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Optimizing Timetable Synchronization for Rail Mass Transit

Systems Engineering and Engineering Management Department, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
Planning and Development Department, MTR Corporation Limited, Hong Kong
Operations Department, MTR Corporation Limited, Hong Kong
Systems Engineering and Engineering Management Department, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong
rachelwong{at}alumni.cuhk.net
tonyyuen{at}mtr.com.hk
kwfung{at}mtr.com.hk
janny{at}se.cuhk.edu.hk

In most urban public transit rail systems, passengers may need to make several interchanges between different lines to reach their destination. The design of coordinated timetables that enable smooth interchanges with minimal delay for all passengers is a very difficult task. This paper presents a mixed-integer-programming optimization model for this schedule synchronization problem for nonperiodic timetables that minimizes the interchange waiting times of all passengers. A novelty in our formulation is the use of binary variables that enable the correct representation of the waiting times to the "next available" train at the interchange stations.

By adjusting trains' run times and station dwell times during their trips and their dispatch times, turnaround times at the terminals, and headways at the stations, our model can construct high-quality timetables that minimize transfer waiting times. We also discuss an optimization-based heuristic for the model. We have tested our algorithm for the Mass Transit Railway (MTR) system in Hong Kong, which runs six railway lines with many cross-platform interchange stations. Preliminary numerical results indicate that our approach improves the synchronization significantly compared with the current practice of using fixed headways and trip times. We also explore the trade-offs among different operational parameters and flexibility and their impact on overall passenger waiting times.

Key Words: mass transit; rail; timetabling; scheduling; transfers
History: Received: February 2005; revised: March 2006; accepted: March 2007.