Analysis of P-time event graphs in (max,+) and (min,+) semirings

Pavel Špaček, Jan Komenda and Sébastien Lahaye

International Journal of Systems Science, 2021, vol. 52, issue 4, 694-709

Abstract: In this paper, we investigate the behaviour of P-time event graphs, a class of time Petri nets with non-deterministic timing of places. Our approach is based on combined linear descriptions in both (max,+) and (min,+) semirings, where lower bounds on the state vector are (max,+)-linear and upper bounds are (min,+)-linear. We present necessary and sufficient conditions for the existence of extremal (fastest and slowest) periodic trajectories that are derived from the new description. The results are illustrated by a realistic example of an electroplating process.

Date: 2021
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DOI: 10.1080/00207721.2020.1837992

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