In this paper we present a railway traffic model and a model predictive controller for online railway traffic management of railway networks with a periodic timetable. The main aim of the controller is to recover from delays in an optimal way by changing the departure of trains, by breaking connections, by splitting joined trains, and - in the case of multiple tracks between two stations - by redistributing the trains over the tracks. The railway system is described by a switching max-plus-linear model. We assume that measurements of current running and dwell times and estimates of future running times and dwell times are continuously available so that they can be taken into account in the optimization of the system’s control variables. The switching max-plus-linear model railway model is used to determine optimal dispatching actions, based on the prediction of the future arrival and departure times of the trains, by recasting the dispatching problem as a Mixed Integer Linear Programming (MILP) problem and solving it. Moreover, we use properties from max-plus algebra to rewrite and reduce the model such that the MILP problem can be solved in less time. We also apply the algorithm to a model of the Dutch railway network.@en

Every day small delays occur in almost all railway networks. Such small delays are often called “disturbances” in literature. In order to deal with disturbances dispatchers reschedule and reroute trains, or break connections. We call this the railway management problem. In this paper we describe how the railway management problem can be solved using centralized model predictive control (MPC) and we propose several distributed model predictive control (DMPC) methods to solve the railway management problem for entire (national) railway networks. Furthermore, we propose an optimization method to determine a good partitioning of the network in an arbitrary number of sub-networks that is used for the DMPC methods. The DMPC methods are extensively tested in a case study using a model of the Dutch railway network and the trains of the Nederlandse Spoorwegen. From the case study it is clear that the DMPC methods can solve the railway traffic management problem, with the same reduction in delays, much faster than the centralized MPC method.@en

In this paper we introduce two distributed model predictive control (DMPC) approaches that significantly improve the quality of the solutions found compared to the DMPC approaches that were introduced by Kersbergen et al. [2014b] for the rescheduling of railway traffic, while the computation time only increased by a small fraction. In DMPC the global rescheduling problem is split up into several local problems that are solved by local model predictive controllers that communicate with each other to achieve a solution for the global rescheduling problem. We improve the solution found by the DMPC approaches by adjusting the weights in the local problems such that the delay propagation through the network is reduced. We compare the performance in terms of computation time and delay reduction of the different DMPC approaches with the global model predictive control approach for different lengths of the prediction horizon. @en