Optimizing Timetable Synchronization for Rail Mass Transit

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.

[1]  K. Nachtigall,et al.  Minimizing waiting times in integrated fixed interval timetables by upgrading railway tracks , 1997 .

[2]  Rolf H. Möhring,et al.  A Case Study in Periodic Timetabling , 2002, ATMOS.

[3]  Martin Desrochers,et al.  Computer-Aided Transit Scheduling , 1992 .

[4]  Rolf H. Möhring,et al.  The modeling power of the periodic event scheduling problem: railway timetables-and beyond , 2004 .

[5]  Leena Suhl,et al.  Design of Customer-oriented Dispatching Support for Railways , 2001 .

[6]  Shing Chung Josh Wong,et al.  Predicting the performance of a mass transit system by using a conventional network model , 2004 .

[7]  K. Nachtigall,et al.  Periodic Network Optimization with Different Arc Frequencies , 1996, Discret. Appl. Math..

[8]  John R. Schroeter,et al.  The Values of Waiting Time, Travel Time, and a Seat on a Bus , 1987 .

[9]  Wolfgang Domschke,et al.  Schedule synchronization for public transit networks , 1989 .

[10]  Theo Muller,et al.  Optimized Transfer Opportunities in Public Transport , 1995, Transp. Sci..

[11]  Michael R. Bussieck,et al.  Discrete optimization in public rail transport , 1997, Math. Program..

[12]  Dirk Van Oudheusden,et al.  Developing railway timetables which guarantee a better service , 2004, Eur. J. Oper. Res..

[13]  Stefan Voß,et al.  Computer-Aided Scheduling of Public Transport , 2001 .

[14]  Stefan Voß,et al.  Practical Experiences in Schedule Synchronization , 1995 .

[15]  Md. Shoaib Chowdhury,et al.  Dynamic Vehicle Dispatching at the Intermodal Transfer Station , 2001 .

[16]  Walter Ukovich,et al.  A Mathematical Model for Periodic Scheduling Problems , 1989, SIAM J. Discret. Math..

[17]  Wolf-Dieter Klemt,et al.  Schedule Synchronization for Public Transit Networks , 1988 .

[18]  Michiel A. Odijk,et al.  A CONSTRAINT GENERATION ALGORITHM FOR THE CONSTRUCTION OF PERIODIC RAILWAY TIMETABLES , 1996 .

[19]  A. Adamski.  Transfer Optimization in Public Transport , 1995 .

[20]  Avishai Ceder,et al.  Timetable Synchronization for Buses , 1999 .

[21]  Karl Nachtigall,et al.  A genetic algorithm approach to periodic railway synchronization , 1996, Comput. Oper. Res..

[22]  James H. Bookbinder,et al.  Transfer Optimization in a Transit Network , 1992, Transp. Sci..

[23]  Rob M.P. Goverde,et al.  Synchronization Control of Scheduled Train Services to Minimize Passenger Waiting Times , 1998 .