Advertisement

Timed Petri Net schedules

  • J. Carlier
  • P. Chretienne
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 340)

Abstract

In this paper, we define Timed Petri Net schedules and study some of their properties. We prove that the set of schedules issued from a firable sequence of the underlying Petri net has a minimum element we call earliest schedule of the sequence. We then propose a polynomial algorithm to compute it. In order to study earliest schedules, we introduce next a graph we call earliest state graph. Finally, for bounded Petri nets, we prove that earliest schedules issued from periodic infinite sequences are K-periodic and constitute a dominant subset.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

VIII. References

  1. BRAMS 82.
    C.ANDRE, G.BERTHELOT, C.GIRAULT, G.MEMMI, G.ROUCAIROL, G.SIFAKIS, R.VALETTE, G.VIDAL NAQUET Réseaux de Petri, Tomes 1 et 2. MASSON, 1982.Google Scholar
  2. CCG 85.
    J.CARLIER, P.CHRETIENNE, C.GIRAULT Modelling scheduling problems with Timed Petri Nets. Advances in Petri Nets 1985.Google Scholar
  3. CAC 82.
    J. CARLIER, P. CHRETIENNE Un domaine très ouvert: les problèmes d'ordonnancement. RAIRO, 16,3,p175–217; 1982Google Scholar
  4. CAR 84.
    J.CARLIER Problèmes d'ordonnancement à contraintes de ressources: algorithmes et complexité Thèse d'état, Université Paris VI; 1984Google Scholar
  5. CHR 83.
    P.CHRETIENNE Les réseaux de Petri temporisés Thèse d'état, Université Paris VI, mai 1983Google Scholar
  6. CHR 84.
    P. CHRETIENNE Exécutions contrôlées des réseaux de Petri temporisés TSI,1,p23–31; 1984Google Scholar
  7. COH 85.
    G.COHEN, D.DUBOIS, J.P. QUADRAT, M.VIOT A linear system theoretic view of discrete event processes and its use for performance evaluation in manufacturing. IEEE Trans on Automatic Control, March 85; 1985Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • J. Carlier
    • 1
  • P. Chretienne
    • 2
  1. 1.Université Technologique de CompiegneFrance
  2. 2.Laboratoire MASIUniversité Pierre et Marie CurieParis Cedex 05

Personalised recommendations