Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

Evaluating line concepts using travel times and robustness

Simulations with the LinTim toolbox

  • Original Paper
  • Published:
Public Transport Aims and scope Submit manuscript

Abstract

Line planning is an early step in the planning process in public transportation, usually followed by designing the timetable. The problems related to both steps are known to be NP-hard, and an integrated model finding a line plan and a timetable simultaneously seems out of scope from a computational point of view. However, the line plan influences also the quality of the timetable to be computed in the next planning step.

In this paper we analyze the impact of different line planning models by comparing not only typical characteristics of the line plans, but also their impact on timetables and their robustness against delays. To this end, we set up a simulation platform LinTim which enables us to compute a timetable for each line concept and to experimentally evaluate its performance under delays. Using the German railway intercity network, we evaluate the quality of different line plans from a line planning, a timetabling, and a delay management perspective.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

Notes

  1. See http://lintim.math.uni-goettingen.de/.

References

  • Borndörfer R, Grötschel M, Pfetsch ME (2007) A column generation approach to line planning in public transport. Transp Sci 41:123–132

    Article  Google Scholar 

  • Borndörfer R, Grötschel M, Pfetsch ME (2008) Models for line planning in public transport. In: Computer-aided scheduling of public transport (CASPT). Lecture notes in economics and mathematical systems, vol 600, pp 363–378

    Chapter  Google Scholar 

  • Barber F, Ingolotti L, Lova A, Marin A, Mesa J, Ortega F, Perea F, Tormos P (2008) Integrating timetabling, network and line design. Technical report, ARRIVAL project

  • Bussieck MR, Kreuzer P, Zimmermann UT (1996) Optimal lines for railway systems. Eur J Oper Res 96(1):54–63

    Article  Google Scholar 

  • Bussieck MR, Lindner T, Lübbecke ME (2004) A fast algorithm for near cost optimal line plans. Math Methods Oper Res 59(2):205–220

    Article  Google Scholar 

  • Bouma A, Oltrogge C (1994) Linienplanung und Simulation für öffentliche Verkehrswege in Praxis und Theorie. ETR Eisenbahntech Rundsch 43:369–378

    Google Scholar 

  • Bussieck MR (1998) Optimal lines in public transport. PhD thesis, Technische Universität Braunschweig

  • Carey M (1994) A model and strategy for train pathing with choice of lines, platforms and routes. Transp Res B 28(5):333–353

    Article  Google Scholar 

  • Cacchiani V, Toth P (2012) Nominal and robust train timetabling problems. Eur J Oper Res 219(3):727–737

    Article  Google Scholar 

  • Cacchiani V, Caprara A, Galli L, Kroon L, Maroti G, Toth P (2012) Railway rolling stock planning: Robustness against large disruptions. Transp Sci 46(2):217–232

    Article  Google Scholar 

  • Claessens MT, van Dijk NM, Zwaneveld PJ (1998) Cost optimal allocation of rail passenger lines. Eur J Oper Res 110:474–489

    Article  Google Scholar 

  • Ceder A, Wilson NHM (1986) Bus network design. Transp Res B 20(4):331–344

    Article  Google Scholar 

  • D’Angelo G, Di Stefano G, Navarra A (2009a) Recoverable-robust timetables for trains on single-line corridors. In: Proceedings of the 3rd international seminar on railway operations modelling and analysis—engineering and optimisation approaches (RailZurich2009)

    Google Scholar 

  • D’Angelo G, Di Stefano G, Navarra A, Pinotti CM (2009b) Recoverable robust timetables on trees. In: Combinatorial optimization and applications. Lecture note in computer science, vol 5573. Springer, Berlin, pp 451–462

    Chapter  Google Scholar 

  • Desaulniers G, Hickman M (2007) Public transit. In: Transportation. Handbooks in operations research and management science, vol 14. Elsevier, Amsterdam, pp 69–127

    Chapter  Google Scholar 

  • Dienst H (1978) Linienplanung im spurgeführten Personenverkehr mit Hilfe eines heuristischen Verfahrens. PhD thesis, Technische Universität Braunschweig (in German)

  • Fischetti M, Monaci M (2009) Light robustness. In: Robust and online large-scale optimization. Lecture note on computer science, vol 5868. Springer, Berlin, pp 61–84

    Chapter  Google Scholar 

  • Fischetti M, Salvagnin D, Zanette A (2009) Fast approaches to improve the robustness of a railway timetable. Transp Sci 43:321–335

    Article  Google Scholar 

  • Goossens J (2004) Models and algorithms for railway line planning problems. PhD thesis, University of Maastricht

  • Goerigk M, Schöbel A (2010) An empirical analysis of robustness concepts for timetabling. In: Proceedings of ATMOS10. OpenAccess series in informatics (OASIcs), vol 14. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik, Dagstuhl, pp 100–113

    Google Scholar 

  • Goerigk M, Schöbel A (2013) Improving the modulo simplex algorithm for large-scale periodic timetabling. Comput Oper Res 40(5):1363–1370

    Article  Google Scholar 

  • Israeli Y, Ceder A (1995) Transit route design using scheduling and multiobjective programming techniques. In: Computer-aided scheduling of public transport (CASPT). Lecture notes in economics and mathematical systems, vol 430. Springer, Berlin, pp 56–75

    Chapter  Google Scholar 

  • Kroon LG, Dekker R, Vromans M (2007) Cyclic railway timetabling: A stochastic optimization approach. In: Algorithmic methods for railway optimization. Lecture notes in computer science, vol 4359. Springer, Berlin, pp 41–66

    Chapter  Google Scholar 

  • Liebchen C (2008) Linien-, Fahrplan-, Umlauf- und Dienstplanoptimierung: Wie weit können diese bereits integriert werden? In: Heureka’08—Optimierung in Transport und Verkehr, Tagungsbericht. FGSV Verlag, Köln

    Google Scholar 

  • Lindner T (2000) Train schedule optimization in public rail transport. PhD thesis, Technische Universität Braunschweig

  • Liebchen C, Möhring R (2007) The modeling power of the periodic event scheduling problem: railway timetables—and beyond. In: Algorithmic methods for railway optimization. Lecture notes on computer science, vol 4359. Springer, Berlin, pp 3–40

    Chapter  Google Scholar 

  • Liebchen C, Proksch M, Wagner FH (2005) Performance of algorithms for periodic timetable optimization. In: Computer-aided scheduling of public transport (CASPT). Lecture notes in economics and mathematical systems. Springer, Berlin

    Google Scholar 

  • Liebchen C, Schachtebeck M, Schöbel A, Stiller S, Prigge A (2010) Computing delay-resistant railway timetables. Comput Oper Res 37:857–868

    Article  Google Scholar 

  • Michaelis M, Schöbel A (2009) Integrating line planning, timetabling, and vehicle scheduling: A customer-oriented approach. Public Transp 1(3):211–232

    Article  Google Scholar 

  • Nachtigall K (1998) Periodic Network Optimization and Fixed Interval Timetables. Deutsches Zentrum für Luft– und Raumfahrt. Institut für Flugführung, Braunschweig. Habilitationsschrift

  • Nachtigall K, Jerosch K (2008) Simultaneous network line planning and traffic assignment. In: ATMOS 2008—8th workshop on algorithmic approaches for transportation modeling, optimization, and systems, Dagstuhl, Germany. http://drops.dagstuhl.de/opus/volltexte/2008/1589

    Google Scholar 

  • Nachtigall K, Opitz J (2008) Solving periodic timetable optimisation problems by modulo simplex calculations. In: Proc ATMOS

    Google Scholar 

  • Nguyen S, Pallottino S (1988) Equilibrium traffic assignment for large scale transit networks. Eur J Oper Res 37(2):176–186

    Article  Google Scholar 

  • Schwarze S (2008) Path player games: analysis and applications. Springer, Berlin

    Google Scholar 

  • Schachtebeck M (2010) Delay management in public transportation: capacities, robustness, and integration. PhD thesis, Universität Göttingen

  • Schöbel A (2012) Line planning in public transportation: models and methods. OR Spektrum 34:491–510

    Article  Google Scholar 

  • Schöbel A, Scholl S (2006) Line planning with minimal travel time. In: 5th workshop on algorithmic methods and models for optimization of railways. Dagstuhl seminar proceedings, vol 06901

    Google Scholar 

  • Schöbel A, Schwarze S (2006) A game-theoretic approach to line planning. In: 6th workshop on algorithmic methods and models for optimization of railways. Dagstuhl seminar proceedings, vol 06002

    Google Scholar 

  • Schachtebeck M, Schöbel A (2010) To wait or not to wait and who goes first? Delay management with priority decisions. Transp Sci 44(3):307–321

    Article  Google Scholar 

  • Serafini P, Ukovich W (1989) A mathematical model for periodic scheduling problems. SIAM J Discrete Math 2:550–581

    Article  Google Scholar 

  • Zwaneveld PJ, Claessens MT, van Dijk NM (1996) A new method to determine the cost optimal allocation of passenger lines. In: Defence or attack: proceedings of 2nd TRAIL Phd congress 1996, Part 2. TRAIL Research School, Delft/Rotterdam

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Kaiserslautern, Paul-Ehrlich-Str. 14, 67653, Kaiserslautern, Germany

    Marc Goerigk

  2. Institut für Numerische und Angewandte Mathematik, Georg-August Universität Göttingen, Lotzestr. 16-18, 37083, Göttingen, Germany

    Michael Schachtebeck & Anita Schöbel

Authors
  1. Marc Goerigk
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Schachtebeck
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Anita Schöbel
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Anita Schöbel.

Additional information

Partially supported by grant SCHO 1140/3-2 within the DFG programme Algorithm Engineering.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Goerigk, M., Schachtebeck, M. & Schöbel, A. Evaluating line concepts using travel times and robustness. Public Transp 5, 267–284 (2013). https://doi.org/10.1007/s12469-013-0072-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12469-013-0072-x

Keywords

Search

Navigation