Capacity of subway station is an important factor to ensure the safety and improve the transportation efficiency. In this paper, based on the M/G/C/C state-dependent queuing model, a probabilistic selection optimization model is proposed to assess the capacity of the station. The goal of the model is to maximize the output rate of the station, and the decision variables of the model are the selection results of the passengers. Finally, this paper takes a subway station of Shanghai Metro as a case study and calculates the optimal selection probability. The proposed model could be used to analyze the average waiting time, congestion probability, and other evaluation indexes; at the same time, it verifies the validity and practicability of the model.

Urban metro systems face increasing pressure to reconcile passenger service quality with infrastructure maintenance demands during late-night operations. This study proposes a coordinated optimization framework that integrates train timetabling with a flexible and selective skip-stop strategy. A mixed-integer programming model is formulated to jointly maximize passenger Origin–Destination (OD) accessibility and extend available maintenance windows. To solve the high-dimensional and computationally intensive model efficiently, a hybrid GWO-CNN algorithm is designed, where a Convolutional Neural Network (CNN)-based surrogate model replaces the time-consuming fitness evaluation process in the Grey Wolf Optimizer (GWO). A real-world case study on the Beijing metro network demonstrates that the proposed method increases OD accessibility by 23.60% and extends maintenance window by 8310 s. Compared to the conventional GWO, the GWO-CNN algorithm achieves superior solution quality with a 98.4% reduction in computation time. Sensitivity analyses further reveal the trade-offs between skip-stop rates, objective weight settings, and optimization outcomes, offering practical insights for metro operators in tailoring late-night scheduling strategies to both passenger demand and maintenance priorities.

At the end of the build-operate-transfer road concession period, an optimal model for the operation of public toll roads is created based on user heterogeneity regarding the values of time for different road users. The impact of user heterogeneity on operation costs for government and private firms is subsequently analyzed on the following critical variables: user values of time, road volume/capacity ratio, and road capacity. Concerning the values of time for different road users, the mean residual and failure functions are established to describe three optimization hypotheses: maximization of social welfare with operation by the government, two extreme cases with operation by a private firm, and a Pareto-optimal solution with operation by a private firm. It is concluded that the mean residual values of the time function are a linear function of the user values of time under a Pareto-optimal operation by the government. It is also determined that private profit is related to the demand-related operational cost of the government and private firm under a Pareto-optimal operation by a private firm. These conclusions suggest relevant recommendations for the government on policymaking for the operation of public toll roads.

With the rapid growth of passenger demand, the imbalance between transport capacity and passenger flow has become increasingly severe. Existing studies seldom consider the impacts induced by passenger demand uncertainty under a flexible train composition mode. To address this issue, this study investigates the integrated optimization of train timetabling and rolling stock circulation planning under a flexible train composition mode. The objective is to minimize the number of stranded passengers and operational costs. A scenario-based robust optimization framework is introduced, and a mean risk objective is formulated by combining the expected objective value with the expected absolute deviation of each scenario’s objective value from the expectation. By using linearization techniques, the model is transformed into a mixed integer programming (MIP) problem, which balances the operating cost and robustness while satisfying safety and service level requirements. The model is validated through a case study of Shanghai Metro Line 16. Numerical experimental results indicate that, in a single scenario, compared with the fixed train composition scheme, the proposed scheme reduces the objective function value by 28.3%. Simultaneously, it can enhance the robustness of the train timetable and rolling stock circulation plan under the condition of uncertain passenger demands. The related findings provide decision support for the design of urban rail transit operating plans.

When build–operate–transfer (BOT) roads are transferred back to the government upon the expiry of their contract, they are typically considered to be public roads and are no longer subject to tolls. However, in China, BOT roads, after being transferred to the government, remain tolled by the government in order to maintain efficiency. Therefore, such roads are termed public toll roads (PTRs). During the operational phase of PTRs, ongoing operating costs become a significant financial burden compared to the initial investment made for their construction. Against the backdrop of global carbon emission efforts, this paper studies the operational strategy of PTRs in terms of car emission costs, which constitute a portion of PTRs’ operation costs. This paper explores the operational strategy of PTRs, including whether the government should operate the road independently or outsource their operation to a competent private firm. Our analysis concludes that the operator should manage PTRs for the entire duration of their operation by maintaining self-financing while also accounting for operation costs. In this study, governmental regulations for the cost of carbon emissions are also studied.