External and internal factors can cause disturbances or disruptions in daily train operations, leading to deviations from official timetables and passenger delays. As a result, efficient train timetable rescheduling (TTR) methods are necessary to restore disrupted train services. Although TTR has been a popular research topic in recent years, the uncertain characteristics of railways have not been sufficiently addressed. This review first identifies the primary uncertainties of TTR and examines their impacts on both TTR and passenger routing during disturbances or disruptions. It finds that only a few uncertainties have been investigated, and the existing solution methods do not adequately meet practical requirements, such as considering the dynamic nature of disturbances or disruptions, which is crucial for real-world applications. Therefore, the review highlights problems associated with TTR uncertainties that need urgent attention and suggests promising methodologies that could effectively address these issues as future research directions. This review aims to help practitioners develop improved automatic train-dispatching systems with better train-rescheduling performance under disturbances or disruptions compared to current systems.@en

Railway operations are subject to deviations from the planned schedule, i.e., delays. In those situations, high-quality traffic control actions are needed to reduce the delays. Existing studies mainly used prescriptive techniques (e.g., mathematical programming, heuristics) to identify the best control action. These methods have limitations in the firm reliance on deterministic parameters prescriptively or normatively determined beforehand, and little understandability by the practitioners. These drawbacks hinder their acceptance in practice. This study exploits instead past realization data to provide decision support for traffic control. The realized data describe the traffic control actions taken by human controllers, and their effects; those latter are more complex than a linear sum of predetermined parameters. We use decision graphs to identify which traffic control action leads to the best solution, in terms of reduction of delays, based on the past performance of the same action in similar conditions. We are also able to explain the reasons and the factors that lead to each suggested action. We focus on the relevant case of merging stations, where multiple lines merge as one line, deciding the relative order between two consecutive trains. The method determines the stochastic effects of the two possible decisions at merge points, which allows for choosing the best one. Compared within the framework of realized data, the action suggested is the best out of a series of benchmarks, including simple rules and optimization, improving (reducing delays) approximately 11.7% on the common benchmarks. The variables with the highest impact on the utility are the length of the planned dwell time and the planned presence of an overtaking. The variables influencing the utility most are the actual delays of trains, the train type, and the order actually implemented.@en

Unexpected disruptions occur in the railways on a daily basis, which are typically handled manually by experienced traffic controllers with the support of predefined contingency plans. When several disruptions occur simultaneously, it is rather hard for traffic controllers to make rescheduling decisions, because (1) the predefined contingency plans corresponding to these disruptions may conflict with each other and (2) no predefined contingency plan considering the combined effects of multiple disruptions is available. This paper proposes a Mixed Integer Linear Programming (MILP) model to reschedule the timetable in case of multiple disruptions that occur at different geographic locations but have overlapping periods and are pairwise connected by at least one train line. The dispatching measures of retiming, reordering, cancelling, adding stops and flexible short-turning are formulated in the MILP model that also considers the rolling stock circulations at terminal stations and platform capacity. We develop two approaches for rescheduling the timetable in a dynamic environment: the sequential approach and the combined approach. In the sequential approach, a single-disruption rescheduling model is applied to handle each new disruption with the last solution as reference. In the combined approach, the multiple-disruption rescheduling model is applied every time an extra disruption occurs by considering all ongoing disruptions. A rolling-horizon solution method to the multiple-disruption model has been developed to handle long multiple connected disruptions in a more efficient way. The sequential and combined approaches have been tested on real-life instances on a subnetwork of the Dutch railways with 38 stations and 10 train lines operating half-hourly in each direction. In a few cases, the sequential approach did not find feasible solutions, while the combined approach obtained the solutions for all considered cases. Besides, the combined approach was able to find solutions with less cancelled train services and/or train delays than the sequential approach. For long disruptions, the proposed rolling-horizon method was able to generate high-quality rescheduling solutions in an acceptable time.@en

Passenger-oriented rescheduling problems receive increasing attention. However, the passenger assignment models used for evaluating the rescheduling solutions are usually simplified by many assumptions. To estimate passenger inconvenience more accurately, this paper establishes a dynamic passenger assignment model during disruptions, in which the time-dependent demand, disruption-induced service variations and vehicle capacities are all taken into account. Event-based simulation is adopted to implement the model of the dynamic loading and unloading procedures of passengers. Based on the model, individual travels can be tracked, thus making the estimation of individual passenger delay possible. By aggregating individual inconvenience, the performance of a given rescheduling solution/contingency plan can be evaluated. Furthermore, recommendations such as adding train units can also be proposed, as illustrated in the case study. @en

Passenger assignment models for major disruptions that require trains to be cancelled/short-turned in railway systems are rarely considered in literature, although these models could make a significant contribution to passenger-oriented disruption timetable design/rescheduling. This paper proposes a dynamic passenger assignment model, where the passengers who start travelling before, during and after the disruption are all considered. The model ensures that on-board passengers are given priority over waiting passengers, and waiting passengers are boarding under the first-come-first-serve rule. Moreover, the model allows information interventions by publishing information about service variations and train congestion at different locations with the aim of distributing passengers wisely to achieve less travel time increase due to the disruption. Discrete event simulation is adopted to implement the model, where loading/unloading procedures are realized and passengers re-plan their paths based on the information they receive. The model tracks individual travels, which helps to evaluate a disruption timetable in a passenger-oriented way.@en

Unexpected disruptions occur frequently in the railways, during which many train services cannot run as scheduled. This paper deals with timetable rescheduling during such disruptions, particularly in the case where all tracks between two stations are blocked for hours. In practice, a disruption may become shorter or longer than predicted. To take the uncertainty of the disruption duration into account, this paper formulates the timetable rescheduling as a rolling horizon two-stage stochastic programming problem in deterministic equivalent form. The random disruption duration is assumed to have a finite number of possible realizations, called scenarios, with given probabilities. Every time a prediction about the range of the disruption end time is updated, new scenarios are defined, and a two-stage stochastic model computes the optimal rescheduling solution to all these scenarios. The stochastic method was tested on a part of the Dutch railways, and compared to a deterministic rolling-horizon method. The results showed that compared to the deterministic method, the stochastic method is more likely to generate better rescheduling solutions for uncertain disruptions by less train cancellations and/or delays, while the solution robustness can be affected by the predicted range regarding the disruption end time.@en

During railway disruptions, most passengers may not be able to find preferred alternative train services due to the current way of handling disruptions that does not take passenger responses into account. To offer better alternatives to passengers, this paper proposes a novel passenger-oriented timetable rescheduling model, which integrates timetable rescheduling and passenger reassignment into a Mixed Integer Linear Programming model with the objective of minimizing generalized travel times: in-vehicle times, waiting times at origin/transfer stations and the number of transfers. The model applies the dispatching measures of re-timing, re-ordering, cancelling, flexible stopping and flexible short-turning trains, handles rolling stock circulations at both short-turning and terminal stations of trains, and takes station capacity into account. To solve the model efficiently, an Adapted Fix-and-Optimize (AFaO) algorithm is developed. Numerical experiments were carried out to a part of the Dutch railways. The results show that the proposed passenger-oriented timetable rescheduling model is able to shorten generalized travel times significantly compared to an operator-oriented timetable rescheduling model that does not consider passenger responses. By allowing only 10 min more train delay than an optimal operator-oriented rescheduling solution, the passenger-oriented model is able to shorten the generalized travel times over all passengers by thousands of minutes in all considered disruption scenarios. With a passenger-oriented rescheduled timetable, more passengers continue their train travels after a disruption started, compared to a rescheduled timetable from the operator-oriented model. The AFaO algorithm obtains high-quality solutions to the passenger-oriented model in up to 300 s.@en

Railway systems are vulnerable to unexpected disruptions, which usually result in track blockages for a few hours. In practice, disruptions are handled manually and the resulting impact to passengers is rarely considered. To enable disruption management more efficiently, operator-friendly and passenger-friendly, this thesis develops mathematical models and solution methods for dynamic passenger assignment, timetable rescheduling, and the integrated passenger assignment with timetable rescheduling during disruptions. @en

Unexpected disruptions occur in the railways on a daily basis, which are typically handled manually by experienced trac controllers with the support of predened contingency plans. When several disruptions occur simultaneously, it is rather hard for trac controllers to make trac management decisions, because 1) the predened contingency plans corresponding to these disruptions may con ictwith each other and 2) no predened contingency plan considering the combined eects of all disruptions is available. This paper proposes a Mixed Integer Linear Programming (MILP) model that reschedules the timetable automatically in case of multiple simultaneous disruptions occurring at dierent geographic locations. This multiple-disruptions rescheduling model considers the interactions between service adjustments made for dierent disruptions. The combined multiple disruptions rescheduling model is applied every time an extra disruption occurs by considering all ongoing disruptions. Also, a sequential single-disruption rescheduling model is considered to handle each new disruption with the last solution as reference. A case study is performed by assuming two simultaneous disruptions occurring in part of the Dutch railways with 38 stations and 10 train lines operating half-hourly in each direction. By setting 3 minutes as the computation time limit in the considered disruption scenario, the combined approach resulted in less cancelled train services and train delays compared to the sequential approach.@en

Real-time railway traffic management is important for the daily operations of railway systems. It predicts and resolves operational conflicts caused by events like excessive passenger boardings/alightings. Traditional optimization methods for this problem are restricted by the size of the problem instances. Therefore, this paper proposes a reinforcement learning-based timetable rescheduling method. Our method learns how to reschedule a timetable off-line and then can be applied online to make an optimal dispatching decision immediately by sensing the current state of the railway environment. Experiments show that the rescheduling solution obtained by the proposed reinforcement learning method is affected by the state representation of the railway environment. The proposed method was tested to a part of the Dutch railways considering scenarios with single initial train delays and multiple initial train delays. In both cases, our method found high-quality rescheduling solutions within limited training episodes.@en

The issue of disruptions in railway systems attracts a growing attention due to its severity to the society. Mitigation strategies are proposed from different perspectives to reduce the system vulnerability resulting by disruptions. However, due to financial limitations, it is not realistic to realize all strategies in the real world. Thus, it is necessary to establish a model based on which the system vulnerability can be measured and the mitigation strategy can be evaluated. In this paper, such a model is constructed by applying a Monte Carlo simulation based on the historical disruption data of railways in the Netherlands. Based on this model, we first construct a baseline scenario that is capable of reflecting the current disruption practice and calculate the top ten vulnerable tracks with the indicator of yearly disruption duration from this scenario. Next, we propose mitigation strategies towards each of the top ten vulnerable tracks of different magnitudes, and construct the mitigation scenarios according to the strategies. Finally, comparison between the baseline scenario and each of the mitigation scenarios is performed with the purpose of strategy evaluation.@en

Unexpected disruptions occur frequently in railway systems, during which many train services cannot run as scheduled. This paper deals with timetable rescheduling during such disruptions, particularly in the case where all tracks between two stations are blocked for a few hours. In practice, the disruption length is uncertain, and a disruption may become shorter or longer than predicted. Thus, it is necessary to take the uncertainty of the disruption duration into account. This paper formulates the robust timetable rescheduling as a rolling horizon two-stage stochastic programming problem in deterministic equivalent form. The random disruption duration is assumed to have a finite number of possible realizations, called scenarios, with given probabilities. Every time a prediction about the range of the disruption end time is updated, new scenarios are defined, and the model computes the optimal rescheduling solution for an extended control horizon, which is robust to all these scenarios. Based on the model, uncertain disruptions can be handled with robust solutions in a dynamic environment. The stochastic method was tested on a part of the Dutch railways, and compared to a deterministic rolling-horizon method. The results showed that compared to the deterministic method, the stochastic method is more likely to generate better rescheduling solutions for uncertain disruptions by less train cancellations and/or delays, while the solution robustness can be affected by the predicted range regarding the disruption end time. @en

Designing a public transport timetable that maximizes passenger service, measured in weighted travel time, is an intricate problem. The weighted travel time depends on the free route choice of passengers. Passenger route choice depends on the timetable. In turn, the timetable that minimizes weighted travel time depends on the route choice of passengers—and therefore requires passenger route choice information. Consequently, a sequential approach where timetables are designed provided pre-fixed passenger assignment to routes may not find the optimal timetable. This paper aims to integrate passenger route choice and timetabling. It addresses the problem of designing maximal passenger service public transport timetables in systems with free route choice within a budget for operating costs. Operating costs are defined by the minimal cost vehicle schedule required to operate the timetable. The proposed methodology integrates a matheuristic for timetabling and vehicle scheduling with a passenger assignment model in an iterative framework, where different forms of integration are evaluated. Focus is on long- to medium-term timetabling, provided an initial timetable. The results for a realistic case study in the Greater Copenhagen area indicate that our approach consistently leads, at no additional cost, to timetables that represent a reduction in passenger weighted travel time in comparison with both an initial timetable and a non-integrated timetabling method that receives a single-passenger assignment as input.@en

Designing a public transport timetable that maximizes passenger service, measured in weighted travel time, is an intricate problem. The weighted travel time depends on the free route choice of passengers. Passenger route choice depends on the timetable. In turn, the timetable that minimizes weighted travel time depends on the route choice of passengers—and therefore requires passenger route choice information. Consequently, a sequential approach where timetables are designed provided pre-fixed passenger assignment to routes may not find the optimal timetable. This paper aims to integrate passenger route choice and timetabling. It addresses the problem of designing maximal passenger service public transport timetables in systems with free route choice within a budget for operating costs. Operating costs are defined by the minimal cost vehicle schedule required to operate the timetable. The proposed methodology integrates a matheuristic for timetabling and vehicle scheduling with a passenger assignment model in an iterative framework, where different forms of integration are evaluated. Focus is on long- to medium-term timetabling, provided an initial timetable. The results for a realistic case study in the Greater Copenhagen area indicate that our approach consistently leads, at no additional cost, to timetables that represent a reduction in passenger weighted travel time in comparison with both an initial timetable and a non-integrated timetabling method that receives a single-passenger assignment as input.@en

In cities where the urban rail transit (URT) systems do not provide 24-h services, passengers may not be able to reach their destinations if the last train services have closed by the time they arrive at the transfer stations. This paper aims to seek a well-coordinated last train timetable that can transport as many passengers as possible to their destinations (referred to as reachable passengers) and also transport those passengers who cannot reach their destinations (referred to as unreachable passengers) to the stations as close as possible to their destinations. A bi-objective mixed-integer linear programming (MILP) model is developed to maximize the number of reachable passengers and minimize the total remaining travel distance of all passengers. The augmented ε-constraint method is applied to generate all Pareto optimal solutions of the bi-objective MILP model. Numerical experiments were implemented in the Chengdu URT network. Results indicate that compared to the current-in-use timetable, the optimized timetable by our methods significantly increased the number of reachable passengers and meanwhile reduced the average remaining travel distance of unreachable passengers. In addition, we discussed two possible strategies to improve passengers’ destination reachability, which are encouraging passengers to arrive early at their origin stations, and optimizing the timetable of last trains and non-last trains at the same time.@en

In cities where the urban rail transit (URT) systems do not provide 24-h services, passengers may not be able to reach their destinations if the last train services have closed by the time they arrive at the transfer stations. This paper aims to seek a well-coordinated last train timetable that can transport as many passengers as possible to their destinations (referred to as reachable passengers) and also transport those passengers who cannot reach their destinations (referred to as unreachable passengers) to the stations as close as possible to their destinations. A bi-objective mixed-integer linear programming (MILP) model is developed to maximize the number of reachable passengers and minimize the total remaining travel distance of all passengers. The augmented ε-constraint method is applied to generate all Pareto optimal solutions of the bi-objective MILP model. Numerical experiments were implemented in the Chengdu URT network. Results indicate that compared to the current-in-use timetable, the optimized timetable by our methods significantly increased the number of reachable passengers and meanwhile reduced the average remaining travel distance of unreachable passengers. In addition, we discussed two possible strategies to improve passengers’ destination reachability, which are encouraging passengers to arrive early at their origin stations, and optimizing the timetable of last trains and non-last trains at the same time.@en

Optimizing the railway timetable to increase synchronous accelerating and braking processes can lead to an improvement in the usage of regenerative energy. However, such a synchronized timetable might result in little or unsuitable transfer connections for the passengers. This paper focuses on the optimization of railway periodic timetables, to increase usage of regenerative energy while ensuring passenger satisfaction. We work by extending the traditional Periodic Event Scheduling Problem (PESP) formulation, to address the problem of synchronization of acceleration and braking phases, (and re-used energy) and including passenger-related events (and their satisfaction). Three objectives are identified, in a resulting Mixed Integer Linear Programming (MILP) model: maximizing the overlapping times of accelerating and braking trains to achieve increased usage of regenerative energy, minimizing the total passengers’ generalized travel times (global passenger dissatisfaction), and minimizing the maximum increase in individual's generalized travel time (local passenger dissatisfaction). A multi-step approach solves the trade-offs among three conflicting objectives. Results on a realistic case study show that the proposed approach can find optimized timetables, which compared to the currently-in-use timetable, can increase the usage of regenerative energy by over 1.5 times, save the average generalized travel time per passenger by 2 min, with only a minor increase on specific individual generalized travel time (up to 4 min). A detailed results analysis imply that to achieve a higher usage of regenerative energy, it is required to have a higher tolerance for the maximum increase in individual generalized travel time, while this is not necessary for the overall passenger generalized travel time, which can even be reduced when the maximum increase in individual generalized travel time becomes larger.@en

Optimizing the railway timetable to increase synchronous accelerating and braking processes can lead to an improvement in the usage of regenerative energy. However, such a synchronized timetable might result in little or unsuitable transfer connections for the passengers. This paper focuses on the optimization of railway periodic timetables, to increase usage of regenerative energy while ensuring passenger satisfaction. We work by extending the traditional Periodic Event Scheduling Problem (PESP) formulation, to address the problem of synchronization of acceleration and braking phases, (and re-used energy) and including passenger-related events (and their satisfaction). Three objectives are identified, in a resulting Mixed Integer Linear Programming (MILP) model: maximizing the overlapping times of accelerating and braking trains to achieve increased usage of regenerative energy, minimizing the total passengers’ generalized travel times (global passenger dissatisfaction), and minimizing the maximum increase in individual's generalized travel time (local passenger dissatisfaction). A multi-step approach solves the trade-offs among three conflicting objectives. Results on a realistic case study show that the proposed approach can find optimized timetables, which compared to the currently-in-use timetable, can increase the usage of regenerative energy by over 1.5 times, save the average generalized travel time per passenger by 2 min, with only a minor increase on specific individual generalized travel time (up to 4 min). A detailed results analysis imply that to achieve a higher usage of regenerative energy, it is required to have a higher tolerance for the maximum increase in individual generalized travel time, while this is not necessary for the overall passenger generalized travel time, which can even be reduced when the maximum increase in individual generalized travel time becomes larger.@en

Virtual coupling technology was recently proposed in railways, which separates trains by a relative braking distance (or even shorter distance) and moves trains synchronously to increase capacity at bottlenecks. This study proposes a real-time cooperative train trajectory planning algorithm for coordinating train movements under virtual coupling by considering stochastic initial delays. The algorithm uses mixed-integer programming models to estimate the delay propagation among trains, detect feasible coupled-running locations, and optimize the trajectories of the two trains such that they coordinate their speeds to achieve energy-efficient, punctual movements, as well as a safe coupled-running process. A robust optimization method is proposed to capture the stochastic delays as an uncertainty set, which is reformulated to its dual problem. Case studies of planning train trajectories for the classical virtual-coupling scenario suggest that (1) the coupled-running distance is greatly affected by the coordination of train timetables, delays, and safe separation constraints at switches; (2) the coordination of train movements for a coupled-running process imposes extra energy costs; and (3) the proposed method can detect feasible coupled-running locations and produce cooperative speed profiles in short computational times.@en

Virtual coupling technology was recently proposed in railways, which separates trains by a relative braking distance (or even shorter distance) and moves trains synchronously to increase capacity at bottlenecks. This study proposes a real-time cooperative train trajectory planning algorithm for coordinating train movements under virtual coupling by considering stochastic initial delays. The algorithm uses mixed-integer programming models to estimate the delay propagation among trains, detect feasible coupled-running locations, and optimize the trajectories of the two trains such that they coordinate their speeds to achieve energy-efficient, punctual movements, as well as a safe coupled-running process. A robust optimization method is proposed to capture the stochastic delays as an uncertainty set, which is reformulated to its dual problem. Case studies of planning train trajectories for the classical virtual-coupling scenario suggest that (1) the coupled-running distance is greatly affected by the coordination of train timetables, delays, and safe separation constraints at switches; (2) the coordination of train movements for a coupled-running process imposes extra energy costs; and (3) the proposed method can detect feasible coupled-running locations and produce cooperative speed profiles in short computational times.@en