Operativ järnvägsdrift och punktlighet Kollektivtrafik och järnväg

3.4.4 - Integrating Delay Prediction in Railway Timetabling

  • Johan Högdahl, Kungliga Tekniska högskolan
  • Johan Högdahl, Kungliga Tekniska högskolan
K&K, Solot (50)
Wed, 08.01.2020
13:15 - 14:45
Presentation Topic
Kollektivtrafik och järnväg



Railway timetabling is known as a complex planning problem and it is important that the operations have high reliability while keeping travel times short. To improve punctuality, margins are added in the timetable, which allows recovery of delays and reduces delay propagation between trains. However, an important question is when, and how, these margins should be added to the timetable to achieve a good balance between short travel times and high reliability.

To address this issue a timetabling approach based on simulating and optimizing a given timetable is proposed. The simulation of the given timetable is carried out to calculate the average delay of the arrival and departure at each station for all trains. These delay estimations are then included in the optimization problem, where the given timetable is rescheduled such that the weighted sum of scheduled travel time and predicted average delay is minimized. In contrast to previous research, the delay prediction model in this study allows the sequence of the trains to be flexible.


In this research a delay prediction model is developed and added to an event-based mixed integer linear programming model for non-periodic timetabling of double-track railway lines. The resulting model is applied in a hybrid simulation-optimization timetabling approach for rescheduling of an existing timetable.

A simulation study is carried out on a section of the Swedish Southern Main Line to:

(1) Validate the delay prediction model.

(2) Evaluate system-level effects with respect to scheduled travel times, time supplements, average delay, and punctuality by applying the hybrid simulation-optimization timetabling approach.

Resultat och slutsats

The preliminary results indicate that the delay prediction model can achieve accurate predictions (The mean absolute prediction error was less than 1 minute, and the mean prediction error was -11,7 seconds for all trains). However, the results also reveal that the model does not perform well in some conditions, which may be due to its simple formulation.

The evaluation of the approach also indicates interesting results. It was observed that by increasing travel times by on average 2% it was possible to improve end-station punctuality from 83.6% to 90.3%, and to reduce average delays by ca 40%.