Skip to main content
SpringerLink
Log in

A Cellular Automaton Approach for Lane Formation in Pedestrian Counterflow

  • Conference paper
  • First Online:
Traffic and Granular Flow '11

Abstract

The formation of lanes is a well known emergent behavior in pedestrian counterflow as well as in some other physical systems. Nevertheless, not much is known quantitatively which is related to the fact that the empirical situation is quite poor. Here we analyze lane formation in a two-dimensional cellular automaton for pedestrian dynamics. To quantify the lane structure, we make use of a laning order parameter which has been used previously to detect lanes in colloidal systems. The main purpose of our work is to determine a phase diagram in dependence on the coupling constants and the particle density. Furthermore, we compare the results of our simulation with experimental data.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. A. Schadschneider, W. Klingsch, H. Klüpfel, T. Kretz, C. Rogsch, and A. Seyfried. In R. A. Meyers, editor, Encyclopedia of Complexity and Systems Science, pages 3142–3176. Springer, 2009.

    Google Scholar 

  2. B. Schmittmann and R. K. P. Zia. Phys. Rep., 301:45–64, 1998.

    Article  Google Scholar 

  3. K. R. Sütterlin, A. Wysocki, A. V. Ivlev, C. Räth, H. M. Thomas, M. Rubin-Zuzic, W. J. Goedheer, V. E. Fortov, A. M. Lipaev, V. I. Molotkov, O. F. Petrov, G. E. Morfill, and H. Löwen. Phys. Rev. Lett., 102:085003, 2009.

    Article  Google Scholar 

  4. R. R. Netz. Europhys. Lett., 63:616, 2003.

    Article  Google Scholar 

  5. J. Dzubiella, G. P. Hoffmann, and H. Löwen. Phys. Rev. E, 65:021402, 2002.

    Article  Google Scholar 

  6. M. E. Leunissen, C. G. Christova, A.-P. Hynninen, P. Royall, A. I. Campbell, A. Imhof, M. Dijkstra, R. van Roij, and A. van Blaaderen. Nature, 437:235–240, 2005.

    Article  Google Scholar 

  7. M. Rex and H. Löwen. Phys. Rev. E, 75(051402), 2007.

    Google Scholar 

  8. A. Schadschneider, A. Kirchner, and K. Nishinari. Lecture Notes in Computer Science, 2493:239–248. Springer, 2002.

    Google Scholar 

  9. D. Helbing, P. Molnar, I. J. Farkas, and K. Bolay. Environment and Planning B, 28:361–383, 2001.

    Article  Google Scholar 

  10. V. J. Blue and J. L. Adler. Transportation Research Record, 1678:135–141, 1999.

    Article  Google Scholar 

  11. F. Weifeng, Y. Lizhong, and F. Weicheng. Physica A, 321:633–640, 2003.

    Article  MATH  Google Scholar 

  12. W. G. Weng, T. Chen, H. Y. Yuan, and W. C. Fan. Phys. Rev. E, 74:036102, 2006.

    Article  Google Scholar 

  13. Y. F. Yu and W. G. Song. Phys. Rev. E, 75:046112, 2007.

    Article  Google Scholar 

  14. C. Burstedde, K. Klauck, A. Schadschneider, and J. Zittartz. Physica A, 295:507–525, 2001.

    Article  MATH  Google Scholar 

  15. M. Muramatsu, T. Irie, and T. Nagatani. Physica A, 267:487–498, 1999.

    Article  Google Scholar 

  16. Y. Tajima, K. Takimoto, and T. Nagatani. Physica A, 313:709–723, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  17. K. Takimoto, Y. Tajima, and T. Nagatani. Physica A, 308:460–470, 2002.

    Article  MathSciNet  MATH  Google Scholar 

  18. H. Kuang, T. Song, X.-L. Li, and S.-Q. Dai. Chin. Phys. Lett., 25:1498, 2008.

    Article  Google Scholar 

  19. T. Nagatani. Physics Letters A, 373:2917–2921, 2009.

    Article  MATH  Google Scholar 

  20. T. Kretz, M. Kaufman, and M. Schreckenberg. Lecture Notes in Computer Science, 5191:555–558. Springer, 2008.

    Google Scholar 

  21. W.G. Weng, S.F. Shen, H.Y. Yuan, and W.C. Fan. Physica A, 375:668–678, 2007.

    Article  Google Scholar 

  22. M. Isobe, T. Adachi, and T. Nagatani. Physica A, 336:638–650, 2004.

    Article  Google Scholar 

  23. W. J. Yu, R. Chen, L. Y. Dong, and S. Q. Dai. Phys. Rev. E, 72:026112, 2005.

    Article  Google Scholar 

  24. Y.Q. Jiang, T. Xiong, S.C. Wong, C.W. Shu, M. Zhang, P. Zhang, and W.H.K. Lam. Acta Mathematica Scientia, 29:1541–1555, 2009.

    Article  MathSciNet  MATH  Google Scholar 

  25. A. Schadschneider and A. Seyfried. In H. J. P. Timmermans, (eds.), Pedestrian Behavior: Models, Data Collection and Applications, pages 27–44. Emerald Group Publishing, 2009.

    Google Scholar 

  26. Hermes project. http://www.fz-juelich.de/jsc/hermes.

  27. A. Schadschneider, C. Eilhardt, S. Nowak, A. Seyfried. This proceedings.

    Google Scholar 

  28. A. Seyfried, B. Steffen, W. Klingsch, and M. Boltes. J. Stat. Mech., 2005:P10002, 2005.

    Google Scholar 

  29. A. Seyfried, M. Boltes, J. Kähler, W. Klingsch, A. Portz, T. Rupprecht, A. Schadschneider, B. Steffen, and A. Winkens. Pedestrian and Evacuation Dynamics 2008, pages 145–156. Springer, 2010.

    Google Scholar 

  30. J. Zhang, W. Klingsch, A. Schadschneider, and A. Seyfried. J. Stat. Mech., 2011:P06004, 2011.

    Google Scholar 

  31. J. Zhang, W. Klingsch, A. Schadschneider, and A. Seyfried. Preprint. J. Stat. Mech., 2012:P02002, 2012.

    Google Scholar 

  32. B. Steffen and A. Seyfried. Physica A, 389:1902–1910, 2010.

    Article  Google Scholar 

  33. M. Boltes, A. Seyfried, B. Steffen, and A. Schadschneider. In W. F. Klingsch, C. Rogsch, A. Schadschneider, and M. Schreckenberg, (eds.), Pedestrian and Evacuation Dynamics 2008, pages 43–54. Springer Berlin Heidelberg, 2010.

    Google Scholar 

  34. A. Kirchner and A. Schadschneider. Physica A, 312:260–276, 2002.

    Article  MATH  Google Scholar 

  35. A. Kirchner, K. Nishinari, and A. Schadschneider. Phys. Rev. E, 67:056122, 2003.

    Article  Google Scholar 

  36. K. Yamori. Psychological Review, 105(3):530–557, 1998.

    Article  Google Scholar 

  37. S. P. Hoogendoorn and W. Daamen. In Traffic and Granular Flow 2003, pages 373–382. Springer, 2005.

    Google Scholar 

  38. Y. Suma, D. Yanagisawa and K. Nishinari. Physica A, 391:248–263, 2012.

    Article  Google Scholar 

  39. T. Kretz, and M. Schreckenberg. Lecture Notes in Computer Science, 4173:712–715. Springer, 2006.

    Google Scholar 

  40. A. Schadschneider, C. Eilhardt, S. Nowak, and R. Will. In R. D. Peacock et al. (eds), Pedestrian and Evacuation Dynamics, pages 557–566. Springer, 2011.

    Google Scholar 

Download references

Acknowledgements

This work was supported by the project Hermes funded by the Federal Ministry of Education and Research (BMBF) Program on “Research for Civil Security – Protecting and Saving Human Life” and the Bonn-Cologne Graduate School of Physics and Astronomy. We thank Jun Zhang and Armin Seyfried for providing the empirical data.

Author information

Authors and Affiliations

  1. Institut für Theoretische Physik, Universität zu Köln, 50937, Köln, Germany

    Stefan Nowak & Andreas Schadschneider

Authors
  1. Stefan Nowak
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andreas Schadschneider
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stefan Nowak .

Editor information

Editors and Affiliations

  1. Institute of Computer Science, Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia

    Valery V. Kozlov

  2. Moscow State Automobile & Road Technical University, Moscow, Russia

    Alexander P. Buslaev

  3. Russian Academy of Sciences, Electronics Institute and Kotel’nikov Radioengineeering, Moscow, Russia

    Alexander S. Bugaev

  4. Mathematical Cybernetics Department, Moscow Technical University of Communications & Informatics, Moscow, Russia

    Marina V. Yashina

  5. Universität Köln, Institut Theoretische Physik, Köln, Germany

    Andreas Schadschneider

  6. und Verkehr, Universität Duisburg-Essen Physik von Transport, Duisburg, Germany

    Michael Schreckenberg

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Nowak, S., Schadschneider, A. (2013). A Cellular Automaton Approach for Lane Formation in Pedestrian Counterflow. In: Kozlov, V., Buslaev, A., Bugaev, A., Yashina, M., Schadschneider, A., Schreckenberg, M. (eds) Traffic and Granular Flow '11. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39669-4_15

Download citation

Publish with us

Policies and ethics

Search

Navigation