Asymptotic continuous Petri nets. (English) Zbl 0769.93010

Summary: A Petri net is basically a discrete model. However, continuous Petri nets, such that the markings are real numbers have been defined. Two continuous Petri net models involving time have been drawn up. They differ by the calculation of the instantaneous firing speeds of the transitions. Both can be used to approximate a timed Petri net. The former considers constant firing speeds (CCPN) and is very easy to simulate (few events have to be considered, even when it approximates a timed Petri net with many reachable markings). The latter considers firing speeds depending on the marking (VCPN). Although it provides a better approximation, its simulation is longer because the markings and speed are given by differential equations. This paper introduces a third model (ACPN) which presents the advantages of the two preceding ones. In most cases, this model represents the asymptotic behavior of the VCPN. Then their precisions are similar. Since the firing speeds of the ACPN are constant, it is as easy to simulate as the CCPN.


93A30 Mathematical modelling of systems (MSC2010)


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[1] Ajmone Marsan, M., Balbo, G., Bobio, A., Chiola, G., Conte, G., and Cumani, A., 1985. On Petri nets with stochastic timing.Int. Workshop in Timed Petri Nets, Turin (I).
[2] Alla, H., and David, R., 1988. Modelling of production systems by continuous Petri nets.3rd Int. Conf. CAD/CAM, CARS & FOF88, Detroit, 344–348.
[3] Chretienne, P., 1983. Les Réseaux de Petri Temporisés. Thèse d’etat, Université Paris VI.
[4] Cohen, G., Moller, P., Quadrat, J.-P., and Viot, J., 1989. Algebraic tools for the performance evaluation of discrete event systems.Proc. IEEE, 77: 39–57.
[5] David, R., and Alla, H. 1987. Continuous Petri nets.8th European Workshop on Application and Theory of Petri Nets, Saragosse (E), 275–294.
[6] David, R., and Alla, H., 1990. Autonomous and timed continuous Petri nets.11th Int. Conf. Application and Theory of Petri Nets, Paris, 367–386.
[7] David, R., and Alla, H., 1989.Du Grafcet aux réseaux de Petri. Paris: Editions Hermès. English version, 1992:Petri Nets and Grafcet: Tools for Modelling of Discrete Event Systems, London: Prentice Hall.
[8] David, R., Xie, X., and Dallery, Y., 1990. Properties of continuous models of transfer lines with unreliable machines and finite buffers.IMA J. Math. Appl. Business Indust., No. 6: 281–308. · Zbl 0718.90040
[9] Dubois, D., and Forestier, J.-P., 1982. Productivité et en-cours moyens d’un ensemble de deux machines separées par un stock.Rev. RAIRO Automat., 16: 105–132. · Zbl 0486.90048
[10] Florin, G., and Natkin, S., 1986. RDPS: A software package for the validation and evaluation of dependable computer systems.Safecomp 86, Proc. Fifth IFAC Workshop, Sarlat.
[11] Gershwin, S.B., and Schick, I.C., 1980. Continuous model of an unreliable two-stage material flow system with a finite interstage buffer. Technical report MIT LIDS-R-1032.
[12] Le Bail, J., 1991. Un nouveau modèle continu: les réseaux de Petri continus asymptotiques, Technical report L.A.G. No. 91/22.
[13] Le Bail, J., Alla, H., and David, R., 1992. Asymptotic continuous Petri nets: an efficient approximation of discrete event systems.IEEE. Int. Conf. Robotics and Automation, Nice, 1050–1056.
[14] Max Plus, 1991. A linear system theory for systems subject to synchronization and saturation constraint.First European Control Conf., Grenoble, France, 1022–1033.
[15] Molloy, M.K., 1985. Fast bounds for stochastic Petri nets.Int. Workshop on Timed Petri Nets, Torino (I), 244–249.
[16] Ramchandani, C., 1973. Analysis of Asynchronous Concurrent Systems by Timed Petri Nets. Ph.D. thesis, MIT. · Zbl 0362.68090
[17] Sifakis, J., 1977. Use of Petri nets for performance evaluation, pp. 75–93 inMeasuring, Modelling and Evaluating Computer Systems, Beilner, H., and Gelenbe, E. (eds.). Amsterdam: North-Holland.
[18] Tarski, A., 1955. A lattice theorical fixpoint theorem and its applications.Pacific J. Math., 5. · Zbl 0064.26004
[19] Zerhouni, N., and Alla, H., 1990. Dynamic analysis of manufacturing systems using continuous Petri nets.IEEE Int. Conf. Robotics and Automation, Cincinnati, 1070–1075.
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