The Dynamic Distance Potential Field in a Situation with Asymmetric Bottleneck Capacities

  • Tobias Kretz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6350)

Abstract

This contribution discusses the application of a fast and sloppy solution of the Eikonal equation – namely the dynamic distance potential field – for the simulation of the flow of a group of pedestrian agents through two bottlenecks with different capacity (width) but identical walking distance toward the destination. It is found that using the method leads to a better distribution of agents on the two corridors.

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References

  1. 1.
    Schadschneider, A., Klingsch, W., Klüpfel, H., Kretz, T., Rogsch, C., Seyfried, A.: Evacuation Dynamics: Empirical Results, Modeling and Applications. In: [26], p. 3142Google Scholar
  2. 2.
    Steffen, B., Seyfried, A.: Modeling of pedestrian movement around 90 and 180 degree bends. In: Proc. of Workshop on Fire Protection and Life Safety in Buildings and Transportation Systems (2009)Google Scholar
  3. 3.
    Rogsch, C., Klingsch, W.: Risk analysis with evacuation software how should we interpret calculated results. In: Interschutz (2010) (in press)Google Scholar
  4. 4.
    Wardrop, J.: Road Paper. Some Theoretical Aspects of Road Traffic Research. Proceedings of the Institute of Civil Engineers 1, 325–362 (1952)CrossRefGoogle Scholar
  5. 5.
    Dafermos, S., Sparrow, F.: The traffic assignment problem for a general network. J. Res. Natl. Bur. Stand., Sect. B 73, 91–118 (1969)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Gentile, G.: Linear User Cost Equilibrium: a new algorithm for traffic assignment. Submitted to Transportation Research B (2009)Google Scholar
  7. 7.
    Bruns, H.: Das Eikonal. S. Hirzel (1895)Google Scholar
  8. 8.
    Frank, P.: Über die Eikonalgleichung in allgemein anisotropen Medien. Annalen der Physik 389 (1927)Google Scholar
  9. 9.
    Sethian, J.: Level Set Methods and Fast Marching Methods. Cambridge University Press, Cambridge (1999)MATHGoogle Scholar
  10. 10.
    Kimmel, R., Sethian, J.: Computing geodesic paths on manifolds. In: PNAS, pp. 8431–8435 (1998)Google Scholar
  11. 11.
    Treuille, A., Cooper, S., Popović, Z.: Continuum crowds. In: Siggraph, p. 1168 (2006)Google Scholar
  12. 12.
    Hartmann, D.: Adaptive pedestrian dynamics based on geodesics. New Journal of Physics 12, 043032 (2010)CrossRefGoogle Scholar
  13. 13.
    Kretz, T.: Pedestrian Traffic: on the Quickest Path. JSTAT P03012 (2009)Google Scholar
  14. 14.
    Kretz, T.: The use of dynamic distance potential fields for pedestrian flow around corners. In: ICEM, TU Delft (2009)Google Scholar
  15. 15.
    Kretz, T.: Applications of the Dynamic Distance Potential Field Method. In: Dai, S., et al. (eds.) TGF 2009, Shanghai. Springer, Heidelberg (2010)Google Scholar
  16. 16.
    Kretz, T., Schreckenberg, M.: F.A.S.T. – Floor field- and Agent-based Simulation Tool. In: Chung, E., Dumont, A. (eds.) Transport simulation: Beyond traditional approaches, pp. 125–135. EPFL press, Lausanne (2009)CrossRefGoogle Scholar
  17. 17.
    Kretz, T., Schreckenberg, M.: The F.A.S.T.-Model. In: El Yacoubi, S., Chopard, B., Bandini, S. (eds.) ACRI 2006. LNCS, vol. 4173, pp. 712–715. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  18. 18.
    Kretz, T.: Computation Speed of the F.A.S.T. Model. In: Dai, S., et al. (eds.) TGF 2009, Shanghai. Springer, Heidelberg (2010) (in press)Google Scholar
  19. 19.
    Kretz, T., Bönisch, C., Vortisch, P.: Comparison of Various Methods for the Calculation of the Distance Potential Field. In: Klingsch, W., Rogsch, C., Schadschneider, A., Schreckenberg, M. (eds.) PED 2008, Wuppertal, pp. 335–346. Springer, Heidelberg (2009)Google Scholar
  20. 20.
    Kretz, T.: Pedestrian Traffic – Simulation and Experiments. PhD thesis, Universität Duisburg-Essen (2007)Google Scholar
  21. 21.
    Helbing, D., Johansson, A.: Pedestrian, Crowd and Evacuation Dynamics. In: [26], p. 6476Google Scholar
  22. 22.
    PTV: VISSIM 5.30 User Manual, PTV Planung Transport Verkehr AG, Stumpfstraße 1, D-76131 Karlsruhe (2010), http://www.vissim.de/
  23. 23.
    Helbing, D., Johansson, A., Al-Abideen, H.: Dynamics of crowd disasters: An empirical study. Physical review E 75, 46109 (2007)CrossRefGoogle Scholar
  24. 24.
    Steffen, B., Seyfried, A.: Methods for measuring pedestrian density, flow, speed and direction with minimal scatter. Physica A (submitted)Google Scholar
  25. 25.
    Jeong, W., Whitaker, R.: A fast eikonal equation solver for parallel systems. In: SIAM Conference on Computational Science and Engineering (2007)Google Scholar
  26. 26.
    Meyers, R. (ed.): Encyclopedia of Complexity and Systems Science. Springer, Heidelberg (2009)MATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Tobias Kretz
    • 1
  1. 1.PTV AGKarlsruhe

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