Approximation of stochastic petri nets by means of continuous petri nets: adaptive approach

  • Authors

    • Nabil Benaya Faculty of Sciences and Techniques of Tangier
    • Nabil El Akchioui Faculty of Sciences and Techniques of Al Hoceima
    • Taoufik Mourabit Faculty of Sciences and Techniques of Al Hoceima
    2019-05-05
    https://doi.org/10.14419/ijet.v7i4.21001
  • Adaptive Approach, Continuous Petri Nets, Fluidification, Reliability Analysis, Stochastic Petri Nets.

  • Abstract

    Reliability analysis is often based on stochastic discrete event models like Markov models or stochastic Petri nets. For complex dynamical systems with numerous components, analytical expressions of the steady state are tedious to work out because of the combinatory explosion with discrete models. The contribution of this paper is to estimate the asymptotic comportement of stochastic nets by mean of continuous Petri nets according to a no linear modification of the maximal firing speed.

     


  • References

    1. [1] Ajmone Marsan and G. Chiola, “On Petri nets with deterministic and exponentially distributed firing timesâ€, Advances in Petri nets (Rozenberg G.), Springer Verlag, 1987, pp. 132- 145. https://doi.org/10.1007/3-540-18086-9_23.

      [2] A. Bobbio, A. Puliafito, M. Telek and K. Trivedi, “Recent Developments in Stochastic Petri Netsâ€, Journal of Circuits, Systems, and Computers, Vol. 8, No. 1, Feb 1998, pp. 119--158.https://doi.org/10.1142/S0218126698000067.

      [3] R. David and H. Alla, “Petri nets and grafcet – tools for modelling discrete events systemsâ€, Prentice Hall, London, 1992.

      [4] M. Diaz, “Les réseaux de Petri: modèlesfondamentauxâ€, Hermes, Paris, 2001.

      [5] G. Júlvez, L. Recalde and M. Silva, “Steady-state performance evaluation of continuous mono-T-semiflow Petri netsâ€, Automatica, Vol. 41, no. 4, 2005, pp. 605-616.https://doi.org/10.1016/j.automatica.2004.11.007.

      [6] M.K. Molloy, “On the integration of delay and troughput in distributed processing modelsâ€, Ph. D, UCLA, Los Angeles, USA, 1981.

      [7] M.K. Molloy, “Performance analysis using stochastic Petri netsâ€, IEEE Transactions on Computers C, vol. 31, 1982, pp. 913 – 917.https://doi.org/10.1109/TC.1982.1676110.

      [8] M. Silva and L. Recalde, “On fluidification of Petri Nets: from discrete to hybrid and continuous modelsâ€, Annual Reviews in Control, Vol. 28, no. 2, 2004, pp. 253-266.https://doi.org/10.1016/j.arcontrol.2004.05.002.

      [9] D. Lefebvre, E. Leclercq, L. Khalij, E. Souza de Cursi and N. El Akchioui, “Approximation of MTS stochastic Petri nets steady state by means of continuous Petri nets: a numerical approachâ€, Proc. IFAC ADHS, Zaragoza, Spain, 2009, pp. 62-67.https://doi.org/10.3182/20090916-3-ES-3003.00012.

      [10] D. Lefebvre, “About the stochastic and continuous Petri nets equivalence in long runâ€, Non-Linear Analysis, Hybrid Systems NAHS, vol.5, pp. 394-406, 2011.https://doi.org/10.1016/j.nahs.2011.02.001.

      [11] M. Rausand and A. Hoyland, “System reliability theory: models, statistical methods, and applicationsâ€, Wiley, Hoboken, New Jersey, 2004.

      [12] L. Recalde, E. Teruel and M. Silva, “Autonomous continuous P/T systems, Lecture notes in computer scienceâ€, vol. 1639, (1999) pp 107 – 126.https://doi.org/10.1007/3-540-48745-X_8.

      L. Recalde and M. Silva, “Petri nets and integrality relaxations: a view of continuous Petri netsâ€, Trans. IEEE – SMC, part C, 32(4), 2002, pp. 314-326.https://doi.org/10.1109/TSMCC.2002.806063

  • Downloads

  • How to Cite

    Benaya, N., El Akchioui, N., & Mourabit, T. (2019). Approximation of stochastic petri nets by means of continuous petri nets: adaptive approach. International Journal of Engineering & Technology, 7(4), 5983-5985. https://doi.org/10.14419/ijet.v7i4.21001