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.

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.

Railways are in need of technological and operational enhancements to achieve the EU strategic vision of a sustainable, integrated transport system. Beside the deployment of digital signalling and automatic train operations, advanced rail traffic management is critical to increase rail transport capacity and provide a seamless intermodal integration. To this aim, the concept of self-organisation has been recently proposed, which involves intelligent trains to autonomously decide and locally negotiate optimised traffic strategies. Although science considers self-organisation key to an efficient flexible rail service, the view of the industry is still unclear. Characterising the industrial perspective is instead essential to evaluate investment and migration plans of future rail developments. This paper addresses such a need by a multi-target Delphi analysis outlining an expert perspective on current traffic management gaps, potentials of self-organisation as well as critical steps and recommendations enabling a paradigm migration. Analysis results indicate that the state-of-practice is limited by technological and legal barriers to transport data sharing, slow rail digitalisation and organisational separation between infrastructure and operations. Traffic self-organisation could overcome current limitations only if it fosters digitalisation, a cooperative business model and policies for intermodal planning and data sharing. The rail market could be expanded by easier investor accessibility and a more attractive demandeffective intermodal rail service. Stakeholders’ reluctance in approving novel business models, policies and rules is however a threat to this paradigm. Feasibility studies, round-tables and joined sector actions are recommended for defining policies, proofof- concepts and plans for migrating to a self-organising rail traffic.

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.

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.

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.

The railway scheduling problem concerns the determination of trains' scheduled departure and arrival times at stops, and the allocation of capacity in the network. The timetable must be both conflict-free given infrastructure constraints, and stable enough for trains to recover from delays that could occur in normal operations. Existing methods for tactical scheduling contain a tradeoff between having an accurate (microscopic) representation of signalling constraints, and having a simple-enough (macroscopic) infrastructure representation to scale to real-world problem instances. This creates issues for infrastructure managers looking to run more trains on their infrastructure by migrating to Distance-To-Go (DTG) signalling systems (e.g. ETCS Level 2), and to exploit the capabilities of Connected Driver Advisory Systems (C-DAS) and Automatic Train Operation (ATO) to control trains more precisely. In this paper, we present a methodology for incorporating the capabilities of DTG signalling in conjunction with C-DAS and ATO systems into a disjunctive scheduling model for both periodic and nonperiodic instances. We show that the resulting model has both a microscopic infrastructure representation, and a macroscopic computational complexity, allowing railways to quickly compute conflict-free and stable timetables for large problem instances. The resulting model also accurately represents the computation of the brake indication point for both conventional and DTG signalling as a function of the trains' current speed. Tests on a large-scale periodic scheduling instance in the UK show that the model produces timetables with reasonable computation time.

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.

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.

In case of disturbed railway operations, traffic management can apply rescheduling measures to resolve conflicts while minimising delay propagation. This can be optimised by conflict detection and resolution (CDR) models. Usually based on alternative graph or mixed integer linear programming (MILP) formulations, existing models mostly refer to conventional signalling systems in which the track is discretised into blocks. Only at block entries, trains can receive a brake indication. Hence, train separation distances are based on a number of blocks. With the implementation of continuous braking curve supervision in distance-to-go (DTG) signalling systems such as the European Train Control System (ETCS), train separation is based on absolute braking distances. Consequently, an explicit relation between speed and train separation is required in CDR models for DTG signalling. Recently, we enhanced the CDR model RECIFE-MILP to DTG operations. The enhancements relate to track discretisation and speed-dependent train separation. In this research, we investigate the effect of track discretisation granularity on the performance of the enhanced model for next-generation DTG signalling systems: ETCS Level 3 Fixed Virtual Block and Moving Block. The performance is assessed regarding total delay and rescheduling decisions. The results indicate that, depending on the track and traffic scenario, a finer granularity can lead to different rescheduling decisions due to shorter train separation.

Moving Block (MB) and Virtual Coupling (VC) rail signalling will change current train operation paradigm by migrating vital equipment from trackside to onboard to reduce train separation and maintenance costs. Their actual deployment is however constrained by the industry's need to identify configurations of MB and VC signalling equipment which can effectively guarantee safe train movements even under degraded operational conditions involving component faults. In this paper, we analyse the effectivity of MB and VC in safely supervising train separation under nominal and degraded conditions by using an innovative approach which combines Fault Tree Analysis (FTA) and Stochastic Activity Networks (SAN). An FTA model of unsafe train movement is defined for both MB and VC capturing functional interactions and cause-effect relations among the different signalling components. The FTA is used as a basis to apportion signalling component failure rates needed to feed the SAN model. Effective MB and VC train supervision is analysed by means of SAN-based simulations in the specific scenario of an error in the Train Position Report (TPR) for five rail market segments featuring different traffic characteristics, namely high-speed, mainline, regional, urban and freight. Results show that the thresholds of the design variables depend on the considered signalling system alternative and the investigated market segment. In particular, the TPR delay threshold allowed for MB is higher than for VC. This means that to ensure a safe train movement, VC cannot absorb a TPR delay of longer than 1.5 s, which corresponds to the mainline market segment. For MB instead, the results show that the maximum TPR delay can reach 3.9 s for high-speed and freight railways. In addition, results showed that the integration of an FTA in a SAN model can provide a better understanding of the safety-performance behaviour of a system where VC showed a higher number of braking indications with respect to MB for the same TPR error failure rate. This means that for VC to effectively supervise the train separation at the same safety level as MB, we would need to have a much higher reliability of the TPR. The overall approach can support infrastructure managers, railway undertakings, and rail signalling suppliers in investigating the effectiveness of MB and VC to safely supervise train movements in scenarios involving different types of degraded conditions and failure events. The proposed method can hence support the railway industry in identifying effective and safe design configurations of next-generation rail signalling systems.

Automatic Train Operation (ATO) is a technology to support or automate train driving for increasing service punctuality, energy efficiency and rail infrastructure capacity. Conflict-free train path planning is crucial to the effective deployment of ATO, which allows ATO-equipped trains to operate according to schedule with different train driving strategies. As different train driving strategies lead to various passing times, current planning practice is inadequate to avoid route conflicts as it only sets target arrival or passing times at stops or major junctions. Therefore, conflict-free train path planning needs the definition of a Train Path Envelope (TPE) that contains time targets or windows defined at discrete locations called timing points to tolerate schedule deviations due to different driving styles. The number and location of the timing points, as well as the associated time targets or windows, is a decision problem. This paper proposes a framework to design a robust set of timing points and their associated time windows in a TPE to enable operational conflict-free train path planning against the driving strategies utilised. This framework relies on a Train Path Slot model which extends the definition of TPE from time windows at a discrete set of locations to an integrated blocking time stairway pattern continuously defined across all locations over a train route. The Train Path Slot model considers three relevant train driving strategies, i.e., energy-efficient driving with or without coasting as well as minimum-time driving considering slight delays. A Linear Programming model is formulated to compute the conflict-free Train Path Slots as constraints for train operation. To meet the optimised Train Path Slots, we analyse several possible sets of timing points in a TPE that are only located at stops or signal positions along the train routes. Those timing point sets are then compared in terms of total Train Path Slot overlap time, capacity, energy efficiency and driving performance indicators. Our research supports infrastructure managers in resolving the imminent problem of timing point determination and TPE computation to reach their capacity goals. At the same time, it allows sufficient driving flexibility for railway undertakings.

Moving Block (MB) and Virtual Coupling (VC) rail signalling will change current train operation paradigm by migrating vital equipment from trackside to onboard to reduce train separation and maintenance costs. Their actual deployment is however constrained by the industry’s need to identify confi gurations of MB and VC signalling equipment which can eff ectively guarantee safe train movements even under de-graded operational conditions involving component faults. In this paper, we analyse the eff ectivity of MB and VC in safely supervising train separation under nominal and degraded conditions by using an innovative approach which combines Fault Tree Analysis (FTA) and Stochastic Activity Network (SAN). A FTA model of unsafe train movement is defi ned for both MB and VC capturing functional interactions and cause-eff ect relations among the diff erent signalling components. The FTA is then used as a basis to apportion signalling component failure rates needed to feed the SAN model. Eff ective MB and VC train supervision is analysed by means of SAN-based simulations in the specifi c scenario of an error in the Train Position Reporting (TPR) for fi ve rail mar-ket segments featuring diff erent traffi c characteristics, namely high-speed, mainline, regional, urban and freight. Results show that the overall approach can support infra-structure managers, railway undertakings, and rail system suppliers in investigating ef-fectiveness of MB and VC in safely supervising train movements in scenarios involving diff erent types of degraded conditions and failure events. The proposed method can hence support the railway industry in identifying eff ective and safe design confi gura-tions of next-generation rail signalling systems.

This paper reviews the concept of self-organisation as defi ned in diff erent fi elds and attempts to provide a defi nition of goal-oriented self-organization that can be applied in the context of railway traffi c. Based on the provided defi nition a modelling approach for self-organising rail traffi c is then proposed to set the basis for future research and exploration of such a concept which could revolutionise the current rail transport to meet long-term capacity and competitiveness goals envisaged by the railway industry.

Developments in the railway industry are continuously evolving and long-term transition strategies can enable an efficient implementation of signalling technologies that provide a significant increase in network capacity and operation efficiency. Virtual Coupling (VC) advances moving block signalling by further reducing train separation to less than an absolute braking distance using train-to-train communication and cooperative train control within a Virtually-Coupled Train Set (VCTS). This paper proposes a method to develop scenario-based roadmaps based on a SWOT and hybrid Delphi-AHP multi-criteria analysis. Step-changes are identified and initially assessed in a Swimlane based on priorities and time order collected from stakeholders through a survey and further developed in a workshop. Optimistic and pessimistic scenarios are assessed regarding various factors and timelines. Step-changes are initially defined in a Swimlane and then enriched with optimistic and pessimistic scenarios to ultimately derive scenario-based roadmaps. Durations for each of the step-changes are developed into scenario-based roadmaps that can be used as an efficient tool for stakeholders to identify and solve potential criticalities/risks to the deployment of VC as well as to setup investment and development plans. The approach is applied to deliver implementation roadmaps of VC for different market segments with particular focus on mainline railways.

Railway traffic management is responsible for the detection and resolution of conflicts in case of disturbed operations. To minimise delay propagation, rescheduling decisions are taken by human dispatchers, possibly supported by mathematical models. Existing conflict detection and resolution (CDR) models mostly refer to conventional fixed-block multi-aspect signalling systems, in which minimum train headways are determined based on a preset number of blocks considering worst-case braking distances and number of signal aspects. In moving-block signalling systems, minimum headways are based on absolute braking distances. This paper reviews literature on CDR with the aim to identify gaps and to propose next steps in the research on CDR under moving-block signalling. A research agenda presents various modelling options, for which modelling approaches are proposed based on a comparative analysis.

Railway industry is developing advanced signalling systems like moving block to improve network capacity. In traditional fixed-block systems, safe train separation is determined based on a fixed number of block sections representing worst-case braking distances. In moving-block systems, the train separation is reduced to absolute braking distances. The introduction of moving-block signalling requires a change in operational rules and hence in real-time conflict detection and resolution methods in case of disturbances. Existing conflict detection and resolution models are mainly based on fixed-block signalling and the available models for moving-block signalling do not sufficiently represent the dynamic relation between safe train separation and actual train speeds.
To address this gap, we propose a conflict detection and resolution model that approximates moving-block operations. The model enhances the state-of-the-art fixed-block model RECIFE-MILP. The enhancements include a reconsideration of the discretisation of the infrastructure, the introduction of a speed profile alternative and a redefinition of blocking times. With this, the model is able to include speed-dependent occupation times, train separation based on absolute braking distances and continuous braking curve supervision.
We present the reformulated MILP (mixed integer linear programming) model and apply it to two French case studies: the Gonesse junction and a part of the Paris-Le Havre line. For various one-hour periods, rescheduling strategies and disturbance scenarios, we compare the optimal solutions of the enhanced and the original RECIFE-MILP model in terms of total train delay and rescheduling decisions. The results show that the enhanced model can propose different rescheduling decisions than the original model, with a better delay recovery exploiting the moving-block system.

Moving Block (MB) and Virtual Coupling (VC) rail signalling will change current train operation paradigm by migrating vital equipment from trackside to onboard to reduce train separation and maintenance costs. Their actual deployment is however constrained by the industry’s need to identify configurations of MB and VC signalling equipment which can effectively guarantee safe train movements even under degraded operational conditions involving component faults. In this paper, we analyse the effectivity of MB and VC in safely supervising train separation under nominal and degraded conditions by using an innovative approach which combines Fault Tree Analysis (FTA) and Stochastic Activity Network (SAN). A FTA model of unsafe train movement is defined for both MB and VC capturing functional interactions and cause effect relations among the different signalling components. The FTA is then used as a basis to apportion signalling component failure rates needed to feed the SAN model. Effective MB and VC train supervision is analysed by means of SAN-based simulations in the specific scenario of an error in the Train Position Reporting (TPR) for five rail market segments featuring different traffic characteristics, namely high-speed, mainline, regional, urban and freight. Results show that the overall approach can support infrastructure managers, railway undertakings, and rail system suppliers in investigating effectiveness of MB and VC in safely supervising train movements in scenarios involving different types of degraded conditions and failure events. The proposed method can hence support the railway industry in identifying effective and safe design configurations of next-generation rail signalling systems.

Conflict detection and resolution models are being developed to support railway traffic management in taking optimised rescheduling decisions in case of disturbances. Existing models mostly concern fixed-block signalling systems, in which minimum train separation distances are determined based on a preset number of blocks representing worst-case braking distances. In a moving-block signalling system, minimum train separation is based on absolute braking distances and hence depends on train speed differently from how fixed-block conflict detection and resolution models. In this paper, we propose a conflict detection and resolution model that approximates moving-block operations. The model enhances the state-of-the-art fixed-block rescheduling model RECIFE-MILP. The enhancements include a reconsideration of the discretisation of the infrastructure, the introduction of a speed profile alternative and a redefinition of the blocking times. We verify the model by comparing the solutions of the moving-block version with the fixed-block version for a specific scenario. The results indicate that the moving-block model can propose different rescheduling decisions than the fixed-block model with a better delay recovery.