Optimizing Urban Rail Timetable under Time-dependent Demand and Oversaturated Conditions

This article focuses on optimizing a passenger train timetable in a heavily congested urban rail corridor. When peak-hour demand temporally exceeds the maximum loading capacity of a train unit, passengers may not be able to board the next arrival train, and they may be forced to wait in queues for the following trains. Based on time-dependent, origin-to-destination trip records from an automatic fare collection system, a nonlinear optimization model is developed to capture the overall passenger delay, subject to resource constraints associated with a limited number of electronic multiple units. A first-in-first-out queuing assumption is introduced to analytically calculate effective passenger loading time periods and the resulting time-dependent waiting times for given dynamic and stochastic demand patterns. Based on cumulative input-output diagrams, two novel solution algorithms, namely, local improvement and dynamic programming methods, are presented to find optimal timetables for individual station cases. A genetic algorithm is developed to solve the multi-station problem through a special binary coding method that indicates a train departure or cancellation at every possible time point. The effectiveness of the proposed model and algorithm are evaluated using a real-world data set.