Optimal train schedule with headway and passenger flow dynamic models

This paper proposes an optimization method of train schedule for metro line, which will make the timetable, including train dwell time, in line with passenger demand. This method is also provide space for timetable improvement in robustness and energy-saving. Train dwell time is modeled to calculate an optimal dwell time at each station for boarding and alighting passengers, except headway equation and passenger equation. Train operation schedule includes the train dwell time at stations, running time between adjacent stations and headway, where dwell time at stations determines the process of passenger exchanging between stations and trains. A train schedule model is established with constrains of headway equations, passenger equations, and train dwell time equations, where the train dwell time is modeled as a function of the passenger boarding and alighting volumes. The aim of the optimal problem is to minimize the waiting time of passengers and operation cost directly or indirectly. Lagrangian duality theory is adopted to solve this optimal problem. Simulation results illustrate that this method is efficient to generate the train schedule, which meets the passengers exchanging requirements between trains and platforms.