In response to the growing demand for rail transport, next-generation signalling systems are increasingly investigated by the railway community. In particular, the concept of Virtual Coupling (VC) is progressively gaining ground thanks to its potential ability to reduce safe train separation to less than an absolute braking distance. That enables trains to move synchronously in a vehicle-to-vehicle radio-connected convoy. One of the major concerns associated with this concept is the safe and effective control of trains in a convoy when considering varying train resistances and risk factors due to, e.g., sudden degradation in the train and communication performance. This paper develops a novel Predictive Artificial Potential Field (PAPF) approach for safe and effective real-time train control under realistic VC operations. The proposed approach uses a realistic homogeneous strip model of train motion. Moreover, it incorporates a dynamically changing safety margin to take into account risk factor occurrences, such as delays in train control and communication, or sudden emergency braking applications. A simulation-based assessment of the developed method is performed for a high-speed rail corridor in China. Results show that the proposed PAPF control algorithm effectively supervises the safe train separation, preventing activation of emergency brakes even when risk events occur. The method contributes to advancing the state of the art on VC train control.

Self-organisation, a concept with wide-ranging applications across disciplines, offers significant potential for advancing railway traffic management. This review synthesises existing definitions, identifies critical gaps, and evaluates the applicability of self-organisation principles to railway traffic management. It also introduces a classification of self-organising systems and emphasises the importance of autonomy and goal orientation for enhancing scalability, robustness, and adaptability in railway operations. Building on insights from common-pool resource management, we propose the concept of autonomous goal-oriented self-organisation, a novel framework that combines decentralised decision-making with dynamic rule adaptation to address the complexities of modern railway systems. Key contributions include a critical synthesis of existing definitions, a novel classification of self-organising systems emphasising autonomy and goal orientation, and a discussion of its implications for railway traffic management. The review bridges disciplinary perspectives to provide a cohesive understanding of self-organisation and proposes a research agenda that prioritises simulation-based validation, interdisciplinary approaches, and adaptive mechanism development. By offering actionable insights and theoretical advancements, the framework has the potential to inspire innovative, equitable, and sustainable solutions for railway traffic management and beyond.

Conflict detection and resolution models typically consider train separation distances based on a number of blocks corresponding to conventional fixed-block signalling systems. However, modern distance-to-go railway signalling systems, such as the European Train Control System (ETCS), use braking curve supervision, resulting in train- and speed-dependent train separation distances. This paper proposes a modelling approach that incorporates train- and speed-dependent brake indication points and the resulting blocking times, enhancing conflict detection and resolution models for distance-to-go signalling. By integrating these enhancements into the state-of-the-art RECIFE-MILP model, a mixed integer linear programming formulation explicitly representing fixed-block distance-to-go signalling is obtained. The enhanced model is evaluated considering the state-of-practice fixed-block distance-to-go signalling system ETCS Level 2, and is compared with the original model for conventional fixed-block signalling in two real-world case studies. Results show that the shorter train separation under distance-to-go signalling leads to different rescheduling decisions, including a significant number of reroutings and some reorderings. With that, reductions in total train delay are achieved for 98% and 55% of the respective case study instances. While the mean reductions are below 1%, reductions of up to 7% are observed. These findings illustrate the operational relevance of incorporating distance-to-go principles into conflict detection and resolution modelling.

In response to the escalating demand for rail transport, the concept of Virtual Coupling (VC) train operations is progressively gaining ground within the railway sector. The concept of VC aims at reducing safe train separation to less than the absolute braking distance by letting trains move synchronously in radio-connected convoys. One of the major concerns associated with VC is ensuring safe train separation considering realistic risk factors, such as heterogeneous train braking performances and varying track conditions. To address such a safe train separation problem under VC, this paper proposes a novel train control model based on the Artificial Potential Field (APF) method to safely supervise the complete braking process of trains moving in a VC convoy. The proposed model uses a homogeneous strip representation of train length and a Dynamic Safety Margin (DSM) to take into account accurate train dynamics as well as potential risk factors, due to different train acceleration/braking rates, communication delays, unexpected emergency train braking applications, and position measurement errors. The method has been applied to the case of a high-speed line in China. Results show that the APF-based control method can effectively adapt to real-time variations in train dynamics and the operational environment to safely supervise the complete train braking process and avoid collisions even in the case of unplanned emergency braking applications. The proposed APF-based approach shows promising real-time performance which can further contribute to advancing the state of the art on safe train control under VC signalling.

Along with much of Europe and the global trend towards in-cab signalling, Great Britain (GB) rail is transitioning to Radio-based European Train Control System (ETCS). In collaboration with several universities and research partners, Network Rail have undertaken a programme of R&D to build on the opportunities that Radio-based ETCS offers, including the move towards automatic train operation (ATO), and integrated, centralised traffic management systems that maximise the potential in capacity, performance and energy efficiency for passenger and freight customers. Bringing the train planning and timetabling capabilities into the modernised, data driven, information rich world is a significant puzzle piece of turning opportunities offered by the signalling and control technologies into the day-to-day operations of the railway. This paper covers the research carried out into the characteristics of a radio-based ETCS railway that can be analysed for a goal-based state of the art train planning capability. It considers the advancement of tools, techniques, processes and skills that are required to plan, operate and regulate the railway through automatic train operations and future traffic management systems, ultimately harmonising planning, real-time operations and post-operations performance analysis.

Automatic Train Operation (ATO) aims to partially or fully automate train driving, enhancing railway capacity, punctuality, and energy efficiency. However, a key challenge arises from the mismatch between discrete event-time decisions at the Traffic Management System (TMS) level, assuming fixed running times, and the continuous speed–distance trajectory optimisation at the ATO level, leading to possible misalignments between planned and executed train movements. To bridge this gap, this paper introduces a novel optimisation-based method that dynamically computes Train Path Envelopes (TPEs) based on multiple driving strategies, defined as time targets or windows over a sequence of timing points, which ATO-equipped trains must comply with to align their movements with traffic management constraints. The method follows a two-stage approach: First, a linear programming model determines conflict-free blocking time ranges across the multiple driving strategies. Second, a structured optimisation process establishes operationally feasible TPEs by determining departure tolerances and configuring intermediate timing points. By integrating a critical-block strategy, the optimised TPEs provide the flexibility needed for ATO while accommodating variations in train driving strategies. The method is validated through experiments and a real-life case study in The Netherlands, demonstrating that optimised timing points at critical track locations improve energy efficiency, enhance punctuality, increase capacity, and provide an approach to align traffic management with ATO.

Passenger railway demand fluctuates daily, peaking at the start and end of the workday due to commuting to school and work. During the off-peak the volumes drop and most people travel for other purposes, like leisure and social visits, which results in different travel destinations. Despite this, many European Railways use fixed line plans and cyclic timetables that remain constant throughout the day. While this approach makes schedules easy to remember and provides ample off-peak travel options, it is primarily designed for peak-hour demand, making it less efficient. Furthermore, due to the different mix of travel purposes, a schedule based on peak-hour demand is not necessarily optimal for off-peak demand. This paper aims to combine the benefits of a cyclic timetable with the flexibility of an acyclic timetable in order to follow the time-dependent demand more closely. We propose a mixed-integer linear programming model that finds a timetable for a day consisting of several periods which each have its own line plan. The resulting timetable is required to be cyclic within each period and provide a good transition between the periods. The model is successfully tested on a case study with changing stopping patterns using data from the Dutch railway network, for which an optimal timetable is found. In this timetable, the transition between cyclic schedules can be done without cancelling trains or shifting trains from the new cyclic times.

Periodic timetabling is a crucial but computationally challenging problem in the railway planning field. Existing approaches often overlook the interaction between passenger routes and timetables, leading to suboptimal solutions. In this paper, we propose a method that incorporates passenger routing into the optimization of periodic timetables. Our goal is to optimize the periodic timetable from the strategic planning perspective, aiming to minimize the total perceived passenger travel time. We propose an iterative heuristic approach that integrates an adaptive large neighborhood search algorithm with a mixed-integer linear programming solver. To improve the efficiency of the algorithm, we design tailored operators and an outer loop. We conduct realworld case studies on real-life instances of Netherlands Railways to illustrate the effectiveness of our approach. The computational results show that our solution method is capable of addressing real-life problems.

Effective rail traffic management is necessary to mitigate the impact of unforeseen train service disturbances. Traditional decomposition methods, while effective in managing complexity, often struggle to maintain global optimality and real-time responsiveness. In this paper, we propose a novel approach that decomposes the rescheduling problem by means of a selforganising paradigm where trains are intelligent autonomous agents deciding on their decisions after reaching a consensus. The proposed Self-Organized Train Rescheduling (SOTR) algorithm is inspired by the Distributed Constraint Optimization Problem (DCOP) framework. This algorithm treats trains as intelligent agents capable of constructing their own traffic plans, communicating with neighbouring agents, and making decisions that lead to an optimal timetable. Each train, acting as an agent, assesses its situation, predicts conflicts, and negotiates with other trains to find the most efficient solution in regard to total delay. This distributed decision-making process allows for rapid adaptation to dynamic disturbances and ensures scalability to large networks. We validate the effectiveness of our approach by using a micro-simulation tool, demonstrating its ability to minimize secondary delays and maintain network continuity in perturbation scenarios.

Widespread congestion in metro systems often hinders passengers from boarding the first arriving train, making them compelled to adopt an alternative route, some of which involve travelling backwards. While this travel strategy has direct consequences for forecasting passenger flow distribution in congested networks, little is known about the travelling backwards phenomenon and why people adopt this travelling behaviour. The aim of this study is to understand passengers’ perception of time in various segments considering travelling backwards. To achieve this, we develop a route choice model using revealed preference data from smart card records. We find that passengers exhibit a greater aversion to waiting time and onboard time while travelling backwards. Specifically, passengers perceive each minute spent waiting on the turn-back stations’ platform as equivalent to 1.97 min on the origin platform. Similarly, each minute spent onboard the backwards train is perceived as equivalent to 1.24 min on the forwards train. Ignoring this difference in perception would result in the underestimation of the expected social benefits of demand management policies. Finally, we assess the potential benefits of travelling backwards under various passenger flow conditions, offering valuable policy insights regarding whether and how this behaviour should be regulated or promoted.

The increasing train traffic over railway networks stretches the demand for capacity of railway yards and rolling stock maintenance locations, which increasingly limits performance and further growth. Therefore, the scheduling of rolling stock maintenance and the choice regarding optimal locations to perform maintenance is increasingly complicated. This research introduces a Maintenance Scheduling and Location Choice Problem (MSLCP). It simultaneously determines maintenance locations and maintenance schedules of rolling stock, while considering the available capacity of maintenance locations. Solving the MSLCP using one large Mixed Integer Programming appears not to perform well enough. Therefore, to solve the MSLCP, an optimization framework based on Logic-Based Benders’ Decomposition (LBBD) is proposed by combining two models, the Maintenance Location Choice Problem (MLCP) and the Activity Planning Problem (APP), to assess the capacity of an MLCP solution. Within the LBBD, four variants of cut generation procedures are introduced to improve the computational performance: a naive procedure, two heuristic procedures and the so-called min-cut procedure that aims to exploit the specific characteristics of the problem at hand. The framework is demonstrated on realistic scenarios from the Dutch railways. It is shown that the best choice for the cut generation procedure depends on the objective: when aiming to find a good but not necessarily optimal solution, the min-cut procedure performs best, whereas when aiming for the optimal solution, one of the heuristic procedures is the preferred option. The techniques used in the current research are new to the current field and offer interesting next research opportunities.

To further improve the capacity on the European railway network, next-generation distance-to-go signalling systems are being developed in the context of the European Train Control System (ETCS). This paper investigates the impact of track discretisation granularity on conflict detection and resolution for ETCS with onboard train integrity monitoring. The study enhances a previously developed model for fixed-block distance-to-go signalling by introducing a track discretisation procedure and reformulating safe train separation constraints at switches. The assessment is performed on a junction and a corridor case study, using track discretisations with maximum section lengths from 50 to 800 m. Though finer discretisations potentially improve the model objective, computation times quickly increase. While the results show minimum effects of the track discretisation on the conflict detection and resolution, they suggest that maximum section lengths of 200 or 400 m may offer a good balance between solution quality and computational complexity, depending on the track layout and traffic density. Generally, reliable rescheduling decisions can already be obtained with a 800-m discretisation.

As regenerative braking systems become more widespread in railways, rising attention is paid to collaborative train operations under optimized timetables to enhance regenerative braking efficiency. The effective usage of regenerative braking energy (RBE) is determined by the dynamic nature of the traction power supply network, driven by constant changes in train power and positions. Solving the power flow with multiple trains significantly, however, increases the computing time required to solve the optimization model. Most existing methods have to solve optimization problems neglecting the dynamic power flow analysis, which sacrifices the accuracy of regeneration efficiency. In order to address this challenge, we propose a data-driven model that emulates the power flow analysis and reduces the computational demands. Initially, data from both single and multitrain simulators are collected and stored in a database, from which critical information regarding train position, power, and substation power is extracted. A neural network is then used to develop a data-driven model that predicts the power of a substation in a power supply network based on train positions and powers. Case studies with Beijing Yizhuang Metro line data show that the calculation time of the data-driven model is 0.33% of the power flow simulation while keeping the accuracy above 99%. Based on this data-driven model, by optimizing train speed profile and dwell time, the energy supplied by substations can be reduced by up to 13% compared to traction optimization.

To further improve the capacity on the European railway network, next-generation distance-to-go signalling systems are being developed in the context of the European Train Control System (ETCS). This paper investigates the impact of track discretisation granularity on conflict detection and resolution for ETCS with onboard train integrity monitoring. The study enhances a previously developed model for fixed-block distance-to-go signalling introducing a track discretisation procedure and reformulating safe train separation constraints at switches. The assessment is performed on a junction and a corridor case study, using track discretisations with maximum section lengths from 50 to 800 metres. Though finer discretisations potentially improve the model objective, computation times quickly increase. While the results show minimum effects of the track discretisation on the conflict detection and resolution, they suggest that maximum section lengths of 200 or 400 metres may offer a good balance between solution quality and computation complexity, depending on the track layout and traffic density.

Railway systems suffer from disturbances in operations, such as extended section running times caused by temporary speed restrictions and prolonged dwell times at stations due to unexpected passenger volumes. These disturbances cause deviations from the original timetable and negatively impact service reliability and passenger experience. Effective and timely rescheduling measures are crucial in reducing the impact of these disturbances. Existing timetable rescheduling models that rely on optimization-based methods often struggle with computational inefficiency, especially when dealing with scenarios involving a large number of train services. To address these challenges, we propose a learning-based timetable rescheduling framework that considers scalability in its formulation to reduce the growing computational burden associated with an increasing number of train services. The proposed framework decomposes the complex rescheduling problem into multiple subtasks, facilitating a systematic approach to managing extensive railway networks with numerous stations and train services. A high-level agent, functioning as a centralized traffic controller, is responsible for decomposing the overall deviation reduction task into subtasks at a low level and assigning them to individual train services with the primary objective of minimizing the time required to restore the original timetable. Low-level agents, acting as distributed train dispatchers, are tasked with rescheduling the timetables of their assigned trains. These low-level agents employ various dispatching strategies, facilitated by inter-train communication, to search for optimal rescheduling solutions while adhering to operational constraints such as minimum headway requirements. The lowlevel agents utilize an actor-critic architecture to generate continuous control decisions for dwell and running times, enabling them to learn and optimize their performance. Knowledge-sharing mechanisms amongst the low-level agents enable faster and more robust learning. Furthermore, advanced exploration methods are integrated to enhance the efficiency of the agents' training process.

Regional non-electrified railway networks require replacement of diesel traction to meet increasingly stringent emission reduction targets. Since full electrification of these networks is often not economically viable due to their low utilization, battery-electric multiple units (BEMUs) are recognized as a potentially suitable long-term solution, offering zero-emission train operation while requiring only partial tracks electrification. One of the main challenges when introducing BEMUs is determining an optimal electrification layout, i.e. the location and the length of electrified track sections while taking into account the vehicles’ and infrastructure technical characteristics and constraints alongside the requirements related to maintaining current timetable and quality of service. This paper formulates this as an intermittent partial electrification network design problem and develops an optimization framework that integrates high-fidelity BEMU simulation model in deriving a cost-optimized network electrification configuration. The proposed method is demonstrated using the existing non-electrified regional railway network in the Netherlands with the rolling stock and transport services of Arriva as a case. The obtained solution provides about 30% lower capital costs compared to the conventional continuous partial electrification approach, and about 3.5 times cut in these costs compared to the fully electrified network. Additionally, further costs reduction is observed by increasing the maximum current absorption limits at standstill and by introducing flexibility in terms of operational margins.

In response to the growing demand for rail transport, next-generation signalling systems are increasingly investigated by the railway community. In particular, the concept of Virtual Coupling (VC) is progressively gaining ground thanks to its potential ability to reduce safe train separation to less than an absolute braking distance allowing trains to move synchronously in a vehicle-tovehicle radio-connected convoy. One of the major concerns associated with this concept is the safe and effective control of trains in a convoy when considering varying train resistances and risk factors due to, e.g., sudden degradation in the train and communication performance. This paper develops a novel Predictive Artificial Potential Field (PAPF) approach for safe and effective real-time train control under realistic VC operations. The proposed approach uses a realistic homogeneous strip model of train motion and refers to a dynamically changing safety margin to take into account risk factor occurrences such as delays in train control and communication, or sudden emergency braking applications. A simulation-based assessment of the developed method is performed for a high-speed rail corridor in China. Results show that the proposed PAPF control algorithm effectively supervises the safe train separation preventing activation of emergency brakes even when risk events occur. The method contributes to advancing the state of the art on VC train control.

Automatic Train Operation (ATO) aims to enhance punctuality, energy efficiency, and reliability by automating driving tasks. Specifically, for mainline railways, an ATO onboard component generates and tracks optimised train trajectories based on time targets or windows at critical network locations, known as timing points, across train routes. These timing points and their associated constraints are specified in the Train Path Envelope (TPE), computed to ensure conflict-free operations. The generation of TPEs relies on dynamic updates of the real-time traffic plan from the Traffic Management System and real-time train statuses (e.g., position and speed). Understanding how TPEs are affected by these updates is essential for effective ATO deployment. To address this, this paper proposes a sensitivity analysis using elementary effects of a TPE generation algorithm, evaluating its response to variations in real-time traffic plans and train status updates. A real-life case study on a Dutch rail corridor with heterogeneous traffic reveals that control timing points can be introduced into the TPE as headways decrease, to homogenise traffic by aligning speed profiles and thus resolving conflicts. Timing point locations remain mostly unchanged, while their associated time windows become more sensitive when placed further along the route. Operational tolerance, which defines the latest conflict-free passing time, becomes more sensitive to headway changes and the distance from the previous stop.

Efficient railway operations are essential to accommodate growing traffic demand and to sustain high levels of system performance on heavily utilized corridors. Conventional train scheduling methodologies often face challenges in preventing train path conflicts arising from deviations in planned trajectories or operational uncertainties. To address this, we developed a framework to automatically generate conflict-free Train Path Envelopes (TPEs) for successive scheduled trains from a real-time traffic plan in a designated railway corridor. Specifically, the TPE is defined as a sequence of time targets or windows at key network locations (known as timing points) and serves as train trajectory constraints in generating conflict-free train trajectories aligned with the real-time traffic plan. The computational framework processes infrastructure and timetable data autonomously, identifies potential track occupation conflicts using blocking time theory across three typical train driving strategies and resolves them through the automated determination of intermediate timing points and dynamic adjustment of departure tolerances. Buffer times are incorporated into the blocking time bounds to tolerate train trajectory tracking errors.Lastly, the framework computes the earliest and latest feasible trajectories for each train. From this the TPEs are derived as a list of timing points with their time windows or targets. This framework not only optimizes track utilization by ensuring conflict-free train operations but also promotes energy efficiency by defining flexible and robust time-distance boundaries for train movements. The efficacy of the proposed framework has been validated through integration with FRISO (Flexible Rail Infrastructure Simulation of Operations), a microscopic simulation tool with discrete, dynamic, stochastic and deterministic properties. This development marks a first step towards a better link between railway traffic management and automatic train operation and is a cornerstone in Europe's Rail FP1-MOTIONAL project.

The adherence to a timetable with precise departure and arrival times becomes increasingly challenging in real-world scenarios due to the daily fluctuations in rail traffic, leading to uncertainties that complicate effective real-time traffic management. In this paper, we introduce and optimise timetable flexibility to enhance operational robustness and reduce conflicts resulting from minor train path deviations. We propose a Train Rescheduling with Flexibility (TRF) model, relying on a Mixed Integer Linear Programming (MILP) formulation. The primary objective is to minimise timetable deviation, while maximising timetable flexibility. The punctuality threshold is utilised to optimise time allowances within the real-time traffic plan, considering passenger connections and preventing early departures. A real-life case study that focuses on part of the Dutch railway characterised by complex track layouts and heterogeneous rail traffic is used to validate our model. Furthermore, we investigate the impact of predictive delays on flexibility, along with conducting sensitivity analyses on key parameters such as flexibility weight and punctuality threshold. The results of our optimisation model demonstrate its effectiveness in exploiting timetable flexibility to deal with disturbances.