Performance Evaluation of Discrete Event Systems Thanks to New Representations for (max,+) Automata

Rabah Boukra, Sébastien Lahaye, Jean-Louis Boimond

Abstract

In this contribution, we study the performances of discrete event systems modeled by (max,+) automata. More precisely, new representations for (max,+) automata are first proposed. From these, several performance indicators can be derived, in particular the maximum time execution and a minorant of the minimum execution time for a sequence of length n. Finally these results are discussed in comparison with several studies of the literature also dealing with performance evaluation of (max,+) automata.

References

  1. Baccelli, F., Cohen, G., Olsder, G.-J., and Quadrat, J.-P. (1992). Synchronization and Linearity. Wiley.
  2. Cassandras, C. G. and Lafortune, S. (2008). Introduction to Discrete Event Systems. Springer.
  3. Gaubert, S. (1995). Performance Evaluation of (max,+) Automata. IEEE Transaction on Automatic Control, vol. 40(12):2014-2025.
  4. Gaubert, S. and Mairesse, J. (1999). Modeling and Analysis of Timed Petri Nets using Heaps of Pieces. IEEE Transaction on Automatic Control, vol. 44(4):683- 698.
  5. Heidergott, B., Olsder, G. J., and Woude, J. V. D. (2006). Max Plus at work. Princeton.
  6. Houssin, L., Lahaye, S., and Boimond, J.-L. (2007). Just in Time Control of Constrained (max,+)-Linear Systems. Discrete Event Dynamic Systems, vol. 17(2):159-178.
  7. Komenda, J., Lahaye, S., and Boimond, J.-L. (2009). Supervisory Control of (max,+) Automata: A Behavioral Approach. Discrete Event Dynamic Systems, vol. 19(4):525-549.
  8. Lahaye, S., Boimond, J.-L., and Hardouin, L. (1999). Optimal Control of (Min,+) Linear Time-Varying Systems. In 8th International Workshop on Petri Nets and Performance Models (PNPM 1999), pages 170- 178, Saragossa, Spain.
  9. Ramadge, P. J. G. and Wonham, W. M. (1989). The control of discrete event systems. Proceedings of the IEEE, 77:81-98.
  10. Su, R. and Woeginger, G. J. (2011). String Execution Time for Finite Languages: Max is Easy, Min is Hard. Automatica, 47(10):2326-2329.
Download


Paper Citation


in Harvard Style

Boukra R., Lahaye S. and Boimond J. (2012). Performance Evaluation of Discrete Event Systems Thanks to New Representations for (max,+) Automata . In Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-8565-21-1, pages 505-510. DOI: 10.5220/0004038905050510


in Bibtex Style

@conference{icinco12,
author={Rabah Boukra and Sébastien Lahaye and Jean-Louis Boimond},
title={Performance Evaluation of Discrete Event Systems Thanks to New Representations for (max,+) Automata},
booktitle={Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2012},
pages={505-510},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0004038905050510},
isbn={978-989-8565-21-1},
}


in EndNote Style

TY - CONF
JO - Proceedings of the 9th International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - Performance Evaluation of Discrete Event Systems Thanks to New Representations for (max,+) Automata
SN - 978-989-8565-21-1
AU - Boukra R.
AU - Lahaye S.
AU - Boimond J.
PY - 2012
SP - 505
EP - 510
DO - 10.5220/0004038905050510