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.

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.

One method to increase the quality of railway traffic flow is to construct a more robust timetable in which trains are able both to recover from delays and the delays are prevented from propagating. Previous research results show that the indicator Robustness in Critical Points (RCP) can be used to increase timetable robustness. In this paper we present the use of a method for RCP optimization: how it can be assessed ex-post via microscopic simulation. From the evaluation we learn more about how increased RCP values influence a timetable's performance. The aim is to understand more about RCP increase at a localised level within a timetable in terms of effects to the pairs of trains that are part of the indicator. We present a case study where an initial timetable and a timetable with increased RCP values are evaluated. The ex-post evaluation includes the quantification of measures concerning train-borne delay and robustness of operations, as well as measures capturing the subsequent quality of service experienced by passengers to assess the broader effects of improved robustness. The result shows that it is necessary to use several key performance indicators (KPIs) to evaluate the effects of an RCP increase. The robustness increases at a localised level, but the results also indicate that there is a need to analyse the relationship between ex-post measures and RCP further, to improve the method used to increase RCP and thus its overall effect on timetable robustness.

Due to high demand and capacity consumption, railway timetables are often sensitive to disturbances. To maintain punctual operations, it is important that timetables are robust, and methods are needed that make them robust without consuming too much capacity. In this paper, we demonstrate how a policy change in the form of new timetable planning rules can be used to achieve more robust timetables. We present the use of the rules in a real-world case from 2019, when our rules were applied for the Swedish Southern mainline. In this paper, we describe how a new policy for scheduling trains can be applied, and we discuss implications observed when going from research to practice. We also describe how the proposed rules affect train paths and runtimes. The outcome of the rules is measured in a comprehensive evaluation of the traffic performance based on empirical operational data. The results from this study show that practical knowledge is necessary when developing a policy, as well as when developing a timetabling model. Insights, given to us by experienced timetable planners, can be used to enhance optimisation models and make the models more applicable in the real world. The main contribution of this paper is to show that it is possible to increase timetable robustness with a minor policy change based on previously presented research results. Even with relatively small timetable modifications, we can learn from the operational data that the new rules had the intended effect and that overall punctuality can be increased.

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.