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

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

Inst. Mathematik

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.