Optimizing Timetable Synchronization for Rail Mass Transit

Abstract

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.

Transit network design and scheduling: A global review

“…The static timetabling problem is tackled by Wong and Leung (2004) who present a timetabling method which aims at maximizing synchronization between lines and enabling smooth transfers with minimum waiting time. Although the method especially suits railway systems, it can be applied to mass transit systems in general.…”

A Comparison between Genetic Algorithms and Simulated Annealing for Minimizing Transfer Waiting Time in Transit Systems

“…This model was modified in [3] in order to prevent bus bunching in urban bus systems using 'Branch and Bound' and multi-start iterated local search methods. Another approach was developed in [5] for minimizing transferwaiting time between railway lines throughan optimization-based heuristic algorithm. Reference [6] presented a model for synchronizing train lines and bus feeders using genetic algorithms.…”

The Optimization Model and Algorithm for Train Connection at Transfer Stations in Urban Rail Transit Network

“…On the basis of existing train schedules separately compiled by line, the running times, the dwelling times or turnaround times are adjusted to optimize the existing train schedules. To achieve this goal, Wong et al (2008) [3] designed a heuristic search algorithm., Vansteenwegen (2006Vansteenwegen ( , 2007 [4,5] designed a discrete event simulation method and Kwan et al (2008) [6] designed a non-dominated sorting genetic algorithm.…”