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Numerical simulation of train traffic in large networks via time-optimal control

Blendinger, Christoph; Mehrmann, Volker; Steinbrecher, Andreas; Unger, Roman

Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin

We discuss the mathematical modelling of schedule based rail traffic. The model is used to develop efficient numerical simulation methods for the time optimal control of a large number of interacting trains in a large network. The time optimal control is used to model the realistic behaviour of driving in a network like that of Deutsche Bahn. It is used to allow a real time simulation with incomplete information on real train velocities. We present numerical examples that demonstrate the efficiency of the model and the simulation method.