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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 for the off-peak. 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.

Recent research in Energy-Efficient Train Control (EETC) and Energy-Efficient Train Timetabling (EETT) has uncovered various strategies that can be utilized to reduce railway energy consumption without placing additional demands on the capacity or compromising the robustness of operations. Several railway undertakings have already integrated aspects of these methodologies both in daily operations by the implementation of Driver Advisory Systems (DAS) and in the timetable design process. The major passenger railway operator in the Netherlands, Nederlandse Spoorwegen (NS), utilizes a tablet-based DAS that provides coasting advice to train drivers, while also displaying the route, timetable, temporary speed restrictions and blocks occupied by preceding traffic. Despite the implementation of this system, historical trajectory data from real world operations in the Netherlands indicate variances in the extent of energy-efficient train driving application. These variations could lessen the energy-savings of EETC and increase operational costs. Hence, the main aim of this poster is to evaluate the application of the EETC strategy in real world operations under varying environmental and operational conditions based on historical timetable and train trajectory data, while identifying the causes leading to the observed differences. Subsequently, a literature review of train trajectory optimization techniques is conducted to examine the extent to which these causes are addressed. Finally, the real world applicability of these methods is discussed and future research directions are provided.

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.

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.

Train passenger demand fluctuates throughout the day. In order to let train services, such as the line plan and timetable, match this fluctuating demand, insights are needed into how the demand is changing and for which periods the demand is relatively stable. Hierarchical clustering on both regular and normalized origin–destination (OD) data is used to determine for each workday continuous time-of-day periods in which the passenger demand is homogeneous. The periods found for each workday are subsequently used as input in a clustering algorithm to look for similarities and differences between workdays. The methods for finding homogeneous periods during the day and week are applied to a case study covering a large part of the railway network in the Netherlands. We find large differences between the periods based on regular OD matrices and those based on normalized OD matrices. The periods based on regular OD matrices are more compact in terms of passenger volumes and average kms travelled and therefore more suitable to use as input for designing a service plan. Comparison of different workdays shows that mainly the peak periods on Friday are far away from Monday to Thursday, and hence could benefit from an altered service plan.

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.