Structural changes in the travel behaviour of rail passengers following the COVID-19 pandemic have led to a strong weekday asymmetry in passenger demand. Demand is becoming more concentrated on the Tuesdays and Thursdays while Monday, Wednesday and Friday have seen a decline in passenger demand. In response a new policy was introduced at the Netherlands Railways (NS) called weekday differentiation. This policy reallocates unplanned servicing activities to low-demand weekdays allowing a higher availability of rolling stock on Tuesday and Thursday. Its implementation is however troubled with low operational performance. Meaning that due to operational constrains only part of the plan is successfully performed. This thesis researches how the robustness of weekday differentiation can be improved by optimising the allocation of rolling stock types to weekday differentiation over a week. The robustness is measured by the ability of the model to fill the weekday differentiation moments, also improving buffers at the weekday differentiation locations and minimizing deadheading. A MILP model is developed to represent the rolling stock flows. The model is an assignment model that assigns rolling stock to one of several states including passenger service and weekday differentiation opportunities. The model captures the trade-off between the passenger service that is rigid and the limited operating room to assign rolling stock units that are not active to the proper tasks. Some computational experiments are conducted in this thesis to analyse the model workings and the outcome of different variants of the model. The results demonstrate that targeted policy interventions can increase the number of successfully allocated rolling stock units while always maintaining careful consideration for the timetable. The findings provide support for refining the current weekday differentiation policy and offer insights for the NS to improve weekday differentiation productivity. ... Read more

Railways are a safe and efficient transport mode, with safety ensured by signalling systems and efficiency maintained by traffic management. This thesis proposes models to support the effective management of real-time railway operations under next-generation, radio-based distance-to-go signalling. It provides insights valuable to both the scientific community and the railway industry, supporting the future implementation of such signalling systems and contributing to the continued development of railways as a safe and efficient mode of transport. ... Read more

Railway operations require alignment between event-time-based timetables and speed-based train trajectories to enable effective interaction between traffic management and train operation across planning levels and real-time control. To support this alignment, this dissertation reviews standardisation activities and develops optimisation methods for Train Path Envelopes and event time flexibility. The proposed approaches support conflict-free operations, improve punctuality and energy efficiency, and provide insights for both academic research and railway practice. ... Read more

Cyclic railway timetables offer passengers a memorable and easy-to-use service, but they lack flexibility in responding to variations in passenger demand throughout the day. To maintain memorability while better adapting train services to fluctuating demand, this dissertation introduces multi-period cyclic timetables. It develops methods to partition the day into demand-homogeneous periods and optimisation models to design tailored line plans and cyclic timetables for each period, thereby improving the alignment between railway services and passenger demand. ... Read more

Delay propagation is a significant driver of flight delay in aviation networks, yet modelling it at a network-wide scale remains challenging. This study investigates to what extent scheduled max-plus linear systems, as used in railway delay modelling, can be applied to aviation networks. Using the Hawaiian Airlines network as a case study, a methodology is developed to model aircraft rotation and passenger transfer precedence relations within a max-plus linear system. The approach enables the calculation of stability indicators such as maximum cycle mean, recovery times, and network slack, as well as the simulation of delay propagation under various initial delay scenarios.

Results show that the recovery matrix is a valuable tool for identifying structurally vulnerable parts of the network and for assessing the impact of holding aircraft for transferring passengers. However, predictive accuracy of delay propagation for individual flights is limited, primarily due to uncertainties in process time estimation and incomplete knowledge of precedence relations. The 24-hour periodicity of aviation timetables, combined with large overnight buffers, further limits multi-day delay propagation modelling. These limitations are partly specific to the case under study and partly inherent to the deterministic, periodic structure of scheduled max-plus systems.

The study concludes that max-plus linear systems can provide meaningful insights into structural robustness and the systemic impact of schedule design choices, but their use for precise short-term delay prediction in aviation is constrained without high-quality operational data. Future work should explore integration of stochastic max-plus models, application to networks with shorter periodicity, and validation using airline-provided operational datasets. ... Read more

Railway digitalisation calls for an effective solution for real-time disturbance management. This thesis proposes dynamic timing points as an approach to improve punctuality and energy efficiency in disturbed ATO-over-ETCS operations. The location and time window of these timing points are calculated in real time by trackside intelligence when small delays occur, offering a proactive alternative to full rescheduling. They are communicated to the following train, allowing the onboard ATO to adjust its speed profile and avoid unnecessary braking. The proposed dynamic timing point method aligns with the modular ERTMS/ATO system architecture, making it suitable for future deployment. The trackside subsystem of ATO is suggested as a suitable location for the required trackside intelligence.
A case study on the Utrecht–’s Hertogenbosch line shows improved arrival times and energy savings of up to 70.9%, demonstrating significant potential for managing disturbed operations on high-density mainline rail corridors.
... Read more

This thesis addresses a hypothetical scenario in which all flights within most of Europe are substituted by rail and estimates the resulting additional rail demand, with a focus on night train demand. Routes, cities and countries with high potential for (night) trains under maximum air-rail substitution are highlighted, and rolling stock requirements are estimated. Several research gaps regarding long-distance travel behaviour and mode choice are shown to require assumptions in the modelling approach; the results are indicative of areas with higher demand potential for night trains than others. ... Read more

On railway lines with scarce infrastructure capacity, allocation methods allow for the assessment of the capacity requests from railway undertakings. The European Commission introduced a regulation to ensure a uniform approach to capacity allocation across all member states through socioeconomic and environmental criteria. However, relevant experiences and methods related to such criteria are hard to come by across Europe, meaning that such criteria' impact on capacity allocation is unknown. In this paper, we provide a method that applies the European criteria and can give insight into the possible impact of this new way of allocating capacity. The railway line Deventer – Bad Bentheim case study allows for the application of the method and defines its possible impacts. Compared to the current Dutch approach of distributing capacity scarcity, open-access train services have higher chances of receiving capacity access. The result shows how railway undertakings will behave more beneficially to society during capacity allocation procedures following the implementation of the method. Recommendations to improve the method are to reduce the number of assumptions, provide an inflation correction across all monetary parameters and consider using minimal frequencies. ... Read more

With the ambition of policy makers to encourage a modal shift to rail, an increase in the demand for running trains can be expected. Capacity wise, this increase in demand could be facilitated by applying moving-block signalling. If railway traffic increases however, so does the difficulty of managing it. Rescheduling systems are currently being developed to help traffic managers with this task. An increase in traffic does however increase the computation time needed for solving the conflict resolution optimization problem tackled by these systems. This could pose a problem since traffic management is a task performed in real-time. An often proposed technique to reduce computation time for conflict resolution is decomposing the problem into multiple coordinated sub-problems. Until now, no research has been performed combining moving-block signalling with decomposition of the conflict resolution problem. This research addresses this gap by developing and testing a distributed moving-block conflict resolution model. The effect of the model on computation time and solution quality in comparison to a centralized model is investigated through a case study of the rail network of the Dutch province Noord-Brabant. The results show a clear improvement in computation time for the distributed model while the solution quality improves or remains the same in the majority of tested scenarios. ... Read more

Virtual Coupling (VC) has the potential to significantly enhance railway infrastructure capacity and enable more flexible scheduling by introducing vehicle-to-vehicle (V2V) communication between consecutive trains. Inspired by platooning implementations in truck and bus platooning, VC could reduce operational costs and improve passenger satisfaction. However, its effective implementation in real-time railway operations remains uncertain, particularly regarding its impact on passengers, infrastructure managers, and railway undertakings. This research explores how VC can be implemented as an operational concept for mainline railway services, leveraging its potential to enhance flexibility and frequency to benefit passengers, railway operators, and infrastructure managers., identifying four operational concepts based on similar transport applications. Four operational concepts were identified, inspired by similar implementations in other transport modes. A SWOT analysis was conducted to qualitatively select the most promising options for further evaluation. For these concepts, running times and headways were calculated and tested within a real-world case study, focusing on key performance metrics such as generalized travel times, capacity utilization, and maximum frequency. The analysis revealed that a skip-stop pattern with synchronized arrivals at major stations is the most effective concept, facilitating efficient transfers and enhancing operational flexibility. Key recommendations include integrating real passenger demand data to better assess the absolute impact of operational variations and refining strategies for effective train coupling to advance VC implementation. ... Read more

The Ministry of Infrastructure and Water Management set up the ERTMS Programme and commissioned ProRail to realize the rollout. In Dutch vernacular, ERTMS is often used, but the system that replaces the legacy dutch system is ETCS Level 2. This rollout of ETCS Level 2 in infrastructure is currently being done on 7 sections of track in collaboration with 5 engineering firms that form the knowledge alliance. Although the rollout of ETCS Level 2 in the Netherlands is still in progress, research into new ETCS variants is ongoing. One of these variants is ETCS Hybrid Level 3. In ETCS Hybrid Level 3, Virtual Sub-Section (VSS) are introduced, allowing smaller track sections without additional investment in Trackside Train Detection (TTD). The use of VSS requires a Train Integrity Monitoring (TIM) system in the train that monitors train integrity. Out of the analysis of this paper, it can be concluded that the implementation of ETCS Hybrid Level 3 will results in changes within the Radio Block Center (RBC), Interlocking (IXL), rolling stock and user processes. The scale of the challenges that will occur by the implementation of ETCS Hybrid Level 3 depends on the implementation strategy that will be applied. Within the rail sector, there is much uncertainty as to what benefits are desired and feasible, and what implementation steps are required to achieve them. Analysis have shown that an potential implementation of ETCS Hybrid Level 3 will arise a significant challenge on an organisational level within the Dutch rail sector. ... Read more

Capacity and performance (evaluated through delay propagation) analysis methods have mostly focused on railway line track sections, but less attention has been given to nodes. Still, a few analytical methods for the capacity and performance assessment of the switch areas between station platform tracks and line tracks can be classified upon their reliance on a timetable (“timetable-based” methods) or not (“timetable-free” methods). The relation between capacity utilisation and performance has rarely been tested for railway nodes, and critical capacity utilisation thresholds remain to be investigated. The comparison of timetable-based and timetable-free methods also needs to be conducted. Filling these knowledge gaps will help the French infrastructure manager SNCF Réseau improve its analyses of nodes capacity utilisation and performance in the long-term planning stages. This paper investigates a small set of timetable-based and timetable-free methods either taken and adapted from the literature, such as the Potthoff and UIC 406 methods, or developed for the need of this research, such as adaptations of the UIC method and a method developed from SNCF Réseau’s previous works. The methods are applied on a case study on the French network, first evaluating their indicators’ magnitude and trends with artificial traffic data, and then comparing their outputs to real data. It is found that the Potthoff method and a timetable-free UIC-adapted method for capacity utilisation evaluation and an SNCF-adapted method for delay propagation provided results that are relevant in terms of magnitude and trends for long-term assessment. The timetable-based UIC 406 method for node capacity utilisation assessment can be used to study specific timetables. No satisfactory timetable-based delay propagation method was found in this paper. The timetable-free methods are further used to study the capacity utilisation – delay propagation relationship, which takes the form of an exponential function. Attempts to determine capacity utilisation thresholds are also conducted. It is recommended to perform further research with extended traffic data on different node layouts to consolidate these preliminary findings before applying them in real studies. ... Read more

The planning of railway operations is a very complex process, in which timetables and other logistical plans need to be both reliable and robust to effectively prevent and cope with disturbances. However, research in the robustness of initial stabling plans, designed in an earlier planning phase, during the following planning phases, has been lacking, with the models created in research in the Train Unit Shunting Problem (TUSP) being generally deterministic in nature, even though stabling plans could quickly become infeasible when the stabling demand in the form of arriving and departing trains changes.
This thesis therefore proposes a definition of the robustness of an initial stabling plan to changes in the stabling demand, such as changes in train lengths, as well as provide an assessment method of said robustness. The created Robustness Assessment Model (RAM) first generates an initial stabling demand and stabling plan, then performs a Monte Carlo simulation to generate a set of stabling plans created for variations of the initial stabling demand, based on changes in stabling demand such as train length. Finally, the RAM estimates the robustness of the initial stabling plan by analysing the differences between the initial and these generated stabling plan variations and how efficiently the initial plan is able to change to these plans to optimally facilitate the variations of the initial stabling demand.
Running this model across three locations, each with three capacity utilisation scenarios, has shown that the model is able to estimate the robustness of an initial stabling with acceptable confidence, and furthermore is able to give insight into how capable the stabling plan creation method is in generating a robust solution. Furthermore, the RAM can also be used to investigate patterns in stabling plans which could predict the robustness of said stabling plans. Current shortcomings to the RAM are its relatively long runtime, the simple stabling plan creation process used in the RAM, and that only one-sided stabling yards without servicing scheduling have been incorporated. Further research is therefore recommended for extending the RAM with other stabling yard layouts and the scheduling of services, as well as improve the stabling plan generation process to take more constraints into account.
... Read more

In order to track the speed profile, a case study using a linear quadratic regulator (LQR) is addressed in this paper. A time-invariant nonlinear train motion model is constructed. To apply LQR, the quadratic term of the aerodynamic drag and the rolling mechanical resistance is linearized. Gradient resistance, curve resistance, and other environmental disturbance are not considered in this paper. An LQR algorithm with constraints is proposed to track a given reference speed profile. Maximum error and cumulative error are used in the evaluation of the tracking performance. The tracking results in plots, parameters tuning, and performance analysis are shown. The results show that the proposed LQR algorithm is able to track the given 1200 seconds speed profile, the cumulative error can be controlled within 4.7478m/s, and the maximum absolute error is 0.90839m/s. The output of the control variable u is also given. ... Read more

This paper presents a train robust control method to optimize train operation based on the concept virtual coupling on train platoon. This approach is inspired by the recent development of platoon control for autonomous vehicles, and it is hoped that this platoon control can be applied to railway transportation. We use a decentralized model predictive control (MPC) to control leading train and followers together. To solve the complexity minimax objective function, we reformulated objective function as a minimization problem subject to linear matrix inequalities (LMIs). We defined four weight parameters to evaluate the model. Simulation result indicated that based on the premise of platoon stability, increase the performance parameters to obtain an optimal solution. We show that after the virtual coupling of less than two minutes, the gap distance between two consecutive trains is reduced and the capacity is increased while ensuring safey. ... Read more

Public transport is important for society, it provides accessibility to opportunities. Accessibility is not distributed evenly. Some inhabitants are disadvantaged, which has negative impacts on society. The distribution of accessibility between inhabitants can be measured with transport equity. The PT network should be improved in order to reduce the disadvantage of inhabitant groups. It is not defined how this could be done for regional PT networks. A six step assessment methodology is created for this purpose. The assessment method addresses what objective focus should be applied to, what improvements are possible in PT networks, what measures should be applied and what the equity effects of these measures are. Application of the assessment method yields that substantial equity improvements are possible within the Alkmaar – Den Helder railway corridor. Marginal equity improvements are achieved by changing rolling stock, significant improvements with local doubling of single track and substantial improvements when additional stations are opened. The assessment methodology is also able to identify the presence of trade-offs between inhabitants by mutual comparison. ... Read more

The impact of delays and disturbances in railway traffic can be mitigated by advanced rail traffic rescheduling models (RTRMs) which make use of mathematical optimization models. In the past several researches have been carried out on the effectiveness of an RTRM in reducing delay and improving punctuality. However, in most of these researches only one case study is used to test the RTRM. Still, it is unclear whether the results found for the application of an RTRM in one particular situation, are also valid for other situations (with different infrastructural and operational characteristics).
With this research, the impact of different infrastructure layouts and traffic patterns on the effectiveness of rail traffic rescheduling models is investigated. It provides insight into whether the benefit of an RTRM depends on the infrastructure and timetable in the area where it is applied.
For this purpose, an evaluation framework has been developed in which an RTRM can be tested using different infrastructure, operational and disturbance scenarios. In this framework, the RTRM is used to generate a real-time traffic plan for each scenario. These traffic plans are compared with the traffic plans of simple dispatching rules, that can be used in practice by dispatchers. For this comparison, KPIs such as the sum of consecutive delay (amount of delay that propagates within the network) and punctuality are used. This framework is applied to an alternative graph-based RTRM, which is formulated as a MILP (mixed integer linear programming).
The results show that the improvement an RTRM can offer over simple dispatching rules, varies per infrastructure layout and traffic pattern. For some infrastructure and operational scenarios, the simple dispatching rules perform as well as the RTRM, which means that for these situations, implementing an advanced RTRM does have much added value. A trend has been observed that the effectiveness of the RTRM increases as more control options are available. ... Read more

Despite advanced communication, monitoring, and control facilities, train operations are still subject to uncertainties that can disturb train services, cause delay to multiple trains, and propagate through the network. One option is to mitigate delay propagation in the timetable design by adding buffer time to the minimum difference between the time two successive train of either direction enter a section. It is still common practice to design buffer times based on a deterministic value, decreasing operational capacity and requiring large amount of manual checking by planners. Existing approaches to effectively allocate buffer time in timetables lack flexibility and require an initial timetable. In this paper, a data-driven approach for determination of buffer time planning rules suitable for usage in an initial timetable is presented. These planning rules are not necessarily generic, but rather depend on timetable characteristic. Two metrics that describe delay propagation, mean secondary delay and hindrance percentage, are extracted from literature and predicted in a regression analysis with the use of timetable characteristics related to headway situations of two succeeding trains. The results of the regression analysis on a case study of the Dutch railway network between Haarlem, Leiden Centraal and Schiphol Airport are used to determine the amount of scheduled buffer time that would ensure a certain amount of hindrance percentage given a specific headway situation. The results show that the mean secondary delay and hindrance percentage for various headway situations can both be predicted with an accuracy of 90.7\% based on timetable characteristics and is quite heterogeneous. Mean secondary delay appeared not significantly impacted by the scheduled buffer time, contrary to hindrance percentage which is significantly influenced by the scheduled buffer time. ... Read more

Moving block signalling promises a significant reduction of the infrastructure occupation compared to a fixed block system, such as NS’54/ATB. This is mainly caused by a strong reduction of the approach and running time. However, to assess the capacity gains track occupation data, such as blocking times are needed. ETCS L3 Moving Block is still in development, so gathering data out of daily operations is not possible. Also gathering moving block data out of simulation isn’t always a convenient solution. For example, in simulation software FRISO, used at ProRail, ETCS L3 Moving Block is not (yet) implemented.
With infrastructure data, rolling stock parameters and planned time-distance data, blocking times for a moving block signalling system can be estimated. The model presented in this thesis has an average error of 0.87s to the blocking time. In 95% of the cases the error is within a range of (-3,3) seconds. Given that ProRail plans with a precision of 6 seconds, it can be concluded that the model both precise as accurate. With the blocking times of all trains, bottlenecks in both railway corridors and complex nodes can be identified. One could sum all blocking times per block and consider blocks with the highest summed blocking times as bottleneck. However, this can only be applied for homogeneous traffic situations. Another approach is identifying bottlenecks by the shortest buffer time between two trains, also called a critical block. This can be applied for both homogeneous as heterogeneous traffic situations. An advantage is that it is not needed to split corridors into line sections. One could analyse a whole network at once and identify bottleneck at a microscopic level. By keeping the same timetable, the buffer time between two trains increases on average by 75 seconds (60%) using moving block over NS’54.
... Read more