Railway transportation offers the potential of transporting a large number of goods and people in a fast and environment-friendly way. A tendency seen over the last decades is a growing demand for capacity, and the increased number of operating trains has led to a high capacity consumption and a delay-sensitive system. Frequent delays result in high costs for the train operating companies, the infrastructure provider as well as high costs for the travellers and society overall. Robust timetables are essential to reduce delays and keep them from propagating. In this thesis, we analyse how timetable robustness can be assessed and increased. The primary aim is to establish quantitative indicators of timetable robustness that can be used to evaluate the robustness and identify weaknesses. The second aim of the thesis is to develop an approach for how the indicators can be used to increase the robustness.

The thesis addresses both theoretical and practical gaps regarding timetable robustness. It introduces the concept of critical points and contributes with two new robustness indicators, Robustness in Critical Points (RCP) and Robustness in Passing Points (RPP). Both RCP and RPP capture the connection between heterogeneity, runtime supplement and headway time in a unique way. The thesis also contributes with a method to measure and increase timetable robustness. The method is implemented in an optimisation tool, to illustrate how robustness can be automatically improved in the future. It is also implemented as real-world planning rules that can be used to support timetable planners in their daily work. The results show that it is possible to increase robustness with the use of RCP and RPP. Higher indicator values lead to less train delays and an increased punctuality.

This thesis consists of two parts. First, the scope of the research is described, with background knowledge on the problem, followed by the motivation, research framework, contributions and conclusions. The second part consists of five appended papers where the research is presented in detail.

When several trains are planned to use the same infrastructure resource, there is always a risk for spreading of delays, which can be hard to recover from. It is a challenge for the Infrastructure Manager to make timetables that accommodate as much traffic as possible, without causing bad on-time performance. Timetable planners are in need of quantitative indicators to assess timetable robustness and accurate methods for how to make the timetable more robust.

In this paper we assess the robustness for single-track lines with non-periodic timetables. At single-track lines, trains use the line for running in both directions and the trains can only pass or overtake each other at passing loops. This makes the system more sensitive for delays. In this paper we present a robustness indicator which captures the dependencies between trains at a single-track line. The indicator can be used to illustrate weaknesses in a timetable and also to indicate where and how to insert more robustness. In a simulation study, we show that it is possible to improve the performance by making small timetable adjustments according the indicator, without increasing runtimes or capacity utilization.

Maintaining high on-time performance and at the same time having high capacity utilization is a challenge for several railway traffic systems. The system becomes sensitive to disturbances and delays are easily propagating in the network. One way to handle this problem is to create more robust timetables; timetables that can absorb delays and prevent them from propagating. This paper presents an optimization approach to reduce the propagating of delays with a more efficient margin allocation in the timetable. A Mixed Integer Linear Programming (MILP) model is proposed in which the existing margin time is re-allocated to increase the robustness for an existing timetable. The model re-allocates both runtime margin time and headway margin time to increase the robustness at specific delay sensitive points in a timetable. We illustrate the model’s applicability for a real-world case where an initial, feasible timetable is modified to create new timetables with increased robustness. These new timetables are then evaluated and compared to the initial timetable. We evaluate how the MILP approach affects the initial timetable structure and its capability to handle disturbances by exposing the initial and the modified timetables to some minor initial disturbances of the range 1 up to 7 minutes. The results show that it is possible to reduce the delays by re-allocating margin time, for example, the total delay at end station decreases with 28 % in our real-world example.

Maintaining high on-time performance and at the same time having high capacity utilization is a challenge for several railway traffic systems and especially those with heterogeneous traffic. With high capacity utilization the system is sensitive to disturbances and delays could easily propagate in the network. One way to handle this problem is to create more robust timetables; timetables that can absorb delays and prevent them from propagating. This paper presents an optimization approach to reduce the propagation of delays by introducing a more efficient margin time allocation in the timetable. A Mixed Integer Linear Programming (MILP) model is proposed, in which the existing margin time is re-allocated to increase the robustness of an existing timetable. The model re-allocates both runtime and headway margin time to increase the robustness at specific delay sensitive points in a timetable, a suitable approach for double-track lines with dense heterogeneous traffic. We illustrate the applicability of the approach in a real-world case, where an initial timetable is modified into new timetables with increased robustness. These new timetables are then evaluated and compared to the initial timetable. We evaluate how the re-allocation of margin time affects the timetable structure and the timetable's capability to handle disturbances by exposing it to some minor initial disturbances in the range of 5–10 min. The results show that it is possible to reduce the delays by re-allocating the existing margin time. For example, the total delay at end station decreases with 10% in our real-world example.

An increase in train traffic is a politically welcomed trend, which on the other hand has led to too high capacity utilisation at times and a railway network sensitive to disturbances. Delays are easily spread, causing high cost. A mean of controlling the secondary delays is to use efficient operational prioritisation rules for trains in conflict. This paper presents an evaluation of the current Swedish prioritisation rule. For two frequent conflict situations the associated cost related to applying the rule is calculated. The result indicates a poor economic efficiency and show that significant savings can be achieved by changing strategy.

A tendency seen for the last decades in many European railway networks is a growing demand for capacity. An increased number of operating trains has led to a delay sensitive system where it is hard to recover from delays, where even relatively small delays are easily propagating to other traffic.

The overall aim of this thesis is to analyse the robustness of railway traffic timetables; why delays are propagating in the network and how the timetable design and dispatching strategies influence the delays. In this context we want to establish quantitative measures of timetable robustness. There is a need for measures that can be used by the timetable constructors. Measures that identify where and how to improve the robustness and thereby indicating how and where margin time should be inserted. It is also important that the measures can capture interdependencies between different trains.

In this thesis we introduce the concept of critical points, which is a practical approach to identify robustness weaknesses in a timetable. In contrast to other measures, critical points can be used to identify specific locations in both time and space. The corresponding measure, Robustness in Critical Points (RCP) provides the timetable constructors with concrete suggestions for which trains that should be given more runtime or headway margin. The measure also identifies where the margin time should be allocated to achieve a higher robustness.

In a case study we show that the delay propagation is highly related to the operational train dispatching. This study shows that the current prioritisation rule used in Sweden results in an economic inefficiency and therefore should be revised. This statement is further supported by RCP and the importance of giving the train dispatchers more flexibility to efficiently solve conflict situations.

The growing demand for railway capacity has led to high capacity consumption at times and a delay-sensitive network with insufficient robustness. The fundamental challenge is therefore to decide how to increase the robustness. To do so there is a need for accurate measures that return whether the timetable is robust or not and indicate where improvements should be made. Previously presented measures are useful when comparing different timetable candidates with respect to robustness, but less useful to decide where and how robustness should be inserted. In this paper, we focus on points where trains enter a line, or where trains are being overtaken, since we have observed that these points are critical for the robustness. The concept of critical points can be used in the practical timetabling process to identify weaknesses in a timetable and to provide suggestions for improvements. In order to quantitatively assess how crucial a critical point may be, we have defined the measure RCP (Robustness in Critical Points). A high RCP value is preferred, and it reflects a situation at which train dispatchers will have higher prospects of handling a conflict effectively. The number of critical points, the location pattern and the RCP values constitute an absolute value for the robustness of a certain train slot, as well as of a complete timetable. The concept of critical points and RCP can be seen as a contribution to the already defined robustness measures which combined can be used as guidelines for timetable constructors.

Several European railway traffic networks experience high capacity consumption during large parts of the day resulting in delay-sensitive traffic system with insufficient robustness. One fundamental challenge is therefore to assess the robustness and find strategies to decrease the sensitivity to disruptions. Accurate robustness measures are needed to determine if a timetable is sufficiently robust and suggest where improvements should be made.

Existing robustness measures are useful when comparing different timetables with respect to robustness. They are, however, not as useful for suggesting precisely where and how robustness should be increased. In this paper, we propose a new robustness measure that incorporates the concept of critical points. This concept can be used in the practical timetabling process to find weaknesses in a timetable and to provide suggestions for improvements. In order to quantitatively assess how crucial a critical point may be, we have defined the measure Robustness in Critical Points (RCP). In this paper, we present results from an experimental study where a benchmark of several measures as well as RCP has been done. The results demonstrate the relevance of the concept of critical points and RCP, and how it contributes to the set of already defined robustness measures.

A tendency seen for quite some time in the Swedish railway network is a growing demand for capacity which no longer can be accommodated. This causes congestion and delays, and the relationships between the trains and how they affect eachother are significantly harder to overview and analyse. Railway traffic timetables normally contain margins to make them robust, and enable trains to recover from certain delays. How effective these margins are, depends on their size and location as well as the frequency and magnitude of the disturbances that occur. Hence, it is important to include marigns so, that they can be used operationally to recover from a variety of disturbances and not restricted to a specific part of the line and/or the timetable. In a case study we compare the performance of a selection of passenger train services to the different prerequisites given by the timetable (e.g. available margins and their location, critical train dependencies). The study focuses on the Swedish Southern mainline between Stockholm and Malmö on which a wide variety of train services operate, e.g. freight trains, local and regional commuter train services as well as long-distance trains with different speed profiles. The analysis shows a clear mismatch between where margins are placed and where delays occur. We also believe that the most widely used performance measure, which is related to the delay when arriving at the final destination, might give rise to an unnecessarily high delay rate at intermediate stations.