Analysing train lateness
Industry representative: Scott Mackenzie, TTG Transportation Technology
Moderators: Kaye Marion, RMIT University; Nick Fewster-Young, University of South Australia
Introduction
Rail operators around the world are using driver advice systems to provide train drivers with driving advice to help them keep trains on time and minimise energy use. TTG Transportation Technology provide driver advice systems to several railways in the UK. These advice units also capture detailed information about the operation of the railway, including the location and speed of each train at 10-second intervals. A typical UK operation will have 200–300 train services per day.
Preliminary analysis of train logs is showing that, on some railways, trains are unable to meet their timetables for 50–75% of the time. This is limiting the scope for on-time running and for energy savings.
The aim of this project was to analyse the data from train logs to determine where and when trains are losing time, to determine factors that contribute to time loss, and to develop new reporting methods that will assist with on-going monitoring of network and driver advice system performance.
Data
TTG provided two types of data for analysis:
- detailed log data that specifies the location of each train on the network at 10-second intervals
- timing data that specified the times that trains arrived, departed or passed key timing points.
The data covered the operation of high speed passenger trains on a UK railway during March 2016—about 6000 journeys.
Lateness
We defined lateness at a station to be the difference between the actual arrival or departure time and the scheduled arrival or departure time.
Train services repeat each day. A particular train service is identified by its origin, destination and departure time. The table below shows the 50-percentile, 75-percentile and 90-percentile lateness values for a weekday service to to London, for which we had 32 trips. The first row is departure lateness from the origin station; the remaining rows show arrival lateness.
| Lateness (s) | |||
|---|---|---|---|
| Station | P50 | P75 | P90 |
| 1 | 20 | 26 | 47 |
| 2 | -82 | -66 | -20 |
| 3 | 2 | 74 | 379 |
| 4 | -3 | 19 | 34 |
| 5 | -72 | -31 | 6 |
| 6 | 32 | 37 | 59 |
| 7 | 58 | 103 | 125 |
| 8 | -1 | 19 | 95 |
| 9 | 239 | 284 | 397 |
| 10 | 249 | 384 | 427 |
| 11 | 92 | 251 | 451 |
Despite the variations in lateness prior to Station 8—perhaps because scheduled arrival times are unrealistic—half of the trains arrived at Station 8 on time. However, trains were 4–7 minutes late at Stations 9 and 10. Some time was recovered between Station 10 and Station 11—the timetables include extra ‘slack’ in this section.
Train operating companies pay penalties for each train that is late at its final destination by more than 5 minutes. There are currently proposals in the UK to impose penalties when trains are more than a minute late at stations. For our data set:
- 36% of trains were late at their final destination by more than 5~minutes. The mean lateness was 18.1 minutes (13.1 minutes beyond 5 minutes)
- 46% of station arrivals were late by more than 1~minute. The mean lateness was 6.5 minutes (5.5 minutes beyond 1 minute).
What causes lateness?
A key aim of the MISG study was to determine the causes of lateness. The proposed method was to construct a model that could predict time loss at stations or between stations, and calculate the dependence of time loss on various measured and derived variables.
Despite this work being incomplete, it was possible to show that about 35% of the time loss or gain on a section or at a station was explained by the scheduled duration being too low or too high. This is consistent with timetable slack not being spread across the journey in an equitable manner.
Stop durations
Stop durations that are longer than scheduled could be a significant cause of time loss. We analysed stop durations at 104 stations for a UK rail operator.
Scheduled stop durations should be achievable. The following table shows the 25-percentile, 50-percentile and 75-percentile actual stop durations, in seconds, for trains that arrived late and were scheduled to stop for two minutes, at the five most-used stations.
| Station | Direction | P25 | P50 | P75 |
|---|---|---|---|---|
| 10 | D | 107 | 119 | 137 |
| U | 102 | 115 | 130 | |
| 8 | D | 113 | 125 | 143 |
| U | 109 | 121 | 135 | |
| 9 | D | 103 | 117 | 132 |
| U | 95 | 105 | 122 | |
| 12 | D | 122 | 139 | 163 |
| U | 109 | 120 | 138 | |
| 13 | D | 111 | 124 | 143 |
| U | 102 | 113 | 127 |
We considered the two different directions for trains at each station—down for trains travelling away from London, and up for trains travelling towards London. Apart from Station 12 in the down direction, the median stop durations are close to the scheduled duration of 120 seconds. However, the 75-percentile values are all greater than 120 seconds. Of the trains that arrive late at these stations, about half lose time at the stop and depart even later.
We also analysed the variation in stop durations. One way of measuring the variation in stop duration is the interquartile range (IQR)—if one quarter of the trains have stop durations less than d1 and one quarter of the trains have stop durations greater than d3 then the IQR is d3 – d1. A larger IQR indicates a greater variation in stop duration. IQR is a robust measure of dispersion—it is not as affected by outliers as standard deviation, for example. The IQR of stop durations varied from 122 seconds to 321 seconds.
One way to reduce lateness would be to increase scheduled stop durations. However, a more efficient solution is to increase the slack in the scheduled section durations. By allowing more slack between stations, the average speed required between stops is reduced slightly and so there is more scope for trains to adjust their speeds to stay on time. This will enable a more reliable service. It will also allow trains that are on time to be driven more efficiently.
Actual stop durations should be as short as possible, to maximise the scope for time recovery between stations.
Constructing robust timetables
There are several ways we could measure the reliability of a train service, including:
- the proportion of trains that arrive at the final destination on time (for various definitions of ‘on time’)
- the proportion of arrivals at key destinations (not just the final destination) that are on time
A robust timetable is a timetable that enables high reliability. A robust timetable can be constructed by basing scheduled arrival times on measured arrival times. For example, if an operator requires 90 per cent of trains to arrive on time, the timetable should be based on the 90-percentile measured arrival times.
The table below shows robust arrival times for our example journey, for various values of reliability.
| Arrival time (minutes) | |||
|---|---|---|---|
| Station | P50 | P75 | P90 |
| 1 | 0.0 | 0.0 | 0.0 |
| 2 | 16.1 | 16.4 | 17.2 |
| 3 | 26.5 | 27.7 | 32.8 |
| 4 | 41.0 | 41.3 | 41.6 |
| 5 | 59.3 | 60.0 | 60.6 |
| 6 | 66.5 | 66.6 | 67.0 |
| 7 | 82.0 | 82.7 | 83.1 |
| 8 | 96.5 | 96.8 | 98.1 |
| 9 | 121.0 | 121.7 | 123.6 |
| 10 | 136.6 | 138.9 | 139.6 |
| 11 | 167.0 | 169.7 | 173.0 |
Conclusion
We developed several methods that could be used to tabulate, visualise and analyse lateness and time loss in a railway operation, using data collected from driver advice systems.
Inappropriate timetables and variation in station stop durations are key contributors to lateness.
To construct a robust timetable, arrival times should be based on the measured performance of trains.
Participants
We thank the MISG delegates who worked on this problem: Ajini Galapitage, Erika Belchamber, Hyeongki Park, Jan Idziak, Luke Schubert, Michal Krason, Nigel Clay, Patrick Hassard, Peng Zhou, Peter Pudney, Tatsuya Yamaguchi, Tony Gibb, Tony Ling, Xuan Vu, Youngjin Kim, and Scott Mackenzie from TTG.