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.