Traffic modeling and real-time control for metro lines. Part II - The effect of passenger demand on the traffic phases

We present traffic flow and control models for the train dynamics in metro lines. In a first model we introduce the effect of passenger demand on the train dwell times at platforms. We recall that, if this effect is not well controlled, then the traffic is unstable. Then we propose a second traffic control model which deals with this instability, by modifying the control of the train dwell times at platforms. We show that the dynamic system admits a unique stable asymptotic regime, and calculate by numerical simulations the asymptotic average train time-headway as a function of the number of moving trains. By that, we obtain the traffic phases of the train dynamics, giving the effect of the passenger travel demand on the frequency of the metro line, under the proposed control model. Finally, we draw some conclusions, and give a direction for the upcoming research.