hall, Englewood Cliffs (1981)Google Scholar
  39. 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. 40.
    Ramchandani, C.: Analysis of asynchronous concurrent systems by timed Petri nets. Ph.D. thesis, Massachussets Institute of Technology (1974)Google Scholar
  41. 41.
    Reisig, W.: Petri Nets: An Introduction. EATCS Monographs on Theoretical Computer Science. Springer, Berlin/New York (1985)Google Scholar
  42. 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. 43.
  44. 44.
    UML 2.0 superstructure specification. Tech. Rep. formal/05-07-04, Object Management Group (2005)Google Scholar
  45. 45.
    Wang, J.: Timed Petri Nets, Theory and Application. Kluwer, Boston (1998)Google Scholar
  46. 46.
    Wang, J., Deng, Y.: Incremental modeling and verification of flexible manufacturing systems. J. Intell. Manuf. 10(6), 485–502 (1999)Google Scholar
  47. 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. 48.
    Zimmermann, A., Knoke, M.: TimeNET 4.0 user manual. Tech. Rep. 2007–13, Technische Universität Berlin, Faculty of EE&CS (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Carlo A. Furia
    • 1
  • Dino Mandrioli
    • 2
  • Angelo Morzenti
    • 2
  • Matteo Rossi
    • 2
  1. 1.Department of Computer ScienceZürichSwitzerland
  2. 2.Dipartimento di Elettronica e InformazionePolitecnico di MilanoMilanItaly

Personalised recommendations