Modeling the first train timetabling problem with minimal missed trains and synchronization time differences in subway networks

Urban railway transportation organization is a systematic activity that is usually composed of several stages, including network design, line planning, timetabling, rolling stock and staffing. In this paper, we study the optimization of first train timetables for an urban railway network that focuses on designing convenient and smooth timetables for morning passengers. We propose a mixed integer programming (MIP) model for minimizing train arrival time differences and the number of missed trains, i.e., the number of trains without transfers within a reasonable time at interchange stations as an alternative to minimize passenger transfer waiting times. This is interesting from the operator's point of view, and we show that both criteria are equivalent. Starting from an intuitive model for the first train transfer problem, we then linearize the non-linear constraints by utilizing problem specific knowledge. In addition, a local search algorithm is developed to solve the timetabling problem. Through computational experiments involving the Beijing subway system, we demonstrate the computational efficiency of the exact model and the heuristic approach. Finally, three practical suggestions are proposed for the operation and management of the urban railway transit system.

[1]  Dung-Ying Lin,et al.  Using Genetic Algorithms to Optimize Stopping Patterns for Passenger Rail Transportation , 2014, Comput. Aided Civ. Infrastructure Eng..

[2]  Liujiang Kang,et al.  A simulated annealing algorithm for first train transfer problem in urban railway networks , 2016 .

[3]  Leonardo Lamorgese,et al.  Optimal Train Dispatching by Benders'-Like Reformulation , 2016, Transp. Sci..

[4]  Paolo Toth,et al.  Nominal and robust train timetabling problems , 2012, Eur. J. Oper. Res..

[5]  Jin-Kao Hao,et al.  Transit network design and scheduling: A global review , 2008 .

[6]  Zhiyuan Liu,et al.  Bus stop-skipping scheme with random travel time , 2013 .

[7]  Xuesong Zhou,et al.  Optimizing urban rail timetable under time-dependent demand and oversaturated conditions , 2013 .

[8]  Matteo Fischetti,et al.  Fast Approaches to Improve the Robustness of a Railway Timetable , 2009, Transp. Sci..

[9]  Paola Pellegrini,et al.  Optimal train routing and scheduling for managing traffic perturbations in complex junctions , 2014 .

[10]  Xiaoning Zhu,et al.  A practical model for last train rescheduling with train delay in urban railway transit networks , 2015 .

[11]  Matteo Fischetti,et al.  Modeling and Solving the Train Timetabling Problem , 2002, Oper. Res..

[12]  Boaz Golany,et al.  Creating bus timetables with maximal synchronization , 2001 .

[13]  Yasmin A. Rios-Solis,et al.  Synchronization of bus timetabling , 2012 .

[14]  Yousef Shafahi,et al.  A practical model for transfer optimization in a transit network: Model formulations and solutions , 2010 .

[15]  Sebastian Stiller,et al.  Computing delay resistant railway timetables , 2010, Comput. Oper. Res..

[16]  Xuesong Zhou,et al.  Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints , 2015 .

[17]  Ziyou Gao,et al.  Timetable coordination of first trains in urban railway network: A case study of Beijing , 2016 .

[18]  Yasmin A. Rios-Solis,et al.  An integrated approach for timetabling and vehicle scheduling problems to analyze the trade-off between level of service and operating costs of transit networks , 2014 .

[19]  Valentina Cacchiani,et al.  Approaches to a real-world train timetabling problem in a railway node , 2016 .

[20]  Anthony Chen,et al.  A stochastic model for the integrated optimization on metro timetable and speed profile with uncertain train mass , 2016 .

[21]  Christian Liebchen,et al.  The First Optimized Railway Timetable in Practice , 2008, Transp. Sci..

[22]  Paolo Toth,et al.  A Survey of Optimization Models for Train Routing and Scheduling , 1998, Transp. Sci..

[23]  Ziyou Gao,et al.  A case study on the coordination of last trains for the Beijing subway network , 2015 .

[24]  Ziyou Gao,et al.  Energy-efficient metro train rescheduling with uncertain time-variant passenger demands: An approximate dynamic programming approach , 2016 .

[25]  Hong Kam Lo,et al.  An energy-efficient scheduling and speed control approach for metro rail operations , 2014 .

[26]  Gilbert Laporte,et al.  Single-line rail rapid transit timetabling under dynamic passenger demand , 2014 .

[27]  Paola Pellegrini,et al.  Energy saving in railway timetabling: A bi-objective evolutionary approach for computing alternative running times , 2013 .

[28]  Ziyou Gao,et al.  Equity-based timetable synchronization optimization in urban subway network , 2015 .

[29]  Janny Leung,et al.  Optimizing Timetable Synchronization for Rail Mass Transit , 2008, Transp. Sci..

[30]  Lucas P. Veelenturf,et al.  An overview of recovery models and algorithms for real-time railway rescheduling , 2014 .