# The Effects of Train Passes on Dwell Time Delays in Sweden
## 5 Conclusions  
This analysis has shown two things: First, only a small percentage (3%) of train passes happened as scheduled, with most (76%) being cancelled and a substantial percentage (21%) being unscheduled. This indicates that there are significantly fewer train passes in actual operations than in timetables and that dispatchers play a very active role in shifting the location of passes.  
Second, we showed that train passes can significantly alter the probability of delays at a station. Compared to when they happened as scheduled, the odds of delays were reduced by about 9.8 times when passes are cancelled. On the other hand, the odds of delay increased by about 2.6 times if a pass is unscheduled, suggesting a low flexibility of the timetable. While cancelling a pass at one station can be used to mitigate the possibility of delays there, there will then either be an unscheduled pass at another station, thus greatly increasing the odds of delays at the following station, or the train will not pass and may need to run at a reduced speed.  
One of the main advantages of using logistic regression is that it is not a \"black box\" and that it is easy to interpret. However, the model is associated with several limitations  
Figure 5: ROC curves for Logistic Regression Model.  
and simplifications. Firstly, our model only accounts for different types of passes and omits many other variables (including other types of train interactions and conflicts). Secondly, it is based on macroscopic train operations data, on a station-by-station level, rather than signal-by-signal, which would be more precise. Finally, the \(R^{2}\) value indicates that the model can only explain around 30% of the variance in dwell time delays and that is only when considering the relatively small part of the data that includes some sort of (scheduled, cancelled, or unscheduled) pass. Including more variables, such as passenger data, other types of train movements, weather conditions, detailed timetable information, infrastructure failures, and so on, as well as using more complex models, would most likely improve the overall predictive power of the model. However, that would not necessarily teach us more about the effects of different types of train passes.  
In future work, we will continue to explore other possible types of interactions such as meets, headway interactions, trains turning around at the terminal station, or trains stopping for passenger transfers. The approach used in this study can also be used to evaluate the consequences of dispatching actions and trade-offs and can help dispatchers make well-informed decisions that improve railway capacity and punctuality. Another direction for future research into train passes is to complement the simplified approach used in this study with more complex models, such as various machine learning algorithms, which tend to be more opaque and difficult to interpret but which can offer much higher predictive power. Similarly, combining data on different types of passes (and other interactions) with other sources of data (such as weather, passengers, etc.) can further increase the ability to predict and understand train delays.  
Not applicable.  
Research data are not shared due to confidentiality reasons.  
The earlier version of this manuscript was presented at The 9 th International Conference on Railway Operations Modelling and Analysis (ICROMA), and the authors would like to thank the anonymous reviewers there for their constructive comments.  
The authors declare no conflict of interest.