Real-time train scheduling is essential for passenger satisfaction in urban rail transit networks. This paper focuses on real-time train scheduling for urban rail transit networks considering uncertain time-dependent passenger origin-destination demands. First, a macroscopic passenger flow model we proposed before is extended to include rolling stock availability. Then, a distributed-knowledgeable-reduced-horizon (DKRH) algorithm is developed to deal with the computational burden and the communication restrictions of the train scheduling problem in urban rail transit networks. For the DKRH algorithm, a cost-to-go function is designed to reduce the prediction horizon of the original model predictive control approach while taking into account the control performance. By applying a scenario reduction approach, a scenario-based distributed-knowledgeable-reduced-horizon (S-DKRH) algorithm is proposed to handle the uncertain passenger flows with an acceptable increase in computation time. Numerical experiments are conducted to evaluate the effectiveness of the developed DKRH and S-DKRH algorithms based on real-life data from the Beijing urban rail transit network. The simulation results indicate that DKRH can be used to achieve real-time train scheduling for the urban rail transit network, while S-DKRH can handle the uncertainty in the passenger flows with an acceptable sacrifice in computation time.

Virtual coupling is regarded as an efficient way to improve the line capacity of rail transportation systems by reducing the spacing between consecutive trains. This paper is the first to compare and assess different distributed model predictive control (MPC) approaches, i.e., cooperative distributed MPC, serial distributed MPC, and decentralized MPC, for virtually coupled trains with a nonlinear train dynamic model. To make a balanced trade-off between computational complexity and efficiency, we also propose and assess convex approximations of the above control approaches. Furthermore, we are the first to introduce the relaxed dynamic programming approach to analyze the stability of the MPC-based nonlinear train control problem. By using the relaxed dynamic programming approach, a distributed stopping criterion with a stability guarantee is developed for the cooperative distributed MPC approach. In real life, masses of trains are different and can change at stations due to changes in passenger loads. This change in mass can significantly affect the dynamics and control of the virtually coupled trains when not taken into account in the control design. Therefore, we explicitly consider heterogeneous train masses when designing MPC approaches. We evaluate the different distributed MPC approaches through case studies based on the data of the Beijing Yizhuang Line. Simulation results indicate that the cooperative distributed MPC approach has the best tracking performance, while the serial distributed MPC approach can reduce communication requirements and computation capabilities with sacrifices of tracking performance.

Real-time timetable scheduling is an effective way to improve passenger satisfaction and to reduce operational costs in urban rail transit networks. In this paper, a novel passenger-oriented network model is developed for real-time timetable scheduling that can model time-dependent passenger origin-destination demands with consideration of a balanced trade-off between model accuracy and computation speed. Then, a model predictive control (MPC) approach is proposed for the timetable scheduling problem based on the developed model. The resulting MPC optimization problem is a nonlinear non-convex problem. In this context, the online computational complexity becomes the main issue for the real-time feasibility of MPC. To reduce the online computational complexity, the MPC optimization problem is therefore reformulated into a mixed-integer linear programming (MILP) problem. The resulting MILP problem is exactly equivalent to the original MPC optimization problem and can be solved very efficiently by existing MILP solvers, so that we can obtain the solution very fast and realize real-time timetable scheduling. Numerical experiments based on a part of Beijing subway network show the effectiveness and efficiency of the developed model and the MILP-based MPC method.

With high line adaptability, low noise and vibration, and potential in super-high operation speed compared to the wheel-rail (WR) train, the magnetic levitation (Maglev) train has attracted extensive attention from academia and industry. Although the Maglev train eliminates the energy consumption of wheel-rail friction, the huge aerodynamic energy consumption caused by its high-speed operation cannot be ignored. Due to the difference of operation mechanism and dynamic model between Maglev and WR train, the energy-efficient train operation for Maglev train considering peculiar characteristics needs to be further studied. This paper proposed a speed trajectory optimization model formulated by mixed-integer linear programming (MILP) to minimize the energy consumption of the Maglev system. Besides, piecewise linear (PWL) was utilized to deal with the nonlinear terms involved in the Maglev model. Finally, commercial software was applied to solve the model with consideration of various practical constraints of the Maglev system. The comparative result indicates that the flexible MILP model can obtain an optimal strategy efficiently with low linearization errors which are less than 0.1 %.

In big cities, the metro lines usually face great pressure caused by huge passengers demand, especially during peak hours. When disruptions occur, passengers accumulate quickly at stations. It is of great importance for dispatchers to take passenger flow control into consideration for the traffic management to ensure passengers’ safety and to maintain their satisfaction. This paper proposes an integrated disruption management model, which incorporates train rescheduling and passenger flow control. In this model, the train services can be short-turned, cancelled and rerouted, while the number of passengers entering a station is managed by controlling the station gates with consideration of the capacities of platforms and trains. Moreover, the number of passengers arriving at a station is calculated according to the origin-destination matrices. The objectives are to recover the train operation to the original timetable as soon as possible and to minimize the waiting time of passengers outside the stations. With the interaction between train services, passengers and station gates, an iterative metaheuristic approach is proposed to solve the integrated disruption management problem. Based on the data of a Beijing metro line, numerical experiments are conducted to test the proposed algorithm. The results demonstrate the importance of integrated disruption management and the effectiveness of our solution method.

Different from the existing train delay studies that had strived to explore sophisticated algorithms, this paper focuses on finding the bound of improvements on predicting multi-scenario train delays with different machine learning methods. Motivated by the observation of deep learning methods failing to improve the prediction performance if the delay occurs rarely, we present a novel augmented machine learning approach to improve the overall prediction accuracy further. Our solution proposes a rule-driven automation (RDA) method, including a delay status labeling (DSL) algorithm, and the resilience of section (RSE) and resilience of station (RST) indicators to generate the forecast for train delays. The experiment results demonstrate that the Random Forest based implementation of our RDA method (RF-RDA) can significantly improve the generalization ability of multivariate multi-step forecast models for multi-scenario train delay prediction. The proposed solution surpasses state-of-art baselines based on real-world traffic datasets, which treat various real-time delays differently. Even when the predictability of conventional deep learning methods decreases, the performance of our method is still acceptable for practical use to provide accurate forecasts.

This paper presents an integrated metro service scheduling and train unit deployment with a proximal policy optimization approach based on the deep reinforcement learning framework. The optimization problem is formulated as a Markov decision process (MDP) subject to a set of operational constraints. To address the computational complexity, the value function and control policy are parameterized by artificial neural networks (ANNs) with which the operational constraints are incorporated through a devised mask scheme. A proximal policy optimization (PPO) approach is developed for training the ANNs via successive transition simulations. The optimization framework is implemented and tested on a real-world scenario configured with the Victoria Line of London Underground, UK. The results show that the performance of proposed methodology outperforms a set of selected evolutionary heuristics in terms of both solution quality and computational efficiency. Results illustrate the advantages of having flexible train composition in saving operational costs and reducing service irregularities. This study contributes to real time metro operations with limited resources and state-of-art optimization techniques.

The real-time train scheduling problem for urban rail transit systems is considered with the aim of minimizing the total travel time of passengers and the energy consumption of the operation of trains. Based on the passenger demand in the urban rail transit system, the optimal departure times, running times, and dwell times are obtained by solving the scheduling problem. A new iterative convex programming (ICP) approach is proposed to solve the train scheduling problem. The performance of the ICP approach is compared with other alternative approaches, i.e., nonlinear programming approaches, a mixed-integer nonlinear programming (MINLP) approach, and a mixed-integer linear programming (MILP) approach. In addition, this paper formulates the real-time train scheduling problem with stop-skipping and shows how to solve it using an MINLP approach and an MILP approach. The ICP approach is shown, via a case study, to provide a better tradeoff between performance and computational complexity for the real-time train scheduling problem. Furthermore, for the train scheduling problem with stop-skipping, the MINLP approach turns out to have a good tradeoff between the control performance and the computational efficiency.

The train scheduling problem for urban rail transit systems is considered with the aim of minimizing the total travel time of passengers and the energy consumption of the trains. We adopt a model-based approach, where the model includes the operation of trains at the terminus and at the stations. In order to adapt the train schedule to the origin-destination-dependent passenger demand in the urban rail transit system, a stop-skipping strategy is adopted to reduce the passenger travel time and the energy consumption. An efficient bilevel optimization approach is proposed to solve this train scheduling problem, which actually is a mixed-integer nonlinear programming problem. The performance of the new efficient bilevel approach is compared with the existing bilevel approach. In addition, we also compare the stop-skipping strategy with the all-stop strategy. The comparison is performed through a case study inspired by real data from the Beijing Yizhuang line. The simulation results show that the efficient bilevel approach and the existing bilevel approach have a similar performance but the computation time of the efficient bilevel approach is around one magnitude smaller than that of the bilevel approach.