A polynomial function of primary delays and cumulative delays on railway lines

Railway planners have several tools to simulate the operation. Simulation allows the evaluation of the railway system’s quality by different points of view. Analyses of timetable stability and robustness include several indicators: recovery time and total delay among others. This paper formulates a model to describe the delay on a railway line. The total delay is characterized as a polynomial function of the primary delay given to a train. We define a simplified delay propagation model to derive the individual delay of a generic train at a station. This is the combination of the hindrance by the previous train and the delay of the same train at the previous station, reduced by means of scheduled buffer times and timetable allowance, respectively. The individual delay is described as a linear function of the individual train number and station position. The total delay results from the summation of the individual delays and results in a cubic function of the primary delay, for small values of primary delays. The model makes it possible to compute the total delay on a railway line with very limited use of microsimulation, with yet high accuracy. Microsimulation is used only for the initial model calibration. Previous studies proved the validity of the model on suburban railway lines. This is significant for the future development of models to analyze timetable stability and robustness. As an industrial application, the model will allow fast and accurate analyses of the timetables, and on-line decision support for rescheduling or dispatching.