A bilevel rescheduling framework for optimal inter-area train coordination

Railway dispatchers reschedule trains in real-time in order to limit the propagation of disturbances and to regulate traffic in their respective dispatching areas by minimizing the deviation from the off-line timetable. However, the decisions taken in one area may influence the quality and even the feasibility of train schedules in the other areas. Regional control centers coordinate the dispatchers\u27 work for multiple areas in order to regulate traffic at the global level and to avoid situations of global infeasibility. Differently from the dispatcher problem, the coordination activity of regional control centers is still underinvestigated, even if this activity is a key factor for effective traffic management. This paper studies the problem of coordinating several dispatchers with the objective of driving their behavior towards globally optimal solutions. With our model, a coordinator may impose constraints at the border of each dispatching area. Each dispatcher must then schedule trains in its area by producing a locally feasible solution compliant with the border constraints imposed by the coordinator. The problem faced by the coordinator is therefore a bilevel programming problem in which the variables controlled by the coordinator are the border constraints. We demonstrate that the coordinator problem can be solved to optimality with a branch and bound procedure. The coordination algorithm has been tested on a large real railway network in the Netherlands with busy traffic conditions. Our experimental results show that a proven optimal solution is frequently found for various network divisions within computation times compatible with real-time operations

Assessment of flexible timetables in real-time traffic management of a railway bottleneck

A standard practice to improve punctuality of railway services is the addition of time reserves in the timetable to recover perturbations occurring in operations. However, time reserves reduce line capacity, and the amount of time reserves that can be inserted in congested areas is, therefore, limited. In this paper, we investigate the new concept of flexible timetable as an effective policy to improve punctuality without decreasing the capacity usage of the lines. The principle of a flexible timetable is to plan less in the timetable and to solve more inter-train conflicts during operations. The larger degree of freedom left to real-time management offers better chance to recover disturbances. We illustrate a detailed model for conflict resolution, based on the alternative graph formulation, and analyze different algorithms for resolving conflicts, based on simple local rules or global optimization. We compare the solutions obtained for different levels of flexibility and buffer time inserted in the timetable. An extensive computational study, based on a bottleneck area of the Dutch railway network, confirms that flexibility is a promising concept to improve train punctuality and to increase the throughput of a railway network

Conflict Resolution and Train Speed Coordination Solving Real-Time Timetable Perturbations

Awaiting permission to publish abstrac

Cooperative train control during the power supply shortage in metro system: A multi-agent reinforcement learning approach

In metro system, the fault of traction power supply system may cause the power supply shortage around the failure substation. In this case, the dispatching measure should be immediately taken to reduce the impacts of disruption on the train operation. To deal with this real-time traffic management problem, a cooperative control approach is proposed in this paper. In this approach, the time to apply tractive force and the level of force are simultaneously adjusted for all the operated trains, to maximize the maintained line capacity when considering the power supply capacity. Compared with the existing train timetable rescheduling approach, cooperative control is more flexible to get a better train regulation solution. To solve the challenges for developing the cooperative control model (i.e., undetermined number and dynamically changing of controlled objects), an imaginary section method is newly developed to transform the original problem into an equivalent cooperative control problem with fixed controlled objects. Then, the mathematical models for the transformed problem are constructed by using the space–time–speed network methodology. According to the formulated model, a Decentralized-Markov Decision Process (Dec-MDP) framework is designed as the basis of the applied algorithm. Next, a Collaboration Mechanism Based-Independent Deep Q-Network (CMB-IDQN) algorithm is proposed to solve the cooperative control problem. Compared with classical IDQN algorithm, a credit assignment method based on the collaboration mechanism among trains is novelly considered in the designed multi-agent reinforcement learning algorithm. Finally, the effectiveness of the proposed cooperative control approach is verified by two case studies. When solving the cooperative control problem, the performance by using CMB-IDQN algorithm can be increased by up to 13.0% and 16.8% compared with other two classical reinforcement learning algorithms (i.e., DQN and IDQN), respectively. Compared with two train timetable rescheduling measures during the power supply shortage, the cooperative control approach can improve the solution quality by more than 180.4% and 17.4%, respectively

Evaluation of green wave policy in real-time railway traffic management

In order to face the expected growth of transport demand in the next years, several new traffic control policies have been proposed and analyzed both to generate timetables and to effectively manage the traffic in real-time. In this paper, a detailed optimization model is used to analyze one such policy, called green wave, which consists in letting trains wait at the stations to avoid speed profile modifications in open corridors. Such policy is expected to be especially effective when the corridors are the bottleneck of the network. However, there is a lack of quantitative studies on the real-time effects of using this policy. To this end, this work shows a comparison of the delays obtained when trains are allowed or not to change their speed profile in open corridors. An extensive computational study is described for two practical dispatching areas of the Dutch railway network

A tabu search algorithm for rerouting trains during rail operations

This paper addresses the problem of train conflict detection and resolution, which is dealt every day by traffic controllers to adapt the timetable to delays and other unpredictable events occurring in real-time. We describe a number of algorithmic improvements implemented in the real-time traffic management system ROMA (Railway traffic Optimization by Means of Alternative graphs), achieved by incorporating effective rescheduling algorithms and local rerouting strategies in a tabu search scheme. We alternate a fast heuristic and a truncated branch and bound algorithm for computing train schedules within a short computation time, and investigate the effectiveness of using different neighborhood structures for train rerouting. The computational experiments are based on practical size instances from a dispatching area of the Dutch railway network and include complex disturbances with multiple late trains and blocked tracks. Several small instances are solved to optimality in order to compare the heuristic solutions with the optimum. For small instances, the new tabu search algorithms find optimal solutions. For large instances, the solutions generated by the new algorithms after 20 s of computation are up to more than 15% better than those achieved within 180 s by the previous version of ROMA

Rescheduling models for railway traffic management in large-scale networks

In the last decades of railway operations research, microscopic models have been intensively studied to support traffic operators in managing their dispatching areas. However, those models result in long computation times for large and highly utilized networks. The problem of controlling country-wide traffic is still open since the coordination of local areas is hard to tackle in short time and there are multiple interdependencies between trains across the whole network. This work is dedicated to the development of new macroscopic models that are able to incorporate traffic management decisions. Objective of this paper is to investigate how different levels of detail and number of operational constraints may affect the applicability of models for network-wide rescheduling in terms of quality of solutions and computation time. We present four different macroscopic models and test them on the Dutch national timetable. The macroscopic models are compared with a state-of-theart microscopic model. Trade-off between computation time and solution quality is discussed on various disturbed traffic conditions

Bi-objective conflict detection and resolution in railway traffic management

Railway conflict detection and resolution is the daily task faced by dispatchers and consists of adjusting train schedules whenever disturbances make the timetable infeasible. The main objective pursued by dispatchers in this task is the minimization of train delays, while train operating companies are also interested in other indicators of passenger dissatisfaction. The two objectives are conflicting whenever train delay reduction requires cancellation of some connected services, causing extra waiting times to transferring passengers. In fact, the infrastructure company and the train operating companies discuss on which connection to keep or drop in order to reach a compromise solution. This paper considers the bi-objective problem of minimizing train delays and missed connections in order to provide a set of feasible non-dominated schedules to support this decisional process. We use a detailed alternative graph model to ensure schedule feasibility and develop two heuristic algorithms to compute the Pareto front of non-dominated schedules. Our computational study, based on a complex and densely occupied Dutch railway network, shows that good coordination of connected train services is important to achieve real-time efficiency of railway services since the management of connections may heavily affect train punctuality. The two algorithms approximate accurately the Pareto front in a limited computation time

Synchronization of train timetables in an urban rail network: A bi-objective optimization approach

As urban rail networks in big cities tend to expand, the synchronization of trains has become a key issue for improving the service quality of passengers because most urban rail transit systems in the world involve more than one connected line, and passengers must transfer between these lines. In contrast to most existing studies that focus on a single line, in this study, we focus on synchronized train timetable optimization in an urban rail transit network, considering the dynamic passenger demand with transfers as well as train loading capacity constraints. First, we propose a mixed-integer programming (MIP) formulation for the synchronization of training timetables, in which we consider the optimization of two objectives. The first objective is to minimize the total waiting time of passengers, involving arriving and transfer passengers. Our second objective is a synchronization quality indicator (SQI) with piecewise linear formulation, which we propose to evaluate the transfer convenience of passengers. Subsequently, we propose several linearization techniques to handle the nonlinear constraints in the MIP formulation, and we prove the tightness of our reformulations. To solve large-scale instances more efficiently, we also develop a hybrid adaptive large neighbor search algorithm that is compared with two benchmarks: the commercial solver CPLEX and a metaheuristic. Finally, we focus on a series of real-world instances based on historical data from the Beijing metro network. The results show that our algorithm outperforms both benchmarks, and the synchronized timetable generated by our approach reduces the average waiting time of passengers by 1.5% and improves the connection quality of the Beijing metro by 14.8%

Integrated optimization of capacitated train rescheduling and passenger reassignment under disruptions

During railway operations, unexpected events may influence normal traffic flows. This paper focuses on a train rescheduling problem for handling large disruptions, such as a rolling stock breakdown leading to a cancelled train service, where passenger reassignment strategies have to be considered. A novel mixed-integer linear programming formulation is established with consideration of train retiming, reordering, rerouting, and reservicing (addition of extra stops). The proposed mathematical formulation considers planning extra stops for non-canceled trains in order to transport the disrupted passengers, which were supposed to travel on the canceled train, to their pre-planned destination stations. Other constraints deal with limited seat capacity and track capacity, and mapping train rescheduling with passenger reassignment. A bi-objective function is optimized by a weighted-sum method to maximize the number of disrupted passengers reaching their destination stations and to minimize the weighted total train delay for all non-canceled trains at their destinations. A series of numerical experiments based on a part of the Beijing-Shanghai high-speed railway line is carried out to verify the effectiveness and efficiency of the proposed model and to perform a sensitivity analysis of various performance factors. The results show that an optimal reassignment plan of disrupted passengers is important to achieve real-time efficiency of traffic and re-ticketing. The impact of passenger reassignment on train rescheduling is influenced by the weights for objectives, duration of disruption, allowed additional dwell and running times, and relationship between passenger demand and total available train capacity