Accurate train delay prediction is vital for effective railway traffic planning and management as well as for providing satisfactory passenger service quality. Despite significant advances in data-driven train delay predictions, it lacks of a systematic review of studies and unified modelling development framework. The paper reviews existing studies with an explicit focus on synthesizing a structural framework that could guide effective data-driven train delay prediction model development. The framework consists of three stages including design concept, modelling and evaluation. The study synthesize and discusses six important modules of the framework: (1) Problem scope, (2) Model inputs, (3) Data quality, (4) Methodologies, (5) Model outputs, and (6) Evaluation techniques. For each module, the important problems and techniques reported are synthesized and research gaps are discussed. The review found that most studies focus on developing complex methodologies for the next stop delay predictions that have limited applications in practice. All studies validate the model accuracy, but very few consider other model performance aspects which makes it difficult to assess their usfulness in practical deployment. Future studies need a holistic view on defining the train delay prediction problem considering both application requirements and implementation challenges. Also, the modelling studies should place more attention to data quality and comprehensive model evaluations in representation power, explainability and validity.

Understanding the impact of various factors on train arrival delays is a prerequisite for effective railway traffic operating control and management. Existing studies analyze the train delay factors using a single, generic regression equation, restricting their capability in accounting for heterogeneous impacts of spatiotemporal factors on arrival delays as the train travels along its route. The paper proposes a set of equations conditional on the train location for analyzing train arrival delay factors at stations. We develop a seemingly unrelated regression equation (SURE) model to estimate the coefficients simultaneously while considering potential correlations between regression residuals caused by shared unobserved variables among equations. The railway data from 2017 to 2020 in Sweden are used to validate the proposed model and explore the effects of various factors on train arrival delays. The results confirm the necessity of developing a set of station-specific train arrival delay models to understand the heterogeneous impact of explanatory variables. The results show that the significant factors impacting train arrival delays are primarily train operations, including dwell times, running times, and operation delays from previous trains and upstream stations. The factors of the calendar, weather, and maintenance are also significant in impacting delays. Importantly, different train operating management strategies should be targeted at different stations since the impacts of these factors could vary depending on where the station is.

Increasing the modal share of the single wagonload transport in Europe requires improving the reliability and predictability of freight trains running between the yards. In this paper, we propose a novel machine learning-assisted macro simulation framework to increase the predictability of yard departures and arrivals. Machine learning is applied through a random forest algorithm to implement a yard departure prediction model. Our yard departure prediction approach is less complex compared to previous yard simulation approaches, and provides an accuracy level of 92% in predictions. Then, departure predictions assist a macro simulation network model (PROTON) to predict arrivals to the succeeding yards. We tested this framework using data from a stretch between two main yards in Sweden; our experiments show that the current framework performs better than the timetable and a basic machine learning arrival prediction model by R2 of 0.48 and a mean absolute error of 35 minutes. Our current results indicate that combination of approaches, including yard and network interactions, can yield competitive results for complex yard arrival time prediction tasks which can assist yard operators and infrastructure managers in yard re-planning processes and yard-network coordination respectively.

In Sweden and other countries it is not an uncommon practice that freight trains depart more or less on-demand instead of strictly following a pre-planned timetable. However, the systematic effects of freight trains departing late or (in particular) early has long been a contested issue. Although some microscopic simulation tools currently have the capability to evaluate the effect of freight trains departing before schedule, it has yet not been established how macroscopic simulation tools, capable of fast simulation of nation-wide networks, can manage such tasks. This paper uses a case study on a line between two large freight yards in Sweden to investigate how the results of microscopic and macroscopic simulation, represented by two modern simulation tools, differ when it comes to this particular problem. The main findings are that both the microscopic and the macroscopic tools replicated the empirical punctuality fairly well. Furthermore, allowing early departures of freight trains increased overall freight train punctuality while the passenger train punctuality decreased slightly, as determined by both tools. The results are encouraging, but further studies are needed to determine if macroscopic simulation is on-par with microscopic simulation.

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.

References

Bešinović, N., Goverde, R., Quaglietta, E., Roberti, R., 2016. An integrated micro–macro approach to robust railway timetabling. Transportation Research Part B: Methodological 87, 14–32. doi:10.1016/j.trb.2016.02.004.

Gestrelius, S., Peterson, A., Aronsson, M., 2020. Timetable quality from the perspective of a railway infrastructure manager in a deregulated market: An interview study with Swedish practitioners. Journal of Rail Transport Planning & Management 15. doi:10.1016/j.jrtpm.2020.100202.

Högdahl, J., Bohlin, M., Fröidh, O., 2019. A combined simulation optimization approach for minimizing travel time and delays in railway timetables. Transportation Research Part B: Methodological 126, 192–382. doi:https://doi.org/10.1016/j.trb.2019.04.003.

van der Kooij, R.B., Landmark, A.D., Seim, A.A., Olsson, N., 2017. The effect of temporary speed restrictions, analyzed by using real train traffic data. Transportation research procedia 22, 580–587.

Lee, Y., Lu, L.S., Wu, M.L., Lin, D.Y., 2017. Balance of efficiency and robustness in passenger railway timetables. Transportation Research Part B: Methodological 97, 142–156.

Lenze, W., Nießen, N., 2021. Quality in rail timetabling - A detailed review of stakeholders’ interests compared with current practices in Germany. Journal of Rail Transport Planning & Management 20.

Olsson, N., Haugland, H., 2004. Influencing factors on train punctuality Results from some Norwegian studies. Transport Policy 11, 387-397.

Palmqvist, C., Lind, A., Ahlqvist, V., 2022. How and Why Freight Trains Deviate From the Timetable: Evidence From Sweden. IEEE Open Journal of Intelligent Transportation Systems, 210–221.

Palmqvist, C., Olsson, N., Hiselius, L., 2017. Some influencing factors for passenger train punctuality in Sweden. International Journal of Prognostics and Health Management.

Palmqvist, C., Olsson, N., Hiselius, L., 2019. Punctuality problems from the perspective of timetable planners in Sweden, in: Proceedings of 20th EURO Working Group on Transportation Meeting (EWGT) 2019, Budapest, Hungary.

Sels, P., Dewilde, T., Cattrysse, D., Vansteenwegen, P., 2016. Reducing the passenger travel time in practice by the automated construction of a robust railway timetable. Transportation Research Part B: Methodological 84, 124–156.

Veiseth, M., Hegglund, P., Wien, I., O., N.O.E., Stokland, Ø., 2007. Infrastructure’s influence on rail punctuality, in: Brebbia, C. (Ed.), Urban Transport XIII Urban Transport and the Environment in the 21st Century. Wessex Institute of Technology, UK, Southampton, UK. volume 96, pp. 481–490.

Watson, R., 2008. Train Planning In A Fragmented Railway-A British Perspective. Doctoral thesis. Loughborough University.

Xia, Y., Van Ommeren, J.N., Rietveld, P., Verhagen, W., 2013. Railway infrastructure disturbances and train operator performance: The role of weather. Transportation research part D: transport and environment 18, 97–102.

Zinser, M., Betz, T., Becker, M., Geilke, M., Terschlüsen, C., Kaluza, A., Johansson, I., Warg, J., 2019. PRISM: A Macroscopic Monte Carlo Railway Simulation, in: Proceedings of 12th World Congress on Railway Research (WCRR) 2019, Tokyo, Japan.

Økland, A., Olsson, N., 2020. Punctuality development and delay explanation factors on Norwegian railways in the period 2005 – 2014. Public Transport.

Real-time prediction of train arrivals is important for proactive traffic control and information provision in passenger rails. Despite many studies in predicting arrival times or delays at stations, they are essentially the next-step time series prediction problem which may limit their applications in practice. For example, passengers on the trains or waiting on platforms may have different destinations and need the predicted train arrival times for any downstream stations rather than only the next station. The paper aims to formulate a real-time train arrival times prediction problem at multiple stations and arbitrary times. We develop multi-output machine learning models and systematically evaluate their performance using train operation data in Sweden. The direct multi-output regression models with different regression functions are tested, including LightGBM, linear regression, random forest regression, and gradient boosting regression models. The hyperparameters are optimized using random grid search and five-fold cross-validation methods. The results show that the Direct Multi-Output LightGBM significantly outperformed other models in terms of accuracy. The predictions at downstream stations improve as the train moves along given more real-time information is observed.

Railway traffic usually adheres to a timetable, but in Sweden, around two-thirds of the freight trains depart before they are scheduled, often by hours. Even though they occur in real operations, early departures have rarely been included in simulation studies and the effects on punctuality are not fully investigated. With a macroscopic simulation tool such as PROTON, large networks can be simulated in a short time, which makes the simulation process easier. This paper uses the tool PROTON to perform a macroscopic simulation case study on the Swedish Western mainline to investigate how early departures of freight trains affect punctuality. The resulting output is a marginal overall punctuality improvement of about +0.5 percentage points. In addition, different levels of primary run time and dwell time delays have been used as simulation input, based on empirical data. The resulting ratio between primary and secondary delays appears to vary greatly between different train types, but overall about 30% were primary and 70% secondary. Future work includes modelling and calibration of departure deviations, which vary more between different train types, and where it is more difficult to separate between primary and secondary delays. Separating distributions based on train type or location will also be considered.

Departure deviations from shunting yards impact the reliability of rail freight services and the punctuality of a railway network. Therefore, the statistical analysis of these deviations are necessary for improving the operation of trains in mixed-traffic networks. In our paper, we conduct a detailed statistical analysis of departure deviations considering individual shunting yards characteristics. We use a large freight train delay dataset comprising 250,000 departures over seven years for the two largest shunting yards in Sweden, comparable to other medium-sized shunting yards in Europe. To find the probability distribution of departure deviations, we compare four distribution functions including the exponential, the log-normal, the gamma, and the Weibull according to the maximum likelihood estimates and results of the Anderson-Darling goodness of fit test. In our experiments, we show that the log-normal distribution fits best for delayed departures across both shunting yards, and for early departures at one of them, whereas the gamma distribution fits best for early departures at the other yard. For the temporal delay distribution, we find that fluctuations in the network usage impact the percentage of delayed departures across hours and weekdays, but not across months or years. In addition, we find that freight trains are mostly delayed in the winter.  In the case of hourly delayed departures, we demonstrate that a shunting yard involved with domestic traffic showed a negative correlation between delayed departures and the network usage, whereas an international shunting yard did not, which indicates individuality in shunting yard operations impact shunting yard-network interactions. Our findings mainly contribute to better understanding of departure deviations from shunting yards, thus enhancing the operations and capacity utilization of shunting yards. Moreover, delay distributions can be beneficial in handling delays in traffic management models as well as enhancing the outputs of freight train simulation models