A Data-Driven Model of Pedestrian Following and Emergent Crowd Behavior

  • Kevin Rio
  • William H. Warren
Conference paper


Pedestrian following is a common behavior, and may provide a key link between individual locomotion and crowd dynamics. Here, we present a model for following that is motivated by cognitive science and grounded in empirical data. In Experiment 1, we collected data from leader-follower pairs, and showed that a simple speed-matching model is sufficient to account for behavior. In Experiment 2, we manipulated the visual information of a virtual leader, and found that followers respond primarily to changes in visual angle.

Finally, in Experiment 3, we use the speed-matching model to simulate speed coordination in small crowds of four pedestrians. The model performs as well in these small crowds as it did in the leader-follower pairs. This cognitively-inspired, empirically-grounded model can serve as a component in a larger model of crowd dynamics.


Cognitive science Data Dynamics Experiment Following 


  1. 1.
    Goldstone, R.L., Gureckis, T.M.: Collective Behavior. Top. Cogn. Sci. 1(3), 412–438 (2009)CrossRefGoogle Scholar
  2. 2.
    Reynolds, C.W.: Flocks, Herds, and Schools: A Distributed Behavioral Model. Comp. Graph. 21(4), 25–34 (1987)CrossRefGoogle Scholar
  3. 3.
    Helbing, D., Molnár., P.: Social Force Model for Pedestrian Dynamics. Phys. Rev. E. 51(5), 4282–4286 (1995)Google Scholar
  4. 4.
    Helbing, D., Farkas, I., Vicsek, T.: Simulating Dynamical Features of Escape Panic. Nature 407(6803), 487–490 (2000)CrossRefGoogle Scholar
  5. 5.
    Piccoli, B., Tosin, A.: Pedestrian Flows in Bounded Domains with Obstacles. Continuum Mech. Therm. 21(2), 85–107 (2009)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Muramatsu, M., Irie, T., Nagatani, T.: Jamming Transition in Pedestrian Counter Flow. Physica A, 267(3–4), 487–498 (1999)CrossRefGoogle Scholar
  7. 7.
    Portz, A., Seyfried, A.: Modeling Stop-and-Go Waves in Pedestrian Dynamics. In: Wryzkowski, R., Dongarra, J., Karczewski, K., Wasniewski, J. (eds.) LNCS, vol. 6068, pp. 561–568. Springer, Heidelberg (2010)Google Scholar
  8. 8.
    Yu, W., Johansson, A.: Modeling Crowd Turbulence by Many-Particle Simulations. Phys. Rev. E 76(4), 046105 (2007)CrossRefGoogle Scholar
  9. 9.
    Ondřej, J., Pettré, J., Olivier, A.-H., Donikian, S.: A Synthetic-Vision Based Steering Approach for Crowd Simulation. ACM T. Graphic. 29(4), 123 (2010)Google Scholar
  10. 10.
    Moussaïd, M., Helbing, D., Theraulaz, G.: How Simple Rules Determine Pedestrian Behavior and Crowd Disasters. Proc. Natl. Acad. Sci. USA 108(17), 6884–6888 (2011)CrossRefGoogle Scholar
  11. 11.
    Lakoba, T.I., Kaup, D.J., Finkelstein, N.M.: Modifications of the Helbing-Molnár-Farkas-Vicsek Social Force Model for Pedestrian Evolution. Simulation 81(5), 339–352 (2005)CrossRefGoogle Scholar
  12. 12.
    Henderson, L.F.: The Statistics of Crowd Fluids. Nature 229, 381–383 (1971)CrossRefGoogle Scholar
  13. 13.
    Kretz, T., Grünebohm, A., Schreckenberg, M.: Experimental Study of Pedestrian Flow through a Bottleneck. J. Stat. Mech. P10014 (2006)Google Scholar
  14. 14.
    Moussaïd, M., Helbing, D., Garnier, S., Johansson. A., Combe, M., Theraulaz, G.: Experimental Study of the Behavioral Mechanisms Underlying Self-Organization in Human Crowds. P. Roy. Soc. B. 276(1688), 2755–2762 (2009)Google Scholar
  15. 15.
    Robin, T., Antonini, G., Bierlaire, M., Cruz, J.: Specification, Estimation, and Validation of a Pedestrian Walking Behavior Model. Transport. Res. B. 43(1), 36–56 (2009)CrossRefGoogle Scholar
  16. 16.
    Moussaïd, M., Perozo, N., Garnier, S., Helbing, D., Theraulaz, G.: The Walking Behaviour of Pedestrian Social Groups and Its Impact on Crowd Dynamics. PLoS One 5(4), e10047 (2010)CrossRefGoogle Scholar
  17. 17.
    Schadschneider, A., Seyfried, A.: Empirical Results for Pedestrian Dynamics and Their Implications for Modeling. Netw. Heterog. Media 6(3), 545–560 (2011)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Warren, W.H.: The Dynamics of Perception and Action. Psychol. Rev. 113(2), 358–389 (2006)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Gibson, J.J.: The Ecological Approach to Visual Perception. Psychology Press, New York (1979)Google Scholar
  20. 20.
    Kugler, P., Turvey, M.: Information, Natural Law, and the Self-Assembly of Rhythmic Movement: Resources for Ecological Psychology. Erlbaum, Hillsdale (1987)Google Scholar
  21. 21.
    Kelso, S.: Dynamic Patterns: The Self-Organization of Brain and Behavior (Complex Adaptive Systems). The MIT Press, Cambridge (1995)Google Scholar
  22. 22.
    Fajen, B.R., Warren, W.H.: Behavioral Dynamics of Steering, Obstacle Avoidance, and Route Selection. J. Exp. Psychol. Human 29(2), 343–362 (2003)CrossRefGoogle Scholar
  23. 23.
    Fajen, B.R., Warren, W.H.: Behavioral Dynamics of Intercepting a Moving Target. Exp. Brain Res. 180(2), 303–319 (2007)CrossRefGoogle Scholar
  24. 24.
    Li, T.-Y., Jeng, Y.-J., Chang, S.-I.: Simulating Virtual Human Crowds with a Leader-Follower Model. In: Proceedings of the Fourteenth Conference on Computer Animation, pp. 93–102 (2001)Google Scholar
  25. 25.
    Brackstone, M., McDonald, M.: Car-Following: A Historical Review. Transport. Res. F. 2(4), 181–196 (1999)CrossRefGoogle Scholar
  26. 26.
    Pipes, L.A.: An Operational Analysis of Traffic Dynamics. J. Appl. Phys. 24(3), 274 (1953)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Herman, R., Montroll, E.W., Potts, R.B., Rothery, R.W.: Traffic Dynamics: Analysis of Stability in Car-Following. Oper. Res. 7(1), 86–106 (1959)CrossRefMathSciNetGoogle Scholar
  28. 28.
    Gazis, D.C., Herman, R., Rothery, R.W.: Nonlinear Follow-The-Leader Models of Traffic Flow. Oper. Res. 9(4), 545–567 (1961)CrossRefMATHMathSciNetGoogle Scholar
  29. 29.
    Helly, W.: Simulation of Bottlenecks in Single Lane Traffic Flow. In: Proceedings of the Symposium on Theory of Traffic Flow, pp. 207–238. Elsevier, New York (1959)Google Scholar
  30. 30.
    Fletcher, R.: Practical Methods of Optimization. Wiley, Hoboken (2000)CrossRefGoogle Scholar
  31. 31.
    Regan, D., Beverley, K.I.: Binocular and Monocular Stimuli for Motion in Depth: Changing-Disparity and Changing-Size Feed the Same Motion in Depth Stage. Vision Res. 19, 1331–1342 (1979)CrossRefGoogle Scholar
  32. 32.
    Heuer, H.: Estimates of Time-to-Contact Based on Changing Size and Changing Target Vergence. Perception 22(5), 549–563 (1993)CrossRefMathSciNetGoogle Scholar
  33. 33.
    Gray, R., Regan, D.: Accuracy of Estimating Time To Collision Using Binocular and Monocular Information. Vision Res. 38, 499–512 (1997)CrossRefGoogle Scholar
  34. 34.
    Rushton, S.K., Wann, J.P.: Weighted Combination of Size and Disparity: A Computational Model for Timing a Ball Catch. Nat. Neurosci. 2(2), 186–190 (1999)CrossRefGoogle Scholar
  35. 35.
    Anderson, G.J., Sauer, C.W.: Optical Information for Car Following: The Driving by Visual Angle (DVA) Model. Hum. Factors 49(5), 878–896.Google Scholar
  36. 36.
    Tarr, M.J., Warren, W.H.: Virtual Reality in Behavioral Neuroscience and Beyond. Nat. Neurosci. 5, 1089–1092 (2002)CrossRefGoogle Scholar
  37. 37.
    Bülthoff, H.H., Mallot, H.A.: Integration of Depth Modules: Stereo and Shading. J. Opt. Soc. Am. A 5(10), 1749–1758 (1988)CrossRefGoogle Scholar
  38. 38.
    Costa, M.: Interpersonal Distances in Group Walking. J. Nonverbal Behav. 34(1), 15–26 (2010)CrossRefGoogle Scholar
  39. 39.
    Dyer, J.R.G., Johansson, A., Helbing, D., Couzin, I.D., Krause, J.: Leadership, Consensus Decision Making and Collective Behaviour in Humans. Phil. Trans. R. Soc. B. 364(1518), 781–789 (2009)Google Scholar
  40. 40.
    Dyer, J.R.G., Ioannou, C.C., Morrell, L.J., Croft, D.P., Couzin, I.D., Waters, D.A., Krause, J.: Consensus Decision Making in Human Crowds. Anim. Behav. 75(2), 461–470 (2008)CrossRefGoogle Scholar
  41. 41.
    Faria, J.J., Dyer, J.R.G., Tosh, C.R., Krause, J.: Leadership and Social Information Use in Human Crowds. Anim. Behav. 79(4), 895–901 (2010)CrossRefGoogle Scholar
  42. 42.
    Bonneaud, S., Rio, K., Chevaillier, P., Warren, W.H.: Accounting for Patterns of Collective Behavior in Crowd Locomotor Dynamics for Realistic Simulations. In: Pan, Z., Cheok, A.D., Müller, W., Chang, M., Zhang, M. (eds.) Transactions on Edutainment VIII, LNCS, vol. 7145, pp. 1–12. Springer, Heidelberg (2012)Google Scholar
  43. 43.
    Bonneaud, S., Warren, W.H.: A Behavioral Dynamics Approach to Modeling Realistic Pedestrian Behavior. In: Weidmann, U., Kirsch, U., Puffe, E., Weidmann, M. (eds.) Pedestrian and Evacuation Dynamics. Springer, Heidelberg (2012)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of Cognitive, Linguistic, and Psychological SciencesBrown UniversityProvidenceUSA

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