A Conjunction of the Discrete-Continuous Pedestrian Dynamics Model SigmaEva with Fundamental Diagrams

  • Ekaterina KirikEmail author
  • Tatýana Vitova
  • Andrey Malyshev
  • Egor Popel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 12044)


This article is focused on dynamics of the computer simulation module SigmaEva in connection with an unidirectional flow under periodic boundary conditions. The module SigmaEva realizes the discrete-continuous stochastic pedestrian dynamics model that is shortly presented here. A fundamental diagram (speed-density dependance) is an input for the model. Simulated specific flow rates are considered versus input ones for different diagrams. A sensitivity of the model to input diagrams is shown and discussed.


Fundamental diagrams Flow rate Pedestrian dynamics model Transition probabilities Evacuation simulation 


  1. 1.
    Schadschneider, A., Klingsch, W., Kluepfel, H., Kretz, T., Rogsch, C., Seyfried, A.: Evacuation dynamics: empirical results, modeling and applications. In: Meyers, R. (ed.) Encyclopedia of Complexity and System Science, vol. 3, pp. 3142–3192. Springer, New York (2009). Scholar
  2. 2.
    Helbing, D., Farkas, I., Vicsek, T.: Simulating dynamical features of escape panic. Nature 407, 487–490 (2000)CrossRefGoogle Scholar
  3. 3.
    Chraibi, M., Seyfried, A., Schadschneider, A.: Generalized centrifugal-force model for pedestrian dynamics. Phys. Rev. E 82, 046111 (2010)CrossRefGoogle Scholar
  4. 4.
    Zeng, W., Nakamura, H., Chen, P.: A modified social force model for pedestrian behavior simulation at signalized crosswalks. Soc. Behav. Sci. 138(14), 521–530 (2014)CrossRefGoogle Scholar
  5. 5.
    Blue, V.J., Adler, J.L.: Cellular automata microsimulation for modeling bi-directional pedestrian walkways. Transp. Res. Part B 35, 293–312 (2001)CrossRefGoogle Scholar
  6. 6.
    Kirchner, A., Klupfel, H., Nishinari, K., Schadschneider, A., Schreckenberg, M.: Discretization effects and the influence of walking speed in cellular automata models for pedestrian dynamics. J. Stat. Mech. Theor. Exp. 10, 10011 (2004)CrossRefGoogle Scholar
  7. 7.
    Nishinari, K., Kirchner, A., Namazi, A., Schadschneider, A.: Extended floor field CA model for evacuation dynamics. IEICE Trans. Inf. Syst. E87–D, 726–732 (2004)Google Scholar
  8. 8.
    Kirik, E., Yurgel’yan, T., Krouglov, D.: On realizing the shortest time strategy in a CA FF pedestrian dynamics model. Cybern. Syst. 42(1), 1–15 (2011)CrossRefGoogle Scholar
  9. 9.
    Seitz, M.J., Koster, G.: Natural discretization of pedestrian movement in continuous space. Phys. Rev. E 86(4), 046108 (2012)CrossRefGoogle Scholar
  10. 10.
    Zeng, Y., Song, W., Huo, F., Vizzari, G.: Modeling evacuation dynamics on stairs by an extended optimal steps model. Simul. Model. Pract. Theor. 84, 177–189 (2018)CrossRefGoogle Scholar
  11. 11.
    Baglietto, G., Parisi, D.R.: Continuous-space automaton model for pedestrian dynamics. Phys. Rev. E 83(5), 056117 (2011)CrossRefGoogle Scholar
  12. 12.
    Schadschneider, A., Seyfried, A.: Validation of CA models of pedestrian dynamics with fundamental diagrams. Cybern. Syst. 40(5), 367–389 (2009)CrossRefGoogle Scholar
  13. 13.
    Kholshevnikov, V.: Forecast of human behavior during fire evacuation. In: Proceedings of the International Conference “Emergency Evacuation of People From Buildings - EMEVAC”, pp. 139–153. Belstudio, Warsaw (2011)Google Scholar
  14. 14.
    Kirik, E., Malyshev, A., Popel, E.: Fundamental diagram as a model input: direct movement equation of pedestrian dynamics. In: Weidmann, U., Kirsch, U., Schreckenberg, M. (eds.) Pedestrian and Evacuation Dynamics 2012, pp. 691–702. Springer, Cham (2014). Scholar
  15. 15.
    Predtechenskii, V.M., Milinskii, A.I.: Planing for Foot Traffic Flow in Buildings. American Publishing, New Dehli (1978). Translation of Proektirovanie Zhdanii s Uchetom organizatsii Dvizheniya Lyudskikh potokov. Stroiizdat Publishers, Moscow (1969)Google Scholar
  16. 16.
    Chattaraj, U., Seyfried, A., Chakroborty, P.: Comparison of pedestrian fundamental diagram across cultures. Adv. Complex Syst. 12, 393–405 (2009)CrossRefGoogle Scholar
  17. 17.
    Weidmann, U.: Transporttechnik der Fussgänger. Transporttechnische Eigenschaften des Fussgängerverkehrs (Literaturauswertung). IVT, Institut für Verkehrsplanung, Transporttechnik, Strassen-und Eisenbahnbau, Zürich (1992)Google Scholar
  18. 18.
    Nelson, H.E., Mowrer, F.W.: Emergency movement. In: DiNenno, P.J. (ed.) The SFPE Handbook of Fire Protection Engineering, pp. 3-367–3-380. National Fire Protection Association, Quincy (2002)Google Scholar
  19. 19.
    Kirik, E., Vitova, T., Malyshev, A., Popel, E.: On the validation of pedestrian movement models under transition and steady-state conditions. In: Proceedings of the Ninth International Seminar on Fire and Explosion Hazards (ISFEH9), St. Peterburg, pp. 1270–1280 (2019)Google Scholar
  20. 20.
    Peacock, R.D., Reneke, P.A., Davis, W.D., Jones, W.W.: Quantifying fire model evaluation using functional analysis. Fire Saf. J. 33(3), 167–184 (1991)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Institute of Computational Modelling, Russian Academy of Sciences, Siberian BranchKrasnoyarskRussia

Personalised recommendations