Abstract
The aim of this paper is the generation of the min-critical and max-critical subsystems which determine the optimal cycle times. Considering a Time Interval Model which can describe Timed Event Graphs and P-time Event Graphs completely, each critical subsystem depends on the lower and upper bounds of the time durations. The proposed approach which is based on linear programming makes a classification of the relations which describe the system. The application to a baking process in a plant bakery shows that the min-critical and max-critical subsystems are not limited to the critical circuits of the Event Graph.
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References
Baccelli F, Cohen G, Olsder GJ, Quadrat JP (1992) Synchronization and Linearity. An Algebra for Discrete Event Systems, available from http://maxplus.org, New York, Wiley
Bernardi S, Campos J (2013) A min-max problem for the computation of the cycle time lower bound in interval-based Time Petri Nets, IEEE Transactions on Systems, Man, and Cybernetics: systems, 43(5)
Declerck P (2013) Cycle Time of a P-time Event Graph with Affine-Interdependent Residence Durations. Journal of Discrete Event Dynamic Systems, available on http://perso-laris.univ-angers.fr/~declerck/
Declerck P (2018) Extremum Cycle Times in Time Interval Models. IEEE Trans. Autom. Control 63(6):1821–1827. http://perso-laris.univ-angers.fr/~declerck/
Giua A, Piccaluga A, Seatzu C (2000) Optimal token allocation in timed cyclic Event-Graphs, Proc. 4th Workshop on Discrete Event Systems, pp 209–218
Gros C (2000) DEA Report in ”Biotechnologies et Industries Alimentaires”, Ecole Nationale supérieure d’Agronomie et des Industries Alimentaires, ENSAIA, INPL
Lee T-E, Park S-H, Jung C (2014) Steady State Analysis of Timed Event Graph with Time Window Constraints. Applied Mathematics 167:202–216
Hanen C, Munier Kordon A (2009) Periodic schedules for linear precedence constraints. Applied Mathematics 157(2):280–291
Murata T (1989) Petri nets: properties, analysis and applications. Proceedings of the IEEE 4:77
Rodríguez RJ, Júlvez J (2010) Accurate Performance Estimation for Stochastic Marked Graphs by Bottleneck Regrowing. From book Computer Performance Engineering - 7th European Performance Engineering Workshop, EPEW, 2010, Bertinoro, italy, september 23-24, 2010, Proceedings, pp 175–190
Schrijver A (1987) Theory of linear and integer programming John Wiley and Sons
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Declerck, P. Critical subsystems in time interval models. Discrete Event Dyn Syst 31, 25–35 (2021). https://doi.org/10.1007/s10626-020-00322-0
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DOI: https://doi.org/10.1007/s10626-020-00322-0