An experimental comparison of periodic timetabling models

Abstract In the Periodic Timetabling Problem, vehicle arrivals and departures need to be scheduled over a periodically repeating time horizon. Its relevance and applicability have been demonstrated by several real-world implementations, including the Netherlands railways and the Berlin subway. In this work, we consider the practical impact of two possible problem variations: firstly, how passenger paths are handled, and secondly, how line frequencies are included. In computational experiments on real-world and close-to real-world networks, we can show that passenger travel times can significantly benefit from extended models.

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

[2]  Leon W P Peeters,et al.  Cyclic Railway Timetable Optimization , 2003 .

[3]  Anita Schöbel,et al.  A Bicriteria Approach for Robust Timetabling , 2009, Robust and Online Large-Scale Optimization.

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

[5]  Marie Schmidt.  Integrating Routing Decisions in Network Problems , 2011, OR.

[6]  K. Nachtigall.  Periodic network optimizationi and fixed interval timetables , 1999 .

[7]  Sebastian Stiller,et al.  Strong Formulations for the Multi-module PESP and a Quadratic Algorithm for Graphical Diophantine Equation Systems , 2010, ESA.

[8]  Mathias Kinder,et al.  Models for Periodic Timetabling , 2008 .

[9]  Marie Schmidt,et al.  The Complexity of Integrating Routing Decisions in Public Transportation Models , 2010, ATMOS.

[10]  Christophe Lecoutre,et al.  Abscon 112 Toward more Robustness , 2008 .

[11]  Rolf H. Möhring,et al.  The Modeling Power of the Periodic Event Scheduling Problem: Railway Timetables - and Beyond , 2004, ATMOS.

[12]  Christian Liebchen,et al.  Integral cycle bases for cyclic timetabling , 2009, Discret. Optim..

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

[14]  Christian Liebchen,et al.  Finding Short Integral Cycle Bases for Cyclic Timetabling , 2003, ESA.

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

[16]  Anita Schöbel,et al.  Line planning in public transportation: models and methods , 2012, OR Spectr..

[17]  Paolo Toth,et al.  Non-cyclic train timetabling and comparability graphs , 2010, Oper. Res. Lett..

[18]  Anita Schöbel,et al.  Improving the modulo simplex algorithm for large-scale periodic timetabling , 2013, Comput. Oper. Res..

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

[20]  Anita Schöbel,et al.  Integrating line planning, timetabling, and vehicle scheduling: a customer-oriented heuristic , 2009, Public Transp..

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

[22]  Karl Nachtigall,et al.  Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations , 2008, ATMOS.

[23]  Ralf Borndörfer,et al.  Models for Railway Track Allocation , 2007, ATMOS.

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