Delay distributions in railway stations

The estimation of the precise arrival and departure times of trains at stations is done by means of a software tool that extracts the occupation and clearance times of each train per track section of the Dutch Railways‘ network. The software tool was applied to the whole automatically collected set of signal data of the area of Eindhoven during one week in September 1997 comprising 140 MB. A total of 1846 trains were detected and used for further analysis. The detailed statistical analysis of the distribution of the train arrivals, dwell times and departures shows a systematic mean arrival delay of almost every line (InterCity, InterRegio, AggloRegio) ranging up to 138 sec per train. All of the IC-lines except the line starting nearby at Heerlen showed a punctuality of less than 90% when punctuality is defined as having less than 3 minutes of delay. The IR- and AR-lines arrived more punctual. The dwell times of all the lines lasted on the average 30 to 90 sec longer than scheduled and more than two thirds of the trains arriving late extended the planned dwell time. Consequently, the mean departure delays per line ranged between 1.5 and 2.5 minutes. There is much statistical evidence that the arrival delays and the dwell times fit to normality, whereas the departure delays have a clear negative exponential distribution.