CYCLE TIME OF P-TIME EVENT GRAPHS

Ph. Declerck, Ab. Guezzi, J-L. Boimond

2007

Abstract

The dater equalities constitutes an appropriate tool which allows a linear description of Timed Event Graphs in the field of (max, +) algebra. This paper proposes an equivalent model in the usual algebra which can describe Timed and P-time Event Graphs. Considering 1-periodic behavior, the application of a variant of Farkas’ lemma allows the determination of upper and lower bounds of the production rate and necessary conditions of consistency.

References

  1. Chrétienne, P. (1985). Analyse des régimes transitoire et asymptotique d'un graphe d'événements temporisé. Technique et Science Informatique, pages 127-142.
  2. F. Baccelli, G. Cohen, G. O. J.-P. Q. (1992). Synchronization and Linearity: An Algebra for Discrete Event Systems. Wiley.
  3. G. Cohen, D. Dubois, J.-P. Q. and Viot, M. (1983). Analyse du comportement périodique de systèmes de production par la théorie des dioides. In Rapport de recherche. INRIA.
  4. Gaubert, S. (November 1995). Resource optimization and (min, +) spectral theory. In IEEE Transactions on Automatic Control, Vol. 40, No. 11.
  5. Hennet, J.-C. (1989). Une extension du lemme de farkas et son application au problème de régulation linéaire sous contraintes. In Compte-Rendus à l'Académie des Sciences, t. 308, Série I, pp. 415-419.
  6. Murata, T. (1989). Petri nets: Properties, analysis and applications. In Proceedings of the IEEE, Vol. 77, No. 4.
  7. Schijver, A. (1987). Theory of linear and integer programming. John Wiley and Sons.
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Paper Citation


in Harvard Style

Declerck P., Guezzi A. and Boimond J. (2007). CYCLE TIME OF P-TIME EVENT GRAPHS . In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: From Planning to Control of Manufacturing Systems, (ICINCO 2007) ISBN 978-972-8865-82-5, pages 489-495. DOI: 10.5220/0001637304890495


in Bibtex Style

@conference{from planning to control of manufacturing systems07,
author={Ph. Declerck and Ab. Guezzi and J-L. Boimond},
title={CYCLE TIME OF P-TIME EVENT GRAPHS},
booktitle={Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: From Planning to Control of Manufacturing Systems, (ICINCO 2007)},
year={2007},
pages={489-495},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001637304890495},
isbn={978-972-8865-82-5},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics - Volume 1: From Planning to Control of Manufacturing Systems, (ICINCO 2007)
TI - CYCLE TIME OF P-TIME EVENT GRAPHS
SN - 978-972-8865-82-5
AU - Declerck P.
AU - Guezzi A.
AU - Boimond J.
PY - 2007
SP - 489
EP - 495
DO - 10.5220/0001637304890495