Time-Optimal Train Traffic in Large Networks Based on a New Model

Abstract From a system-theoretic standpoint, a constrained state-space model for train traffic in a railway network is developed. It is based on transforming the directed graph of the network to some parallel lists. All the aspects of a real network (such as that of the German Rail) are completely captured by this model. It is generic and can be used to establish an operating system for other large railway networks. By way of 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. 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 (ODE) whereby all the static switching points are computed offline.