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Preprint 27-2006

Modeling, Analysis, Synthesis, and Simulation of Time-Optimal Train Traffic in Large Networks

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Author(s) : Yazdan Bavafa-Toosi , Christoph Blendinger , Volker Mehrmann , Andreas Steinbrecher , Roman Unger

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 27-2006

MSC 2000

93C15 Systems governed by ordinary differential equations
65L05 Initial value problems

Abstract :
From a system-theoretic standpoint, a constrained state-space model for train traffic in a large railway network is developed. The novelty of the work is the transformation or rather reduction of the directed graph of the network to some parallel lists. Mathematization of this sophisticated problem is thus circumvented. All the aspects of a real network (such as that of the German Rail) are completely captured by this model. Some degrees of freedom as well as some robustness can be injected into the operation of the system. The problem of time-optimal train traffic in large networks is then defined and solved using the maximum principle. The solution is obtained by reducing the boundary value problem arising from the time-optimality criterion to an initial value problem for an ordinary differential equation. A taxonomy of all possible switching points of the control actions is presented. The proposed approach is expected to result in faster-than-real-time simulation of time-optimal traffic in large networks and thus facilitation of real-time control of the network by dispatchers. This expectation is quantitatively justified by analysis of simulation results of some small parts of the German Rail Network.

Keywords : Large networks, train traffic, time optimality, boundary value problem, initial value problem.

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