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In many densely populated mega-cities around the world, metro systems are becoming overly saturated by the ever-increasing travel demand, which results in overcrowded stations, excessive delay, and unsafe anxieties among riders. The concept of extra-long trains (i.e., trains longer than station platforms) was recently proposed in the literature as a promising way to increase a metro line's capacity without additional infrastructure construction. This paper develops a general modeling framework to optimize train block configuration and operation protocols of a metro line so that extra-long trains can be used under varying demand distribution and infrastructure setting. The design problem is formulated as the integration of two coupled vehicle routing problems which simultaneously optimizes the train block configuration plan, door opening strategy, stop skipping strategy, and train dispatch schedule. This paper proposes two customized solution methods, including an adapted savings heuristic and a destroy-and-repair algorithm. A series of hypothetical examples are tested to demonstrate how the proposed solution approaches outperform an existing commercial solver even for small to moderate problem instances. Moreover, two real-world case studies, with very different demand patterns from two continents, are presented to test the effectiveness of using extra-long trains. Our results show that a metro line with extra-long train operations is capable of serving up to 20%–30% more passenger demand as compared to that with only regular trains, while at the same time producing a similar or lower passenger average travel time. • Design of extra-long trains (i.e., longer than station platforms) in a general setting. • Mixed-integer program to optimize train block configuration and operation protocols. • Customized solution methods (adapted savings and destroy-and-repair). • Extensive experiments with hypothetical and real-world data (from Beijing and Santiago). • Results show significantly increase in metro line capacity without infrastructure construction. [ABSTRACT FROM AUTHOR]

Integrating emerging shared mobility with traditional fixed-line public transport is a promising solution to the mismatch between supply and demand in urban transportation systems. The advent of modular vehicles (MVs) provides opportunities for more flexible and seamless intermodal transit. The MVs, which have been implemented, are comprised of automated modular units (MUs), and can dynamically change the number of MUs comprising them at different times and stops. However, this innovative intermodal urban transit brings with it a new level of dynamism and uncertainty. In this paper, we study the problem of jointly optimizing the timetable and the vehicle schedule within an intermodal urban transit network utilizing MVs within the context of distributionally robust optimization (DRO), which allows MVs to dynamically (de)couple at each stop and permits flexible circulations of MUs across different transportation modes. We propose a DRO formulation to explore the trade-off between operators and passengers, with the objective of minimizing the worst-case expectation of the weighted sum of passengers' and operating costs. Furthermore, to address the computational intractability of the proposed DRO model, we design a discrepancy-based ambiguity set to reformulate it into a mixed-integer linear programming model. In order to obtain high-quality solutionss of realistic instances, we develop a customized decomposition-based algorithm. Extensive numerical experiments demonstrate the effectiveness of the proposed approach. The computational results of real-world case studies based on the operational data of Beijing Bus Line illustrate that the proposed integrated timetabling and vehicle scheduling method reduces the expected value of passengers' and operating costs by about 6% in comparison with the practical timetable and fixed-capacity vehicles typically used in the Beijing bus system. • We address the timetabling and vehicle scheduling problem concerning modular units. • We formulate a distributionally robust model for the investigated problem. • We develop an algorithm combining ALNS and GUROBI to generate high-quality solutions. • We verify the effectiveness of our proposed approaches by numerical experiments. [ABSTRACT FROM AUTHOR]

• A multitask learning model for short-term inflow prediction of multi-traffic modes is proposed. • The adaptive matrix and attention mechanism are used to extract the spatiotemporal features of multi-traffic modes. • We analyze the interaction mechanism in the multi-traffic modes system. • The research highlights the significance of jointly predicting the inflow of multi-traffic modes. Network-wide short-term inflow prediction is important in efficiently managing the urban transportation system. Nowadays, all kinds of traffic modes gradually become interconnected and form a complex multi-traffic modes system, while extensive studies focus on the single-traffic mode and ignore the correlations among different traffic modes. There exist some challenges for short-term inflow prediction of multi-traffic modes: (1) the interaction mechanism among multi-traffic modes is difficult to learn and few studies explore the mechanism, (2) the data of multi-traffic modes are usually heterogenous due to the different spatial units of different traffic modes, and (3) it is challenging to extract the complex and dynamic features of the multi-traffic modes and most existing methods apply static spatiotemporal correlations among multi-traffic modes, while the genuine correlations among different traffic modes might be missing. To tackle these challenges, this study proposed a multitask-learning-based model called M ulti M ode-former (M2-former) with the encoder-decoder structure for network-wide short-term inflow prediction of the multi-traffic modes system. Specifically, the encoder is designed to learn and capture the complex and dynamic spatiotemporal correlations of multi-traffic modes, and the decoder is designed to extract the features of the target traffic mode and share knowledge among multi-traffic modes. Extensive experiments are conducted based on the real-world multi-traffic modes system data of Beijing, China. Results prove the superiority of the M2-former. In addition, the spatial and temporal information interaction mechanisms among multi-traffic modes are also explored. This paper can provide a reliable method and critical insights for the management and understanding of a multi-traffic modes system. [ABSTRACT FROM AUTHOR]

• A two-population 3-strategy evolutionary game model for subway network operation extension. • Theoretical analysis and numerical simulation of Evolutionary Equilibria for the replicator dynamics system. • The best long-term strategies of networks and key factors (motivations) analysis. • An extended game model for investigating the impact of adjustment minutes. With the growing demand for night travel and the development of the night-time economy, extending the operation time of metropolitan subway networks has become essential. This paper proposes a 2-population 3-strategy evolutionary game model for subway network operation extension decisions, which considers the interests of subway companies, passengers, and the government while addressing transfer failure between lines due to uncoordinated subway operation time adjustments. The study resolves the Evolutionary Equilibria (EEs) of the replicator dynamics system and identifies key factors influencing the evolutionary path using theoretical calculations and a ternary phase diagram. Additionally, an extended game model investigates the impact of adjustment minutes. To verify the models, a case study based on the Beijing subway network is conducted. We show that the rule of maximum total fitness ensures the priority of EE strategies for all lines, selecting Nash equilibrium strategies for the lines which cannot select EE in a vastly reduced network strategy profile space (from 729 to 2). The study concludes that combining subsidy measures can eliminate multiple equilibria produced by implementing only penalty measures, and combining penalty measures can have the effect of making small subsidies as effective as large subsidies. The variation of the satisfaction/loyalty affects the system equilibrium only when both game players value passenger satisfaction/loyalty. Finally, we find that the proper adjustment minutes not only can make operation extension a long-term best strategy but also increase the payoff (106,158 RMB/year) and enhance the occupancy rate (20 %) of the last train. The study provides a theoretical foundation for the government to regulate the operation extension of subway companies from multiple perspectives. [ABSTRACT FROM AUTHOR]