A Lagrangian Method for Calculation of Passing Capacity on a Railway Hub Station

This research paper proposes a Lagrangian method to address the passing capacity of calculation problem (PCCP) for hub station in high-speed railway (HSR) system. The is critical determining train timetable and maximizing number trains that can operate on different lines. objective this study determine maximum pass through, start at, or end at station. To achieve objective, mathematical model was introduced solve PCCP. decomposed into two parts using relaxation algorithm. first part simple arrival (TAP) reflected timing with simultaneous departure time constraints. second spatio-temporal routing (TSRP) aimed shortest path free conflict train’s trajectory. A real instance provided demonstrate feasibility proposed approach effectiveness method. results showed efficiently PCCP maximize an HSR