A cycle time optimization model for generating stable periodic railway timetables

As train passengers expect a high degree of reliability from a railway network with minimal delays, during the timetabling process planners need to balance the goals of maximizing the offered capacity and delay resistance. This is often done in a two-step process where first a feasible timetable is found for a given line structure, and consecutively the stability of this timetable is evaluated and local modifications are performed to the timetable. This paper describes an optimization method to find a feasible periodic timetable that also ensures maximum stability for heterogeneous railway networks. The model is capable to handle flexible train orders, running and dwell times, and overtaking locations. We use the minimum cycle time of the periodic timetable as an indicator for stability, and define an optimization problem with this minimum cycle time as the objective function to be minimized. We also present dimension reduction methods and an iterative optimization approach to improve the mathematical optimization process. We show the applicability of the approach with case studies on the central part of the Dutch railway network.

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

[2]  Matteo Fischetti,et al.  A Lagrangian Heuristic for Robustness, with an Application to Train Timetabling , 2012, Transp. Sci..

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

[4]  Geert Jan Olsder,et al.  Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications , 2005 .

[5]  Steffen Hölldobler,et al.  Solving Periodic Event Scheduling Problems with SAT , 2012, IEA/AIE.

[6]  I. Schuele,et al.  Synchronization of Regional Public Transport Systems , 2009 .

[7]  Erhan Kozan,et al.  Techniques to effectively buffer schedules in the face of uncertainties , 2015, Comput. Ind. Eng..

[8]  Ingo A. Hansen,et al.  Performance indicators for railway timetables , 2013, 2013 IEEE International Conference on Intelligent Rail Transportation Proceedings.

[9]  Tobias Lindner.  Applicability of the analytical UIC Code 406 compression method for evaluating line and station capacity , 2011, J. Rail Transp. Plan. Manag..

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

[11]  Daniel Sparing,et al.  An optimization model for periodic timetable generation with dynamic frequencies , 2013, 16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013).

[12]  Matthias Ehrgott,et al.  Routing Trains Through Railway Junctions: A New Set-Packing Approach , 2011, Transp. Sci..

[13]  Rolf H. Möhring,et al.  The Concept of Recoverable Robustness, Linear Programming Recovery, and Railway Applications , 2009, Robust and Online Large-Scale Optimization.

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

[15]  Paolo Toth,et al.  Solution of the Train Platforming Problem , 2011, Transp. Sci..

[16]  Alexander Schrijver.  Routing and timetabling by topological search , 1998 .

[17]  Rob M.P. Goverde,et al.  A delay propagation algorithm for large-scale railway traffic networks , 2010 .

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

[19]  D. Malcolm,et al.  Application of a Technique for Research and Development Program Evaluation , 1959 .

[20]  Lorenzo Mussone,et al.  An analytical approach to calculate the capacity of a railway system , 2013, Eur. J. Oper. Res..

[21]  Hayriye Ayhan,et al.  A probabilistic (max, +) approach for determining railway infrastructure capacity , 2003, Eur. J. Oper. Res..

[22]  Matthew E. H. Petering,et al.  Mixed-Integer Programming for Railway Capacity Analysis and Cyclic, Combined Train Timetabling and Platforming , 2016, Transp. Sci..

[23]  Rommert Dekker,et al.  Stochastic Improvement of Cyclic Railway Timetables , 2006 .

[24]  Rob M.P. Goverde,et al.  Railway Timetable Stability Analysis Using Max-plus System Theory , 2007 .

[25]  Uwe T. Zimmermann,et al.  Cost optimal periodic train scheduling , 2005, Math. Methods Oper. Res..

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

[27]  Paolo Toth,et al.  A three-level framework for performance-based railway timetabling , 2015 .

[28]  Rob M.P. Goverde,et al.  An integrated micro–macro approach to robust railway timetabling , 2016 .

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

[30]  Dennis Huisman,et al.  Delay Management with Rerouting of Passengers , 2012, Transp. Sci..

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

[32]  Dennis Huisman,et al.  The New Dutch Timetable: The OR Revolution , 2008, Interfaces.

[33]  L. C. Thomas,et al.  Model Building in Mathematical Programming (2nd Edition) , 1986 .

[34]  Matteo Fischetti,et al.  Light Robustness , 2009, Robust and Online Large-Scale Optimization.

[35]  Matthew E. H. Petering,et al.  Mixed integer programming for minimizing the period of a cyclic railway timetable for a single track with two train types , 2013, Comput. Ind. Eng..

[36]  R.M.P. Goverde,et al.  IMPROVING PUNCTUALITY AND TRANSFER RELIABILITY BY RAILWAY TIMETABLE OPTIMIZATION , 1999 .

[37]  Paolo Toth,et al.  Scheduling extra freight trains on railway networks , 2010 .

[38]  Leo Liberti,et al.  Automatic Generation of Symmetry-Breaking Constraints , 2008, COCOA.

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

[40]  Jurjen S. Hooghiemstra,et al.  The use of simulation in the planning of the Dutch railway services , 1998, 1998 Winter Simulation Conference. Proceedings (Cat. No.98CH36274).

[41]  D. R. Bergmann.  INTEGER PROGRAMMING FORMULATION FOR DERIVING MINIMUM DISPATCH INTERVALS ON A GUIDEWAY ACCOMMODATING THROUGH AND LOCAL PUBLIC TRANSPORTATION SERVICES , 1974 .

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

[43]  Leo G. Kroon,et al.  A Variable Trip Time Model for Cyclic Railway Timetabling , 2003, Transp. Sci..

[44]  Fabián A. Chudak,et al.  Design of a Railway Scheduling Model for Dense Services , 2009 .