Aim and research questions

The aim of this paper is to use simulation to investigate the relationship between primary delays and the resulting punctuality. Furthermore, by utilising a fast, macroscopic railway traffic simulation tool for the study, the potential for macroscopic simulation to cover larger networks and/or several cases is also highlighted. As a case study, we use the region of Scania in Southern Sweden, using the real timetable and operational data for 2019, as well as a draft timetable for 2025. In particular, this paper seeks to answer the following research questions:

• What proportions of delays are primary and secondary?
• By how much would primary delays have to be reduced to meet the Swedish railway industry target of 95% punctuality, today?
• By how much would primary delays have to be reduced to meet the target of 95% punctuality, using a draft timetable for 2025?
• What would the punctuality be in 2025, given the current level of primary delays?

State of the art

Punctuality is known to be a key factor for railway customers. While passengers can plan for longer travel times that are known in advance, it is difficult to plan for unreliable services. Passengers must compensate by adding margins of an unknown size, and thus value delay time much higher than regular travel time. Extensive research has been done, and continues to be done, on creating timetables that are robust to delays. Högdahl et al. (2019), Lee et al. (2017), Sels et al. (2016), and Bešinović et al.(2016) are only some examples of a vast literature. There is also a literature that more broadly investigates the concept of timetable quality (i.e. Watson 2008, Gestrelius et al. 2020, Palmqvist et al. 2019, Lenze & Nießen 2021 to name a few). An increasing amount of research has also been done into factors that influence punctuality (e.g. Økland & Olsson 2020, Olsson & Haugland 2004, Palmqvist et al. 2017, Palmqvist et al. 2022, van der Kooij et al. 2017, Veiseth et al. 2007, Xia et al. 2013). Simulation is a common tool in railway research for evaluating punctuality and robustness of timetables and disturbance scenarios. Often, microscopic simulation is used, characterised by a high level of detail for the infrastructure as well as the vehicles and the timetable. Examples of such simulators are RailSys, OpenTrack, LUKS, and Trenissimo. Another approach is to use macroscopic simulation, modelling the railway network with a given number of tracks along the lines and the stations as nodes, not accounting for the exact track layout or what happens during operations aside from station arrival and departure times. PROTON is a macroscopic simulation tool under development by DB Analytics enabling computationally efficient and fast simulation on a network scale (Zinser et al. 2019).

Method

The simulated network covers most of the railway lines in the southernmost part of Sweden. It consists of parts of two double-tracked main lines, Southern Main Line and West Coast Line, as well as the track network in the Malmö area and multiple single track lines. Especially on the main lines, the traffic is highly mixed with long-distance, regional, and local passenger trains as well as freight trains. The single track lines are to varying degrees operated by regional and local passenger trains, and freight trains. Empirical data from weekdays during 2019 within the simulated area were used as inputs into the model. All in all, this contains about 4.9 million observed train movements between adjacent timing points. These data were then separated by train type (local, regional, and long-distance passenger trains, as well as freight trains) and direction (North- or Southbound) to generate distributions for departure (at the entrance to the simulation area), run time, and dwell time delays. Each of these distributions contain both positive and negative delays, expressed in 1-minute intervals in the pm60 minute range. Larger deviations than these were not included, because they are extremely rare, with 99.4% of run and dwell time deviations in the ±10-minute range, 92.7% in the ±3-minute range, a full 75% in the ±1 range. To calibrate the simulation, we ran the timetable for the three selected dates in 2019 with a set of 21 different scaling levels of primary delays. These ranged from 0% to 100%, in 5% intervals. The logic is that a proportion of empirically observed delays were primary, with the rest being secondary, but that this proportion is not explicitly observed. By testing a range of scenarios, we can find a level of input delays that yields an output in terms of punctuality that is close to what was observed empirically. We found that the lines for the simulated and observed punctuality intersect at about the level of 36%, and the closest scenario we simulated was 35%.

Analysis and results

We find that that 36% of delays in the empirical data from 2019 were primary, corresponding to a punctuality level of 87%. Thus, every one part of primary delays on average caused about two parts of secondary delays. This is in line with earlier simulations we have done for similar case studies. The same level of primary delays in the timetable of 2025 would result in a punctuality level of about 82%. With the same distribution of primary delays as in 2019, punctuality would thus be expected to fall by about 5 percentage points in 2025, due to an increase in the number of trains run. A scale factor of 19% in 2019 would have resulted in the desired level of punctuality. This implies that about half of the primary delays would have to be removed to reach a punctuality of 95%, given the same infrastructure and timetable. In other words, there were about twice as many delays as would have been required to reach the target punctuality. To reach the desired punctuality in 2025, a scale factor of 13% would have been required. This would imply a reduction in primary delays by about two thirds from the observed level in 2019. This is a tall order and highlights the need for drastic delay reduction measures.

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