Modelling Railway Infrastructure Constraints in Max-Plus Algebra
E. M. van Duinkerken · 2005
In the design of railway timetables the robustness and stability of a timetable are of major importance. An analytical method to evaluate the performance of a periodic railway timetable is to model it using max-plus algebra. The software package PETER, based on max-plus algebra, has been designed to assess periodic railway systems on robustness and stability. Minimum time separations between train pairs using the same infrastructure points in a network are called infraconstraints. In the current situation PETER needs the infraconstraints of a network to be predefined in order to include them in the max-plus model. This thesis describes the investigation of the deduction of infraconstraints in a network from the timetable the network operates according to, and information on the infrastructure of the railway network. The infraconstraints in a network can be divided in two types: infraconstraints arising from successor conflicts and those arising from hindrance conflicts. Successor conflicts are conflicts between train pairs using the same track, whereas hindrance conflicts arise between trains that do not use the same track but still have a (mutual) hindrance at some point in the network. Most of the infraconstraints in a network arise from successor conflicts. The infraconstraints in successor conflicts can be deduced from the available information on the railway network. An algorithm is presented to construct all infraconstraints that model minimum time separations in successor conflicts. The required input data for the deduction of these infraconstraints is described. A small part of the infraconstraints in a network arise from hindrance conflicts. At this moment there is not enough information available on station and crossing layouts to derive the exact location of hindrance conflicts. Therefore infraconstraints in hindrance conflicts can not be deduced. To incorporate these infraconstraints in the max-plus model, they can be constructed from an existing list containing all hindrance conflicts in the network. Two case studies are conducted on small parts of the Dutch railway network. From these case studies it can be concluded that when the infraconstraints are deduced as described in this thesis, considerably fewer constraints are necessary to ensure the required minimum time separations in the network. Furthermore, on single-track parts of the network, the minimum time separations in successor conflicts can even be ensured by a reduced number of infraconstraints. The deduction of infraconstraints for a railway network as described in this thesis can be implemented in PETER. Some adjustments on this program are proposed, in order to correctly include the deduced infraconstraints in the max-plus model.