Railway transport plays an important role in creating a more sustainable transport system and contributes to the European Commission's ambitions of reducing the transport emissions by 90% by 2050. In 2022, the Belgian government and railway companies shared their aim to increase the number of passengers by 30% over ten years. To achieve this goal, an extensive and reliable service must be provided. However, the railway network in Belgium, and other European countries, is very dense and already heavily used. As a consequence, even small delays can easily propagate through the network. It is crucial to develop robust timetables that can absorb delays as much as possible and limit their impact on other trains. In the first part of this thesis, we examine how the robustness of a timetable can be improved in a bottleneck area of the network. This is done in a joint project with the Belgian railway companies: Infrabel, the infrastructure manager, and NMBS, the operator of domestic passenger trains. We specifically apply the developed methods to the bottleneck area centered around Halle, which is located just outside of Brussels, the center of the Belgian railway network. First, a thorough analysis of the capacity usage in a bottleneck area is required. Therefore, the well-known timetable compression method is extended to be applicable for large areas, instead of only single lines or stations as is typically done. We present two methods to perform timetable compression: one that is based on the max-plus algebra and one that uses a mathematical optimization model. The experiments show that, while it is possible to analyze the capacity for large and complex networks, the results should be interpreted with care. The capacity occupation heavily depends on the size of the considered network, which makes it difficult to give a clear, practical interpretation of what this means. Nevertheless, timetable compression remains useful to identify critical resources in the network. In areas where the capacity usage is very high, even small delays can easily be knocked-on to other trains. Therefore, in the second part of this research we aim to make a timetable in a bottleneck area more robust, such that small delays can be absorbed as much as possible. To do this, we propose a Mixed-Integer Linear Programming (MILP) model that starts from an existing timetable in microscopic detail. The objective is to maximize the buffer times between each pair of trains, leading to a good spreading in time of the trains. Focusing on this objective will lead to less propagation of delays and therefore shorter and more reliable travel times for the passengers. The model can adapt both the timing and the microscopic routing of the trains. To ensure that the proposed timetable is practically relevant for the railway companies, constraints can be added easily depending on the specific properties that the resulting timetable should have. The results show that the spreading objective can be improved with 18% compared to the current situation in the bottleneck area of Halle. Due to the flexibility of the proposed model, it can also be used to analyze and optimize alternative scenarios where the level of service is adapted. When optimizing the timetable, different levels of detail can be used to model the network. While microscopic models are required to accurately represent the train operations, they are typically quite complex and require long computation times. Therefore, macroscopic models are often used instead. Microscopic simulation is then used in a later stage to determine if the timetable is conflict-free. In this thesis, we examine the impact of the considered level of detail on the optimization of the timetable. This way, we obtain more insight into which level of detail is most useful in practice in terms of the quality of the solution and the computation time. To do this, three different network representations with an increasing level of detail are considered: a macroscopic, a mesoscopic and a microscopic representation. The robustness optimization model that was developed previously is adapted such that it can consider each of these representations. These models are then applied to two case studies with very different properties: a line on the Swedish network and the bottleneck area in Halle that was considered earlier. For both case studies, the results show that including more details in the optimization leads to better solutions compared to optimizing with less details and solving the conflicts in a later stage. However, the computation times are very different for the two case studies. Surprisingly, including more details does not always lead to longer computation times. Although developing robust timetables is crucial to have a reliable service, unexpected incidents that have a large impact on the timetable are inevitable during operations. We specifically consider large incidents that cause a partial blockage of a corridor for a longer period of time. When such a disruption occurs, the timetable needs to be rescheduled in real-time. We propose a novel approach for disruption handling that is based on the concept of an Archetypical Infrastructure Piece (AIP), which is a frequently occurring piece of infrastructure. The general idea is that a large part of the network can be covered by a limited number of AIPs and that similarities in the infrastructure can be exploited when handling a disruption. For the limited number of AIPs, a mathematical model is developed to reschedule the trains during a disruption such that the impact on the passengers is minimized. This way, many possible disruption scenarios can be handled with a limited number of models by only changing some parameter values to describe the specific situation. We develop models for two common AIPs: a double-track and a multi-track corridor. Because real-world railway operations are inherently uncertain, a rolling horizon approach is used to solve the problem dynamically. This way, the delays that trains already have when arriving at the disrupted area are taken into account during the optimization. Our experiments show that the rolling horizon approach obtains high-quality solutions. Additionally, considering the current train delays during the rescheduling leads to a significant decrease, ranging from 12% to 30%, in the total train delay compared to simply considering the planned timetable.
Inneke Van Hoeck (Tue,) studied this question.