The Institute of Mathematics and its Applications

Scottish Branch

Evening lecture

“Timetable Synchronisation for RAIL Mass Transit”

Janny M.Y. Leung

Systems Engineering and Engineering Management Department,

The Chinese University of Hong Kong

Wednesday 2^nd April 2008, 6.30 p.m.

G38: Napier University

We propose a mixed integer programming (MIP) optimization model for a timetable synchronization problem for rail mass transit. The objective is to minimize the sum of all waiting times of all passengers at interchange stations. By adjusting the trains’ run-times and station dwell-times during their trips, and their dispatch times, turnaround times and headways at the terminals, we can construct high-quality timetables. A novelty in our formulation is the use of binary variables to determine the relative sequencing of trains on different lines with passenger transfers, which enables the correct representation of the waiting times for transfers to the “next available” train at interchange stations.

With trains departing every few minutes from each terminal, there are a large number of trips to consider, and hence the MIP formulation for the timetable synchronization contains thousands of binary variables and tens of thousands of continuous variables and constraints. We also investigated an optimization-based heuristic for this problem, whereby we can get good-quality solutions within a reasonably short time.

The train schedule for the MTR system in Hong Kong is used as an illustrative example, which indicates that our approach improves the synchronization of the current schedule significantly. We also explore the trade-offs among different operational parameters and flexibility and their impact on overall passenger waiting-times.

Non-IMA members welcome to attend.

Refreshments available from 6.00 pm