Timetable synchronization of last trains for urban rail networks with maximum accessibility

In urban rail networks, passengers usually make transfers from one line to another during their trips. Toward the closure of daily service, certain destinations will become inaccessible for last trains as the connecting service may have already been closed when passengers arrive at the transfer station. This study focuses on timetable synchronization of last trains to improve the network accessibility. A mixed integer programming model is first proposed to determine the scheduled time of last trains. The objective of the model is to maximize the weighted sum of accessible origin-destination (OD) pairs for last train services on the network, which indicates the percentage of passengers using last trains at origins who can reach their destinations successfully. A simple network is used to highlight the difference of the proposed model from existing transfer models in the literature. To solve for large networks, a genetic algorithm combining with a timetable-based Dijkstra's algorithm is developed. A real-life metro network is applied to evaluate the proposed model and solution methodology in practice. The results indicate the proposed model and algorithm enhances the network accessibility, as well as the transfer connections. Comparison analysis shows that the proposed model significantly outperforms the transfer model in network accessibility optimization.