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Variable traffic conditions cause travel time uncertainty and further lead to time-varying accessibility. Most current studies do not fully consider fluctuations in accessibility and use complicated methods that likely overestimate the level of accessibility and hinder the application of accessibility measures. To address this issue, we utilized large-scale open-source data and proposed an interpretation of the reliability of accessibility concept that incorporates reliability, travel time uncertainty, and a cumulative opportunity measure. We examined the reliability of accessibility to Shenzhen, a major city in China, focusing on transit accessibility and job opportunities. The results demonstrate that the reliability of accessibility displays a bimodal distribution along urban railway lines and can be used to calculate the impact of urban railways in terms of punctuality. The new approach illustrates time-varying characteristics in the form of probabilities and provides further guidance on accessibility for governments. [ABSTRACT FROM AUTHOR]

Last train coordination aims to synchronize the arrival and departure times of the last feeder trains and the last connecting trains at transfer stations to improve the transfer accessibility of urban rail networks. This study focuses on the transfer accessibility between last trains with considering heterogeneous transfer walking time. Three mathematical models are developed on the last train timetable optimization. The first model fine-tunes the last train timetable under the given bound of the dwell time. The second one aims to allow the mutual transfers with the prolonged dwell time to maximize the transfer accessibility. A biobjective function is proposed to seek the trade-off between the maximal transfer accessibility and the minimal extension of dwell time. The third model considers the heterogeneity of transfer walking time that is represented as a random variable following a probability distribution. A discrete approximation method is proposed to reformulate the nonlinear model. The embedded Branch & Cut algorithm of CPLEX is applied to solve the models. A real case on the Shenzhen metro network is conducted to demonstrate the performance of the models. The three models all provide better last train timetable than the current timetable in practice. The sensitivity analysis manifests that the third model are always advantageous in the optimization of successful transfer passengers. [ABSTRACT FROM AUTHOR]