Literature

One last time in this course we refer to Cassandras and Lafortune (2021), a comprehensive and popular introduction do discrete event systems. A short introduction to the framework (max,+) algebra can be found (under the somewhat less known name “Dioid algebras”) in Chapter 5.4.

But as a recommendable alternative, (any one of) the a series of papers by Bart de Schutter (TU Delft) and his colleagues can be read instead. For example De Schutter et al. (2020) and De Schutter and van den Boom (2000).

For anyone interested in learning yet more, a beautiful (and freely online) book is Baccelli et al. (2001), which we have also mentioned in the context of Petri nets.

Max-plus algebra is relevant outside the domain of discrete-event systems – it is also investigated in optimization for its connection with piecewise linear/affine functions. Note that the community prefers using the name tropical geometry (to emphasise that they view it as a branch of algebraic geometry). A lovely tutorial is Rau (2017).

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References

Baccelli, François, Guy Cohen, Geert Jan Olsder, and Jean-Pierre Quadrat. 2001. Synchronization and Linearity: An Algebra for Discrete Event Systems. Web edition. Chichester: Wiley. https://www.rocq.inria.fr/metalau/cohen/documents/BCOQ-book.pdf.
Cassandras, Christos G., and Stéphane Lafortune. 2021. Introduction to Discrete Event Systems. 3rd ed. Cham: Springer. https://doi.org/10.1007/978-3-030-72274-6.
De Schutter, Bart, and Ton van den Boom. 2000. “Model Predictive Control for Max-Plus-Linear Discrete-Event Systems: Extended Report & Addendum.” Technical Report bds:99-10a. Delft, The Netherlands: Delft University of Technology. https://pub.deschutter.info/abs/99_10a.html.
De Schutter, Bart, Ton van den Boom, Jia Xu, and Samira S. Farahani. 2020. “Analysis and Control of Max-Plus Linear Discrete-Event Systems: An Introduction.” Discrete Event Dynamic Systems 30 (1): 25–54. https://doi.org/10.1007/s10626-019-00294-w.
Rau, Johannes. 2017. “A First Expedition to Tropical Geometry.” https://www.math.uni-tuebingen.de/user/jora/downloads/FirstExpedition.pdf.