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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]

• A network-based passenger flow control method is proposed for the oversaturated metro network. • A bi-objective integer linear programming model is formulated. • The equivalent single objective linear integer programming model is deduced. • Numerical examples demonstrate the effectiveness of the proposed approaches. The oversaturated situation is now very common in the metro system of some megacities due to large commuting demands in peak hours, which leads to passenger accumulation on platforms and causes potential accident risks. To improve the transport efficiency and passenger accumulation safety at each station, this paper proposes a cooperative passenger flow control optimization in a specific metro network, in which each passenger can freely switch trains between different metro lines with a single ticket. Through considering the dynamic characteristics and transfer behaviors of passengers, an effective bi-objective integer linear programming model is formulated to characterize the passenger control process, in which the objectives are to minimize the total passenger waiting time and passenger accumulation risks at all the involved stations. To solve the proposed model conveniently, the above model is transformed into a single-objective model through reformulating the risk objective as a threshold-based constraint. Finally, two sets of numerical experiments, including a small-scale case and a real-world instance with operation data of the Beijing metro system, are implemented to demonstrate the performance and effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

• Construct a unified model for integrating timetable, bus formation and vehicle scheduling problems. • Schedule autonomous modular vehicles (AMVs) in both directions simultaneously. • Design a decomposition-based iterative solution framework based on Alternating Direction Method of Multipliers (ADMM) algorithm to solve the origin model efficiently. • Solve the subproblem efficiently with a customized time-dependent shortest path algorithm. • Introduce AMVs into public transport systems can reduce overall system costs and increase vehicle utilization. This paper presents a joint optimization of the timetable, bus formation, and vehicle scheduling in a flexible public transport (PT) system that utilizes autonomous modular vehicles (AMVs). In this system, AMVs have the capability to detach or join with each other at intermediate stops along the route to dynamically adjust the bus formation (capacity). To increase vehicle utilization, a flexible scheduling strategy is proposed that allows AMVs to detach from one modular bus and join another modular bus in either direction of a bidirectional line. In particular, the penalty cost for each detachment or joining operation, as well as the limited number of available AMVs is explicitly considered. We formulate a unified model for the integrated optimization of the modular bus service (timetable and bus formation) and vehicle scheduling by introducing two types of decision variables. The objective is to minimize overall system costs, including passenger waiting time cost, operational costs, and detachment/joining penalty costs. The two types of decision variables are coupled by a vehicle resource consistency constraint, ensuring the conformity of the modular bus service and vehicle scheduling decisions. To tackle the complexity of our model, the Alternating Direction Method of Multipliers (ADMM) is employed to decompose it into two subproblems, which can be efficiently solved using a customized forward dynamic programming algorithm and a commercial solver. The model is validated using illustrative examples and a real-world instance from the Beijing Public Transport system, and it is compared with two benchmark models. Our results demonstrate the efficiency of the ADMM-based solution framework for solving the integrated optimization model. Furthermore, our findings indicate that the use of AMVs in PT systems can lead to reduced overall system costs and increased vehicle utilization. [ABSTRACT FROM AUTHOR]

• Developed a macro framework optimized transportation network utility. • Proposed a general passenger utility maximization model considered efficiency and proportional fairness. • Proved the existence of optimal passenger allocation with maximum passenger utility. • Jointly optimize passenger allocation and vehicle schedules by maximizing transportation network utility. • Numerical tests verified the improvement of passengers' fairness and operation's cost. To deal with the contradiction between oversaturated demand and the restricted transport infrastructure and capacity during peak periods in a rail transit system, several passenger flow control methods that include soft pricing incentive, rigorous physical barrier and so on are widely used in current scenarios. However, the traffic disorderliness at the bottleneck and the control unfairness for the flows on specific stations may occur with those methods in the rail transit corridor. To alleviate those problems, this paper focus on the passenger allocation and matching with the corresponding schedules by considering the fairness of passengers and cost of operation from a macro perspective, where the passenger trip plan can be collected via a reservation platform in advance. A passenger utility maximization model that programs passenger allocation is proposed firstly, and we theoretically prove that there is an optimal traffic flow allocation with maximum utility under the oversaturated flow condition for any network. The model is solved by the Newton iteration algorithm and further proven to effectively make a tradeoff between efficiency and fairness. Furthermore, the transportation network utility maximization model is constructed by jointly optimizing the passenger allocation and vehicle schedules, thereby saving the cost of vehicle operation while guaranteeing the fairness of passenger allocation macroscopically. The model is solved by Multi-tree depth-first search algorithm based on Lagrangian relaxation with a subgradient in an iterative manner. A real-world case from the Batong subway line in Beijing is studied to validate the proposed models and algorithms. The results show that the model can jointly optimize the passenger allocation and vehicle schedules effectively in both an economical and fair manner, and the passengers can pass through the bottleneck in an orderly way. [ABSTRACT FROM AUTHOR]

• A method to solve train rescheduling and passenger reassignment simultaneously. • An integrated optimization model is formulated with a bi-objective function. • Our method can facilitate real-time rescheduling and re-ticketing efficiently. • Non-dominated train rescheduling and passenger reassignment solutions are obtained. 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. [ABSTRACT FROM AUTHOR]