Traffic modeling and real-time control for metro lines. Part I - A max-plus algebra model explaining the traffic phases of the train dynamics
Résumé : We present in this article a traffic flow model for metro lines. It is a discrete event model written in the max-plus algebra, where the traffic dynamics take into account time constraints such as minimum train inter-station running times, minimum train dwell times on platforms, and minimum safety times between successive trains. We show that the dynamics admit a unique stable stationary regime. Moreover, the asymptotic average train time-headway, dwell time, as well as safe-separation time, are derived analytically, as functions of the number of moving trains on the metro line. This derivation allows the comprehension of the traffic phases of the train dynamics.
Nadir Farhi, Cyril Nguyen van Phu, Habib Haj-Salem, Jean-Patrick Lebacque. Traffic modeling and real-time control for metro lines. Part I - A max-plus algebra model explaining the traffic phases of the train dynamics. The 2017 American Control Conference, May 2017, Seattle, United States. Institute of Electrical and Electronics Engineers - IEEE, The 2017 American Control Conference, 6p, 2017, 〈10.23919/ACC.2017.7963542〉. 〈hal-01610117〉
