Influence of Rhythm and Velocity Variance on Pedestrian Flow

  • Daichi Yanagisawa
  • Akiyasu Tomoeda
  • Katsuhiro Nishinari
Conference paper


We have developed a simple model for pedestrians by dividing walking velocity into two parts, which are step size and pace of walking (number of steps per unit time). Theoretical analysis on pace indicates that rhythm that is slower than normal-walking pace in a low-density regime increases flow. We have verified this result by our experiment with real pedestrians.

The experimental result also indicates that the rhythm contribute to synchronize the movement of pedestrians. In order to investigate whether the synchronized movement improves pedestrian flow, we develop a variable transformation method and apply to the total asymmetric simple exclusion process and a simple evacuation model. Our theoretical result implies that pedestrian flow in a circuit increases, while pedestrian outflow decreases by the synchronized movement. We have examined the result of the circuit case by the real experiment again.


Rhythm Synchronization Variance Pedestrian dynamics Asymmetric simple exclusion process Cellular automaton 



We thank Kozo Keikaku Engineering Inc. in Japan for the assistance of the experiment 1 in Sect. 4. This work is financially supported by the Japan Society for the Promotion of Science and the Japan Science and Technology Agency.


  1. 1.
    Helbing, D.: Traffic and related self-driven many-particle systems. Rev. Mod. Phys., 73(4), pp. 1067–1141 (2001)CrossRefGoogle Scholar
  2. 2.
    Schadschneider, A., Chowdhury, D. and Nishinari, K.: Stochastic Transport in Complex Systems. ELSEVIER (2010)Google Scholar
  3. 3.
    Helbing, D. and Molnar, P.: Social force model for pedestrian dynamics. Phys. Rev. E, 51(5), pp. 4282–4286 (1995)CrossRefGoogle Scholar
  4. 4.
    Muramatsu, M,, Irie, T. and Nagatani. T.: Jamming transition in pedestrian counter flow. Physica A, 267, pp. 487–498 (1999)Google Scholar
  5. 5.
    Burstedde, C., Klauck, K., Schadschneider, A. and Zittartz, J.: Simulation of pedestrian dynamics using a two-dimensional cellular automaton. Physica A, 295, pp. 507–525 (2001)CrossRefMATHGoogle Scholar
  6. 6.
    Parisi, D.R., Gilman, M. and Moldovan, H.: A modification of the social force model can reproduce experimental data of pedestrian flows in normal conditions. Physica A, 388, pp. 3600–3608 (2009)CrossRefGoogle Scholar
  7. 7.
    Chraibi, M., Seyfried, A. and Schadschneider. A.: Generalized centrifugal-force model for pedestrian dynamics. Phys. Rev. E, 82(4), 046111 (2010)Google Scholar
  8. 8.
    Seyfried, A. Steffen, B. Klingsch, W. and Boltes, M.: The fundamental diagram of pedestrian movement revisited. J. Stat. Mech., 2005, P10002 (2005)Google Scholar
  9. 9.
    Online-Database at homepage ( and the references there in (2008)
  10. 10.
    Zhang, J., Klingsch, W., Schadschneider, A. and Seyfried, A.: Transitions in pedestrian fundamental diagrams of straight corridors and T-junctions. J. Stat. Mech., 2011, P06004 (2011)Google Scholar
  11. 11.
    Zhang, J., Klingsch, W., Schadschneider, A. and Seyfried, A.: Ordering in bidirectional pedestrian flows and its influence on the fundamental diagram. J. Stat. Mech. 2012, P02002 (2012)Google Scholar
  12. 12.
    Jelic, A. Appert-Rolland, C. Lemercier, S. and Pettre, J.: Properties of pedestrians walking in line: Fundamental diagrams. Phys. Rev. E, 85(3), 036111 (2012)CrossRefGoogle Scholar
  13. 13.
    Yanagisawa, D., Kimura, A., Tomoeda, A., Nishi, R., Suma, Y., Ohtsuka, K. and Nishinari, K.: Introduction of frictional and turning function for pedestrian outflow with an obstacle. Phys. Rev. E, 80(3), 036110 (2009)CrossRefGoogle Scholar
  14. 14.
    Styns, F., Noorden, L., Moelants, D. and Leman, M.: Walking on music, Human Movement Sci. 26, pp. 769–785 (2007)CrossRefGoogle Scholar
  15. 15.
    Yanagisawa, D., Tomoeda, A. and Nishinari, K.: Improvement of pedestrian flow by slow rhythm. Physical Review E, 85(1), 016111 (2012)CrossRefGoogle Scholar
  16. 16.
    Kanai, M.: Calibration of the Particle Density in Cellular-Automaton Models for Traffic Flow. J. Phys. Soc. Jpn., 79(7), 075002 (2010)CrossRefGoogle Scholar
  17. 17.
    Spitzer, F.: Interaction of markov processes. Adv. Math., 5(2), pp. 246–290 (1970)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Yanagisawa, D. and Nishinari, K.: Mean-field theory for pedestrian outflow through an exit. Phys. Rev. E, 76(6), 061117 (2007)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Daichi Yanagisawa
    • 1
  • Akiyasu Tomoeda
    • 2
    • 3
  • Katsuhiro Nishinari
    • 4
    • 5
  1. 1.College of ScienceIbaraki UniversityMitoJapan
  2. 2.Meiji Institute for Advanced Study of Mathematical SciencesMeiji UniversityTama-ku, KawasakiJapan
  3. 3.CREST, Japan Science and Technology AgencyTama-ku, KawasakiJapan
  4. 4.Research Center for Advanced Science and TechnologyThe University of TokyoMeguro-kuJapan
  5. 5.Department of Aeronautics and Astronautics, School of EngineeringThe University of TokyoBunkyo-kuJapan

Personalised recommendations