We propose a traffic flow and control model for the train dynamics in a linear metro line without junction. The model takes into account time constraints such as minimum inter-station running times, minimum train dwell times at platforms, and minimum safe separation times between successive trains. Moreover, it includes a control law that sets the train dwell times at platforms based on the feedback of the train time-headways and of the passenger arrival rates at platforms. We show that the dynamic system converges to a stable stationary regime with a unique average growth rate, and derive, by numerical simulation, the traffic phases of the train dynamics. We compare the obtained traffic phases with the ones derived with an existing max-plus algebra traffic model, and derive the effect of the passenger travel demand on the train dynamics. Finally, we draw some conclusions and discuss perspectives of the proposed approach.