Train timetabling plays a major role in railway planning processes, serving as a link between service providers and commuters to ensure reliable service delivery. However, mathematical optimization application to expansive subway systems is uncertain due to challenges in coordinating multiple lines, the necessity for integration with passenger demand, and multi-modal coordination. This study comprehensively reviews three main sub-stages of timetabling research areas: nominal, robust, and rescheduling problems. We synthesized the relevant studies considering the mathematical modeling of designed strategies, the incorporated stakeholders’ views, the characteristics of solution methods, and the extent of their practical use. Recent efforts to enhance subway system resiliency have had a limited focus on applying artificial intelligence methodologies to subway train timetabling, particularly emphasizing rescheduling problems. In the future, the research community is expected to broaden the application of artificial intelligence to encompass various aspects of subway train timetabling, incorporating four suggested considerations. These include coordination between multiple traffic modes, risk control, deep learning and mathematical optimization, and carbon peaking and neutrality goals to achieve standardized net-zero carbon emission objectives. These considerations represent a strategic pathway towards the next generation of subway train control systems. To conclude, the study aims to introduce theoretical aspects and research gaps in subway timetabling for the dedicated subway network and to provide future research directions.

The integrated ride-sourcing mode, developed by third-party integrators, is a feasible solution to market fragmentation because it integrates travel demand and vehicle supply. However, intense competition between platforms reduces the efficiency of the dispatching process. To tackle this issue, a two-stage dispatching framework is proposed, utilizing a partially observable Markov decision process (POMDP) to model the dispatching problem as a mixed cooperative-competitive reinforcement learning task. Within this framework, the Multi-Graph Hierarchical Multi-Head Attention-Deep Deterministic Policy Gradient (MGHMHA-DDPG) algorithm is proposed to determine the generalized values of driver-passenger pairs. A combinatorial optimization model is then formulated to identify the dispatching scheme that maximizes these values. Furthermore, the MGHMHA-DDPG algorithm incorporates a multi-graph convolutional module, a hierarchical multi-head attention module, and a gated recurrent module to model the global supply-demand distribution, the cooperation potential of vehicles, and the hidden features of the temporal dimension, respectively. Experiments using Beijing-based data demonstrate that the MGHMHA-DDPG algorithm outperforms benchmark methods in terms of market revenues and order response rates. This indicates that the MGHMHA-DDPG algorithm effectively mitigates dispatching conflicts between platforms and enhances overall market efficiency.

An advanced metro system becomes imperative towards efficient and sustainable operations with the rapid growth of urban construction. As the essential factors to implement transport sustainability, a referred energy-efficient trajectory and an energy-saving infrastructure for train operations could guide trains running through with conquering complicated environmental impacts and help to control the energy flows in traction processes. Thus, we attempt to discover the optimal way of adapting to the track changes and resistances in train running and evaluate the energy exchanges with Energy Storage System (ESS) in an extended power supply network. In this study, we firstly optimize a train trajectory with consideration of air and track resistances by using a modified Q-Learning (QL) method. Secondly, for coordinated application between ESS and trains, an integration module is designed by implanting train trajectories. Specifically, based on the working properties of ESS, a deceleration-acceleration time separation is matched for supplementing the charging/discharging times of the devices. The space-time presentation is introduced to portray train running phases for connections with control processes of ESS. Then, a Mixed Integer Linear Programming (MILP) model is proposed for minimizing deceleration-acceleration overlaps. A Tabu Search (TS) algorithm is introduced to solve such complex problems. Finally, a numerical test is conducted to demonstrate the feasibility of the model in Beijing, China.

Reassignment strategies are of great significance to improve the dispatching efficiency of the ride-sourcing market by reassigning drivers and passengers. However, due to the focus on the feasibility of the reassignment strategy in the short period, previous studies ignore possible reassignment opportunities in the future and inevitably make short-sighted reassignment decisions. To fully exploit the effect of the reassignment strategy, this study proposes a two-stage reassignment framework, which integrates a reinforcement learning algorithm and the bilateral matching reassignment model. The Markov decision process is adopted to dynamically model the reassignment problem. In the framework, the reinforcement learning algorithm is utilized to first learn the randomness and dynamics of travel patterns from historical data and select vehicles participating in the reassignment process. Then, the bilateral matching reassignment model formulates the matching relationship after reassignment for passengers (drivers). Furthermore, for the cases where reassignment may increase individual matching distance, a personalized bilateral matching reassignment model is developed to avoid that. Experiments based on real data in Beijing found that learning passenger travel patterns and adjusting vehicle reassignment moments can greatly improve the passenger experience and reduce driving costs. The results also suggest that the efficiency of the reassignment strategy is influenced by the supply and demand conditions of the ride-sourcing system. This justifies that the framework can be applied to optimize the dispatching process, reduce carbon emissions, and build an eco-friendly travel system.

The timetable of a metro system is essential for trains running safely and efficiently. For the design of a timetable, the potential power interruptions of energy supplies from the substations to the trains should be borne in mind. In case potential power interruptions occur, the backup running plan should be completed responsively to accommodate the passenger and energy demands In this study, we propose an energy supplementation strategy utilizing regenerative energy from decelerating trains in the event of power interruptions and develop a tri-objective optimization model incorporating passenger travel time, potential power interruption, and energy consumption. Particularly, for calculating regenerative energy utilization, we suggest a many-to-many energy allocation mechanism between decelerating and accelerating trains based on the real-time energy demands and supplies. A heuristic algorithm is developed to obtain a regular and cyclic timetable for minimizing passenger travel time, the potential power interruptions, and energy consumption. The suggested model and algorithm are tested based on the smart-card data collected from a bidirectional metro line in Beijing (China). The results show that the suggested approach significantly improves energy efficiency, reduces passenger waiting time, and decreases power interruption risks, compared with the currently used scheduling method.

In urban rail transit systems, energy conservation is a challenging problem due to the rising environmental and social issues. The existing literature on this topic usually ignores time-variant characteristics of passenger demand at each station. Based on the real-world time-dependent smart-card automated fare collection data, this paper develops a bi-objective timetable optimization model to minimize the total passenger waiting time and the pure energy consumption. In the model formulation, the total passenger waiting time is subjected to the train capacity in the oversaturated condition, and the pure energy consumption is represented by the difference between the traction energy consumption and the regenerative energy within a given period. Numerical examples based on the real-world data from Beijing Yizhuang metro line are conducted. The results indicate that the developed model can improve passenger service and reduce energy consumption efficiently in comparisons with the timetable used currently.