Feedback Control for Metro Lines With a Junction

We propose in this article macroscopic control laws for the number of trains running on a metro line with a junction, in feedback of the train run and dwell times as well as the required train frequency (responding to a given level of the passenger travel demand). Often, on dense traffic metro lines, human experience-based traffic control strategies do not efficiently stabilize the train dynamics or respond to the passenger travel demand. Our work is based on a mathematical model of the train dynamics permitting closed-form solutions of the traffic phases on the metro line. We first give a complete description of the derived traffic phases of the train dynamics. Second, we focus on the traffic phases where the train frequency is optimal with respect to given parameters, and identify set points which we use for the macroscopic control of the number of running trains. The objective of the control is to derive from the set points of the phase diagram, the optimal number of running trains with regard to possible variations and/or perturbations of the metro line parameters (train run times, train dwell times and the required train frequency). Finally, based on infrastructure parameters, passenger travel demand, and run and dwell times, we simulate a case study on the metro line 13 of Paris (France) demonstrating how the feedback traffic control practically works.