Microscopic Cycling Behavior Model Using Differential Game Theory

  • Alexandra GavriilidouEmail author
  • Yufei Yuan
  • Haneen Farah
  • Serge P. Hoogendoorn
Conference paper


In order to develop design guidelines and assess the implications on traffic flow operations and safety, microscopic behavioral models are used. The increasing interest in cycling in cities necessitates the development of a model that captures the movement of cyclists. Given the fact that cyclists exert effort for their motion, the theory of effort minimization can be adopted from the micro-economic theory of subjective utility maximization. Also, due to their size and flexibility, close interactions between cyclists are possible, which can be resolved by solving a differential game. This solution determines the optimal control strategy of a cyclist and is, hence, a microscopic cycling model. In this paper we explain the derivation of such a model. Moreover, we demonstrate its plausibility by interpreting the derived equations and face validating the model. The results indicate the need to consider traffic rules and to collect bicycle trajectory data.



This research was supported by the ALLEGRO project (no. 669792), which is financed by the European Research Council and Amsterdam Institute for Advanced Metropolitan Solutions.


  1. 1.
    Antonini, G., Bierlaire, M., Weber, M.: Discrete choice models of pedestrian walking behavior. Transp. Res. B Methodol. 40(8), 667–687 (2006)CrossRefGoogle Scholar
  2. 2.
    Anvari, B., Bell, M.G., Sivakumar, A., Ochieng, W.Y.: Modelling shared space users via rule-based social force model. Transp. Res. C Emerg. Technol. 51, 83–103 (2015)CrossRefGoogle Scholar
  3. 3.
    Falkenberg, G., Blase, A., Bonfranchi, T., Cossé, L., Draeger, W., Vortisch, P., Kautzsch, L., Stapf, H., Zimmermann, A.: Bemessung von radverkehrsanlagen unter verkehrstechnischen gesichtspunkten. Berichte der Bundesanstalt fuer Strassenwesen. Unterreihe Verkehrstechnik (103) (2003)Google Scholar
  4. 4.
    Fellendorf, M., Vortisch, P.: Microscopic traffic flow simulator VISSIM. In: Fundamentals of Traffic Simulation, pp. 63–93. Springer, New York (2010)CrossRefGoogle Scholar
  5. 5.
    Helbing, D., Molnar, P.: Social force model for pedestrian dynamics. Phys. Rev. E 51(5), 4282 (1995)CrossRefGoogle Scholar
  6. 6.
    Helbing, D., Farkas, I., Vicsek, T.: Simulating dynamical features of escape panic. Nature 407(6803), 487–490 (2000)CrossRefGoogle Scholar
  7. 7.
    Helbing, D., Farkas, I.J., Molnar, P., Vicsek, T.: Simulation of pedestrian crowds in normal and evacuation situations. In: Pedestrian and Evacuation Dynamics, vol. 21(2), pp. 21–58. Springer, New York (2002)Google Scholar
  8. 8.
    Hoogendoorn, S., Daamen, W.: Bicycle headway modeling and its applications. Transp. Res. Rec. 2587, 34–40 (2016)CrossRefGoogle Scholar
  9. 9.
    Hoogendoorn, S., HL Bovy, P.: Simulation of pedestrian flows by optimal control and differential games. Optimal Control Appl. Methods 24(3), 153–172 (2003)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Isaacs, R.: Differential Games: A Mathematical Theory with Applications to Warfare and Pursuit, Control and Optimization. Courier Corporation, New York (1999)zbMATHGoogle Scholar
  11. 11.
    Kong, J., Pfeiffer, M., Schildbach, G., Borrelli, F.: Kinematic and dynamic vehicle models for autonomous driving control design. In: Intelligent Vehicles Symposium (IV), 2015 IEEE, pp. 1094–1099. IEEE, Piscataway (2015)Google Scholar
  12. 12.
    Luo, Y., Jia, B., Liu, J., Lam, W.H., Li, X., Gao, Z.: Modeling the interactions between car and bicycle in heterogeneous traffic. J. Adv. Transp. 49(1), 29–47 (2015)CrossRefGoogle Scholar
  13. 13.
    Nagel, K., Schreckenberg, M.: A cellular automaton model for freeway traffic. J. Phys. I 2(12), 2221–2229 (1992)Google Scholar
  14. 14.
    Pontryagin, L.S.: Mathematical Theory of Optimal Processes. CRC Press, New York (1987)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexandra Gavriilidou
    • 1
    Email author
  • Yufei Yuan
    • 1
  • Haneen Farah
    • 1
  • Serge P. Hoogendoorn
    • 1
  1. 1.Delft University of TechnologyDelftThe Netherlands

Personalised recommendations