Abstract
This paper studies the periodic functioning of deterministic timed Petri Nets for generalized nets (i.e with integer valued arcs). From the formulation of the average marking in steady-state, we first establish a set of necessary conditions between the initial marking, the firing times and frequencies of transitions, the dates of first firing occurences and the minimal delays of tokens at places. These conditions are shown to provide a lower bound to the cycle time, using the minimal S-invariants of the net. A modeling of multi-stage production systems is further developed, based on timed Petri Nets, and the results obtained are used to conduct a performance evaluation of the system.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Ramchandani, C. (1974). "Analysis of asynchronous concurrent systems by Timed Petri Nets", Technical Report no 120, Laboratory for Computer Science, MIT, Cambridge, MA.
Sifakis, J. (1980). "Performance Evaluation of Systems using nets", Net Theory and Applications, Lecture Notes in Computer Science, Springer-Verlag, Berlin, FRG, pp. 307–319.
Ramamoorthy, C.V and G.S. Ho (1980). "Performance Evaluation of asynchronous concurrent systems using Petri Nets", IEEE Trans. on Software Engineering, vol. SE-6, no 5, pp. 440–449.
Chretienne, P. (1984). "Exécutions contrôlées des réseaux de Pétri temporisés", Technique et Sciences Informatiques, volume 3, no 1, pp. 23–31; see also "Les Réseaux de Pétri Temporisés", Thèse d'Etat, Université Paris VI, Paris.
Chretienne, P. and J. Carlier (1984). "Modeling Scheduling Problems with Timed Petri Nets", Advances in Petri Nets 1984, Lecture Notes in Computer Science no 188, Springer-Verlag, Berlin, FRG, pp. 62–82.
Doetsch, G. (1974). Introduction to the theory and application of the Laplace Transform, Springer-Verlag.
Halbwachs, N. (1984). "Modélisation et Analyse des Systèmes Informatiques Temporisés", Thèse d'Etat, INPG Grenoble.
Alla, H. (1987). "Réseaux de Pétri colorés et Réseaux de Pétri continus", Thèse d'Etat, INPG Grenoble.
Memmi, G. (1980). "Linear Algebra in Net theory", Net theory and Applications, Lecture Notes in Computer Science, no 84, Springer-Verlag, Berlin, FRG, pp. 213–223.
Orlicky, J.A, G. plossl and O.W. Wight (1972). "Structuring the Bill of Material for MRP", Production and Inventory Management, volume 13, no 4, pp. 19–42.
Martinez, J. and M. Silva (1980). "A simple and fast algorithm to obtain all invariants of a generalized Petri Net", Lecture Notes in Computer Science, no 52, Springer-Verlag, Berlin, pp. 302–310.
Buzacott, J.A. and D.D. Yao (1986). "On Queueing Network Models of Flexible Manufacturing Systems", Queueing Theory and Applications, vol. 1.
Hillion, H.P and J.M. Proth (1989). "Performance Evaluation of job-shop systems using timed Event-Graphs", IEEE trans. on Automatic Control, vol. 34, no1, jan. 89.
Hillion, H.P, J.M. Proth and X.L. Xie (1987). "A heuristic algorithm for the periodic scheduling and sequencing job-shop problem", proc. 26th IEEE Conference on Decision and Control, Los-Angeles, Dec. 9–11.
Hillion, H.P. (1989). "Modélisation et analyse des systèmes de production discrets par les réseaux de Petri temporisés", Doctorat de l'Université Paris VI, Paris, jan. 1989.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1990 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hillion, H.P. (1990). Timed Petri nets and application to multi-stage production systems. In: Rozenberg, G. (eds) Advances in Petri Nets 1989. APN 1988. Lecture Notes in Computer Science, vol 424. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52494-0_34
Download citation
DOI: https://doi.org/10.1007/3-540-52494-0_34
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-52494-6
Online ISBN: 978-3-540-46998-8
eBook Packages: Springer Book Archive