With the advantages of high speed and punctuality, urban rail transit has become the preferred choice for many commuters. However, overcrowding of urban rail transit lines during peak hours is a common problem in megacities owing to the excessive passenger demand. To address this problem, this study proposes an integrated optimization method that combines passenger flow control and bus-bridging services. An integer nonlinear optimization model is developed to minimize the weighted passenger waiting time and operating cost of bus-bridging services by considering the coupling relationships between passenger movements on both the metro and buses. Then, the proposed model is equivalently transformed into a linear form with better mathematical properties, and variants of this model are further formulated to extend the usability. Finally, real-world case studies based on the operational data of the Beijing Metro Batong line are conducted to verify the effectiveness of the proposed methods. The computational results indicate that the proposed approach can effectively alleviate overcrowding and reduce passengers' waiting time, thereby improving the operational efficiency and safety of the urban rail transit system.@en

Due to the advantages of high punctuality and speed, urban rail transit systems are attracting more and more commuters. In consequence, overcrowding during peak periods has become the norm in megacities, which poses a great challenge to operations. To address this challenge, this paper investigates the integrated optimization of passenger flow control and bus-bridging on oversaturated urban rail transit lines. Based on the time-dependent passenger demand, we propose an integer nonlinear programming model that aims to minimize the overall system cost. Then, to cope with the solving difficulty due to nonlinearity, the proposed formulation is further transformed into an equivalent mixed-integer linear programming model. Finally, real-world case studies based on the operating data of Beijing metro Batong line are applied to verify the effectiveness of our proposed approach. The computational results illustrate that our proposed method can significantly reduce the average passenger waiting time and improve operational safety.@en

With the rapid development and expansion of the urban rail transit network in China, the coordination between different lines brings great challenges to the operation due to its high complexity. In order to minimize the unsuccessful transfer-passenger flows of last-train under the worse case with the given level of tolerance, a distributionally robust chance-constrained programming model is proposed for the last-train connection planning problem in urban rail transit networks under uncertain transfer-passenger demand. In particular, the probability distribution of uncertain parameters is only partially known. By analyzing the relationship between the distributionally robust optimization model and the corresponding robust optimization model, it is proved that the former is an extension of the latter. Furthermore, the original model can be reformulated into a second-order mixed-integer conic programming form under the Gaussian perturbations ambiguity set based on the limited information of expectation and variance, which can be solved by CPLEX. The results of numerical examples indicate that the proposed model can be solved to optimality quickly by CPLEX on a small network, and can effectively avoid over-conservative solutions compared to the robust optimization model and reduce unsuccessful transfer-passenger flows in the extreme situation compared with the stochastic programming model, which exhibits more robust performance.@en

With the rapid increase in residents in megacities, the passenger demand of metro systems is rising sharply and steadily, bringing immense pressure to train operations. To improve the service quality, this paper discusses systematically investigating a joint optimization of the robust passenger flow control strategy and train timetable on a congested metro line. A deterministic model for train timetabling and passenger flow control at each station is first developed to make a trade-off between operation efficiency and service fairness. Then, the uncertain passenger demand is further considered at each station, and three integer linear programming models are formulated to derive the robust passenger flow control strategies. The first two models are related to the technique of Light Robustness, in which the uncertainty is handled by inserting expected protection levels at stations or on trains. In addition, with a stochastic scenario set that characterizes the uncertain passenger information, the last model aims to find a solution that is feasible for all involved scenarios, and thus, reduces the impact of the uncertainty in metro systems. To improve the computational efficiency of large-scale instances, a customized decomposition-based algorithm is developed. Finally, some real-world case studies based on the operation data of the Beijing metro Batong line are conducted to verify the performance and effectiveness of the proposed approaches.@en

Regular coronavirus disease 2019 (COVID-19) epidemic prevention and control have raised new requirements that necessitate operation-strategy innovation in urban rail transit. To alleviate increasingly serious congestion and further reduce the risk of cross-infection, a novel two-stage distributionally robust optimization (DRO) model is explicitly constructed, in which the probability distribution of stochastic scenarios is only partially known in advance. In the proposed model, the mean-conditional value-at-risk (CVaR) criterion is employed to obtain a tradeoff between the expected number of waiting passengers and the risk of congestion on an urban rail transit line. The relationship between the proposed DRO model and the traditional two-stage stochastic programming (SP) model is also depicted. Furthermore, to overcome the obstacle of model solvability resulting from imprecise probability distributions, a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form. A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming (MILP) solver is developed to improve the computational efficiency of large-scale instances. Finally, a series of numerical examples with real-world operation data are executed to validate the proposed approaches. @en

Aiming to increase successful transfers at stations for late-night passengers, we first propose an efficient dwell time adjustment strategy for the last-train coordination planning problem under transfer-passenger flows uncertainty. Unlike the traditional robust optimization model, we present a novel distributionally robust chance-constrained program to model this problem, where the probability distributions of the uncertain parameters are only partially available. By introducing a pessimistic ambiguous chance constraint, the proposed distributionally robust model guarantees that the probability of satisfying the service-oriented objective, i.e., maximum successful transfer-passenger flows in the whole subway system is larger than a predetermined confidence level in the worst case. We then draw the connection of the distributionally robust model with the traditional robust optimization model, and show that the proposed model can be interpreted as a generalized version of the robust optimization model. We further propose a safe tractable approximation method to reformulate the original model as a mixed-integer second-order conic programming under the bounded-perturbation ambiguous set, which can be solved to optimality on only small instances by the CPLEX. Hence, we develop a tabu search heuristic algorithm to obtain high-quality solutions for large-sized instances. We also use local search as a baseline algorithm to observe the improvements of the tabu search algorithm. Finally, we illustrate the superiority of the developed model on the Nanjing and Beijing subway networks and compare the performance of the proposed algorithms.@en

Considering the continuous arrival characteristics of outside arrival passenger flow and the impulsive feature of transferring passengers, this paper investigates the metro train timetabling and passenger flow control strategy under the influence of transferring passengers. This paper formulates an integer nonlinear collaborative optimization model for the metro train timetabling and passenger flow control strategy, which aims to minimize the number of detained passengers. The proposed model is reformulated into an integer linear programming model by introducing the 0-1 decision variables. A case study of a real-world urban rail transit line is performed to verify the effectiveness of the proposed approach, which is solved by the CPLEX software. The results reveal that, the proposed approach has good optimization quality and computational efficiency. Compared to the plan only optimize timetables, the obtained plan reduced the number of detained passengers by 17.69% and the service level was significantly improved. This study provides theoretical support for the high-quality operation of the urban rail transit system. @en

To relieve severe traffic congestion and the over- saturation of rail transit system, this study integrates the service and demand from the perspective of system optimization, and considers the continuous arrival characteristics of passenger flow in the analysis. A collaborative optimization method is developed for the train operation schedule and passenger flow control at stations using the skip-stop pattern strategy. By introducing the train schedule and passenger flow control decision variables, a bi-objective integer nonlinear collaborative optimization model is formulated to improve the train operation efficiency and to reduce the number of delayed passengers. Then, the nonlinear constraints are linearized by time reconstruction and big-M method with 0-1 variables to solve the proposed model. The model is reconstructed into an integer linear programming model, which can be easily solved by the CPLEX solver. The numerical examples are executed to verify the effectiveness of the proposed model. The results show that compared to the single objective optimization method and only with the train service time，the proposed model significantly reduces the number of delayed passengers. Compared to only considering number of delayed passengers, the train running time is reduced by 2% to 3%.@en