An Overview of Transience Bounds in Max-Plus Algebra

Thomas Nowak (1) , Bernadette Charron-Bost (2)

1 DYOGENE - Dynamics of Geometric Networks
2 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]

We survey and discuss upper bounds on the length of the transient phase of max-plus linear systems and sequences of max-plus matrix powers. In particular, we explain how to extend a result by Nachtigall to yield a new approach for proving such bounds and we state an asymptotic tightness result by using an example given by Hartmann and Arguelles.

Domaines: Mathématique discrète [cs.DM]

Thomas Nowak, Bernadette Charron-Bost. An Overview of Transience Bounds in Max-Plus Algebra. G. L. Litvinov; S. N. Sergeev. Tropical and Idempotent Mathematics and Applications, AMS, pp.277-289, 2014, Contemporary Mathematics, 978-0-8218-9496-5 (print); 978-1-4704-1684-3 (online). ⟨10.1090/conm/616/12306⟩. ⟨hal-00993630⟩