Skip to main content
SpringerLink
Log in
Book cover

Crowd Dynamics, Volume 1 pp 259–292Cite as

Birkhäuser

Pedestrian Models Based on Rational Behaviour

  • Chapter
  • First Online:

Abstract

Following the paradigm set by attraction-repulsion-alignment schemes, a myriad of individual-based models have been proposed to calculate the evolution of abstract agents. While the emergent features of many agent systems have been described astonishingly well with force-based models, this is not the case for pedestrians. Many of the classical schemes have failed to capture the fine detail of crowd dynamics, and it is unlikely that a purely mechanical model will succeed. As a response to the mechanistic literature, we will consider a model for pedestrian dynamics that attempts to reproduce the rational behaviour of individual agents through the means of anticipation. Each pedestrian undergoes a two-step time evolution based on a perception stage and a decision stage. We will discuss the validity of this game theoretical-based model in regimes with varying degrees of congestion, ultimately presenting a correction to the mechanistic model in order to achieve realistic high-density dynamics.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD   169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. C. Appert-Rolland, A. Jelić, P. Degond, J. Fehrenbach, J. Hua, A. Cretual, R. Kulpa, A. Marin, A.-H. Olivier, S. Lemercier, and J. Pettré. Experimental Study of the Following Dynamics of Pedestrians. In Pedestr. Evacuation Dyn. 2012, pages 305–315. Springer International Publishing, Cham, 2014.

    Google Scholar 

  2. I. L. Bajec, M. Mraz, and N. Zimic. Boids with a fuzzy way of thinking. Proc. ASC, 25:58–62, 2003.

    MATH  Google Scholar 

  3. M. Batty. Predicting where we walk. Nature, 388(6637):19–20, jul 1997.

    Article  Google Scholar 

  4. N. Bellomo and A. Bellouquid. On the modelling of vehicular traffic and crowds by kinetic theory of active particles. In Math. Model. Collect. Behav. Socio-Economic Life Sci., pages 273–296. Birkhäuser Boston, Boston, 2010.

    Google Scholar 

  5. N. Bellomo and A. Bellouquid. On the modeling of crowd dynamics: Looking at the beautiful shapes of swarms. Networks Heterog. Media, 6(3):383–399, aug 2011.

    Google Scholar 

  6. N. Bellomo, C. Bianca, and V. Coscia. On the modeling of crowd dynamics: An overview and research perspectives. SeMA J., 54(1):25–46, apr 2011.

    Article  MathSciNet  MATH  Google Scholar 

  7. N. Bellomo and C. Dogbe. On the Modeling of Traffic and Crowds: A Survey of Models, Speculations, and Perspectives. SIAM Rev., 53(3):409–463, jan 2011.

    Article  MathSciNet  MATH  Google Scholar 

  8. A. Borzì and S. Wongkaew. Modeling and control through leadership of a refined flocking system. Math. Model. Methods Appl. Sci., 25(02):255–282, feb 2015.

    Article  MathSciNet  MATH  Google Scholar 

  9. V. Braitenberg. Vehicles: Experiments in Synthetic Psychology. MIT Press, Cambridge, Massachusetts, 1984.

    Google Scholar 

  10. M. Caponigro, M. Fornasier, B. Piccoli, and E. Trélat. Sparse stabilization and optimal control of the Cucker-Smale model. Math. Control Relat. Fields, 3(4):447–466, sep 2013.

    Article  MathSciNet  MATH  Google Scholar 

  11. J. A. Carrillo, M. Fornasier, J. Rosado, and G. Toscani. Asymptotic Flocking Dynamics for the Kinetic CuckerSmale Model. SIAM J. Math. Anal., 42(1):218–236, jan 2010.

    Article  MathSciNet  MATH  Google Scholar 

  12. J. A. Carrillo, M. Fornasier, G. Toscani, and F. Vecil. Particle, kinetic, and hydrodynamic models of swarming. In Math. Model. Collect. Behav. Socio-Economic Life Sci., pages 297–336. Birkhäuser Boston, Boston, 2010.

    Google Scholar 

  13. J. A. Carrillo, S. Martin, and M.-T. Wolfram. An improved version of the Hughes model for pedestrian flow. Math. Model. Methods Appl. Sci., 26(04):671–697, apr 2016.

    Article  MathSciNet  MATH  Google Scholar 

  14. E. Cristiani, B. Piccoli, and A. Tosin. Modeling self-organization in pedestrians and animal groups from macroscopic and microscopic viewpoints. In Math. Model. Collect. Behav. Socio-Economic Life Sci., pages 337–364. Birkhäuser Boston, Boston, 2010.

    Google Scholar 

  15. F. Cucker and S. Smale. Emergent Behavior in Flocks. IEEE Trans. Automat. Contr., 52(5):852–862, may 2007.

    Article  MathSciNet  MATH  Google Scholar 

  16. F. Cucker and S. Smale. On the mathematics of emergence. Japanese J. Math., 2(1):197–227, 2007.

    Article  MathSciNet  MATH  Google Scholar 

  17. J. E. Cutting, P. M. Vishton, and P. A. Braren. How we avoid collisions with stationary and moving objects. Psychol. Rev., 102(4):627–651, 1995.

    Article  Google Scholar 

  18. W. Daamen and S. P. Hoogendoorn. Controlled Experiments to derive Walking Behaviour. Eur. J. Transp. Infrastruct. Res., 3(1):39–59, 2003.

    Google Scholar 

  19. W. Daamen and S. P. Hoogendoorn. Experimental Research of Pedestrian Walking Behavior. Transp. Res. Rec. J. Transp. Res. Board, 1828(January):20–30, jan 2003.

    Article  Google Scholar 

  20. P. Degond, C. Appert-Rolland, M. Moussaïd, J. Pettré, and G. Theraulaz. A Hierarchy of Heuristic-Based Models of Crowd Dynamics. J. Stat. Phys., 152(6):1033–1068, sep 2013.

    Article  MathSciNet  MATH  Google Scholar 

  21. P. Degond, C. Appert-Rolland, J. Pettré, and G. Theraulaz. Vision-based macroscopic pedestrian models. Kinet. Relat. Model., 6(4):809–839, nov 2013.

    Article  MathSciNet  MATH  Google Scholar 

  22. M. R. D’Orsogna, Y. L. Chuang, A. L. Bertozzi, and L. S. Chayes. Self-Propelled Particles with Soft-Core Interactions: Patterns, Stability, and Collapse. Phys. Rev. Lett., 96(10):104302, mar 2006.

    Google Scholar 

  23. J. J. Fruin. Pedestrian Planning and Design. Metropolitan Association of Urban Designers and Environmental Planners, New York, 1971.

    Google Scholar 

  24. Q. Gibson. Social Forces. J. Philos., 55(11):441, may 1958.

    Google Scholar 

  25. G. Gigerenzer. Why Heuristics Work. Perspect. Psychol. Sci., 3(1):20–29, jan 2008.

    Article  Google Scholar 

  26. J. R. Gill and K. Landi. Traumatic Asphyxial Deaths Due to an Uncontrolled Crowd. Am. J. Forensic Med. Pathol., 25(4):358–361, dec 2004.

    Article  Google Scholar 

  27. S.-Y. Ha, T. Ha, and J.-H. Kim. Emergent Behavior of a Cucker-Smale Type Particle Model With Nonlinear Velocity Couplings. IEEE Trans. Automat. Contr., 55(7):1679–1683, jul 2010.

    Google Scholar 

  28. B. D. Hankin and R. A. Wright. Passenger Flow in Subways. Oper. Res. Q., 9(2):81, jun 1958.

    Article  Google Scholar 

  29. D. Helbing. A mathematical model for the behavior of pedestrians. Behav. Sci., 36(4):298–310, oct 1991.

    Article  Google Scholar 

  30. D. Helbing. A Fluid Dynamic Model for the Movement of Pedestrians. Complex Syst., 6:391–415, may 1992.

    Google Scholar 

  31. D. Helbing. Self-organization in Pedestrian Crowds. In Soc. Self-Organization, pages 71–99. 2012.

    Google Scholar 

  32. D. Helbing, L. Buzna, A. Johansson, and T. Werner. Self-Organized Pedestrian Crowd Dynamics: Experiments, Simulations, and Design Solutions. Transp. Sci., 39(1):1–24, feb 2005.

    Article  Google Scholar 

  33. D. Helbing, I. J. Farkas, and T. Vicsek. Simulating dynamical features of escape panic. Nature, 407(6803):487–490, 2000.

    Article  Google Scholar 

  34. D. Helbing, A. Johansson, and H. Z. Al-Abideen. Crowd turbulence: the physics of crowd disasters. Fifth Int. Conf. Nonlinear Mech., (June):967–969, aug 2007.

    Google Scholar 

  35. D. Helbing, A. Johansson, and H. Z. Al-Abideen. Dynamics of crowd disasters: An empirical study. Phys. Rev. E, 75(4):046109, apr 2007.

    Google Scholar 

  36. D. Helbing and P. Molnár. Social force model for pedestrian dynamics. Phys. Rev. E, 51(5):4282–4286, may 1995.

    Article  Google Scholar 

  37. D. Helbing, P. Molnár, I. J. Farkas, and K. Bolay. Self-organizing pedestrian movement. Environ. Plan. B Plan. Des., 28(3):361–383, 2001.

    Article  Google Scholar 

  38. D. Helbing and T. Vicsek. Optimal self-organization. New J. Phys., 1:13.1–13.7=17, 1999.

    Article  MATH  Google Scholar 

  39. L. F. Henderson. The Statistics of Crowd Fluids. Nature, 229(5284):381–383, feb 1971.

    Article  Google Scholar 

  40. L. F. Henderson. On the fluid mechanics of human crowd motion. Transp. Res., 8(6):509–515, dec 1974.

    Article  Google Scholar 

  41. S. P. Hoogendoorn and W. Daamen. Pedestrian Behavior at Bottlenecks. Transp. Sci., 39(2):147–159, may 2005.

    Article  Google Scholar 

  42. B. Hopkins, A. Churchill, S. Vogt, and L. Rönnqvist. Braking Reaching Movements: A Test of the Constant Tau-Dot Strategy Under Different Viewing Conditions. J. Mot. Behav., 36(1):3–12, may 2004.

    Article  Google Scholar 

  43. R. L. Hughes. A continuum theory for the flow of pedestrians. Transp. Res. Part B Methodol., 36(6):507–535, jul 2002.

    Article  Google Scholar 

  44. R. L. Hughes. The Flow of Human Crowds. Annu. Rev. Fluid Mech., 35(1):169–182, jan 2003.

    Google Scholar 

  45. A. Jelić, C. Appert-Rolland, S. Lemercier, and J. Pettré. Properties of pedestrians walking in line: Fundamental diagrams. Phys. Rev. E, 85(3):036111, mar 2012.

    Google Scholar 

  46. Y.-q. Jiang, P. Zhang, S. Wong, and R.-x. Liu. A higher-order macroscopic model for pedestrian flows. Phys. A Stat. Mech. its Appl., 389(21):4623–4635, nov 2010.

    Article  Google Scholar 

  47. A. Johansson and D. Helbing. Analysis of Empirical Trajectory Data of Pedestrians. In Pedestr. Evacuation Dyn. 2008, pages 203–214. Springer Berlin Heidelberg, Berlin, Heidelberg, 2010.

    Google Scholar 

  48. N. R. Johnson. Panic at the ‘Who Concert Stampede’: An Empirical Assessment. Soc. Probl., 34(4):362–373, 1987.

    Article  Google Scholar 

  49. T. Kretz, A. Grünebohm, M. Kaufman, F. Mazur, and M. Schreckenberg. Experimental study of pedestrian counterflow in a corridor. J. Stat. Mech. Theory Exp., 2006(10):P10001–P10001, oct 2006.

    Article  MATH  Google Scholar 

  50. T. Kretz, A. Grünebohm, and M. Schreckenberg. Experimental study of pedestrian flow through a bottleneck. J. Stat. Mech. Theory Exp., (10), 2006.

    Google Scholar 

  51. S. Lemercier, A. Jelić, R. Kulpa, J. Hua, J. Fehrenbach, P. Degond, C. Appert-Rolland, S. Donikian, and J. Pettré. Realistic following behaviors for crowd simulation. Comput. Graph. Forum, 31(2pt2):489–498, may 2012.

    Article  MATH  Google Scholar 

  52. K. Lewin. Field Theory in Social Science. Harper, 1951.

    Google Scholar 

  53. M. J. Lighthill and G. B. Whitham. On Kinematic Waves I - Flood Movement in Long Rivers. Proc. R. Soc. A Math. Phys. Eng. Sci., 229(1178):281–316, may 1955.

    Google Scholar 

  54. M. J. Lighthill and G. B. Whitham. On Kinematic Waves II - A Theory of Traffic Flow on Long Crowded Roads. Proc. R. Soc. A Math. Phys. Eng. Sci., 229(1178):317–345, may 1955.

    Google Scholar 

  55. L. Luo, Z. Fu, X. Zhou, K. Zhu, H. Yang, and L. Yang. Fatigue effect on phase transition of pedestrian movement: experiment and simulation study. J. Stat. Mech. Theory Exp., 2016(10):103401, oct 2016.

    Article  MathSciNet  Google Scholar 

  56. M. Moussaïd, E. G. Guillot, M. Moreau, J. Fehrenbach, O. Chabiron, S. Lemercier, J. Pettré, C. Appert-Rolland, P. Degond, and G. Theraulaz. Traffic instabilities in self-organized pedestrian crowds. PLoS Comput. Biol., 8(3), 2012.

    Article  Google Scholar 

  57. M. Moussaïd, D. Helbing, S. Garnier, A. Johansson, M. Combe, and G. Theraulaz. Experimental study of the behavioural mechanisms underlying self-organization in human crowds. Proc. R. Soc. B Biol. Sci., 276(1668):2755–2762, 2009.

    Article  Google Scholar 

  58. M. Moussaïd, D. Helbing, and G. Theraulaz. How simple rules determine pedestrian behavior and crowd disasters. Proc. Natl. Acad. Sci., 108(17):6884–6888, 2011.

    Article  Google Scholar 

  59. M. Moussaïd, N. Perozo, S. Garnier, D. Helbing, and G. Theraulaz. The walking behaviour of pedestrian social groups and its impact on crowd dynamics. PLoS One, 5(4):1–7, 2010.

    Article  Google Scholar 

  60. M. Mri and H. Tsukaguchi. A new method for evaluation of level of service in pedestrian facilities. Transp. Res. Part A Gen., 21(3):223–234, may 1987.

    Google Scholar 

  61. K. M. Ngai, F. M. Burkle, A. Hsu, and E. B. Hsu. Human Stampedes: A Systematic Review of Historical and Peer-Reviewed Sources. Disaster Med. Public Health Prep., 3(04):191–195, dec 2009.

    Article  Google Scholar 

  62. S. J. Older. Movement of Pedestrians on Footways in Shopping Streets. Traffic Eng. Control, 10(4):160–163, 1968.

    Google Scholar 

  63. A. Polus, J. L. Schofer, and A. Ushpiz. Pedestrian Flow and Level of Service. J. Transp. Eng., 109(1):46–56, jan 1983.

    Article  Google Scholar 

  64. C. W. Reynolds. Flocks, herds and schools: A distributed behavioral model. ACM SIGGRAPH Comput. Graph., 21(4):25–34, aug 1987.

    Google Scholar 

  65. C. W. Reynolds. Steering behaviors for autonomous characters. Game Dev. Conf., pages 763–782, 1999.

    Google Scholar 

  66. P. R. Schrater, D. C. Knill, and E. P. Simoncelli. Mechanisms of visual motion detection. Nat. Neurosci., 3(1):64–68, jan 2000.

    Article  Google Scholar 

  67. A. Seyfried, B. Steffen, W. Klingsch, and M. Boltes. The fundamental diagram of pedestrian movement revisited. J. Stat. Mech. Theory Exp., (10):41–53, 2005.

    MATH  Google Scholar 

  68. D. Strömbom. Collective motion from local attraction. J. Theor. Biol., 283(1):145–151, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  69. D. Strömbom, R. P. Mann, A. M. Wilson, S. Hailes, A. J. Morton, D. J. T. Sumpter, and A. J. King. Solving the shepherding problem: heuristics for herding autonomous, interacting agents. J. R. Soc. Interface, 11(100):20140719–20140719, aug 2014.

    Article  Google Scholar 

  70. Transportation Research Board. Highway Capacity Manual: Special Report 209. U.S. Dept. of Transportation, Federal Highway Administration, Washington, D.C., 1985.

    Google Scholar 

  71. Transportation Research Board. Highway Capacity Manual 2000. U.S. Dept. of Transportation, Federal Highway Administration, Washington, D.C., 2000.

    Google Scholar 

  72. H. M. Traquair. Clinical perimetry. Kimpton, London, 1876.

    Google Scholar 

  73. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet. Novel Type of Phase Transition in a System of Self-Driven Particles. Phys. Rev. Lett., 75(6):1226–1229, aug 1995.

    Article  MathSciNet  Google Scholar 

  74. W. H. Warren and B. R. Fajen. From Optic Flow to Laws of Control. In Opt. Flow Beyond, pages 307–337. Springer Netherlands, Dordrecht, 2004.

    Chapter  Google Scholar 

  75. U. Weidmann. Transporttechnik der Fussgänger, Transporttechnische Eigenschaften des Fussgängerverkehrs (Literturauswertung), volume 90. Institut für Verkehrsplanung, Transporttechnik, Strassen- und Eisenbahnbau (IVT), ETH Zürich, 1993.

    Google Scholar 

Download references

Acknowledgements

JAC acknowledges support by the EPSRC grant no. EP/P031587/1. PD acknowledges support by the EPSRC grant no. EP/M006883/1, by the Royal Society and the Wolfson Foundation through a Royal Society Wolfson Research Merit Award no. WM130048. PD is on leave from CNRS, Institut de Mathmatiques de Toulouse, France. JAC and PD acknowledge support by the National Science Foundation (NSF) under Grant no. RNMS11-07444(KI-Net).

Author information

Authors and Affiliations

  1. Department of Mathematics, Imperial College London, London, UK

    Rafael Bailo, José A. Carrillo & Pierre Degond

Authors
  1. Rafael Bailo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. José A. Carrillo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pierre Degond
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Rafael Bailo .

Editor information

Editors and Affiliations

  1. School of Engineering, University of Edinburgh, Edinburgh, UK

    Livio Gibelli

  2. Department of Mathematical Sciences, Politecnico di Torino, Torino, Italy

    Nicola Bellomo

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bailo, R., Carrillo, J.A., Degond, P. (2018). Pedestrian Models Based on Rational Behaviour. In: Gibelli, L., Bellomo, N. (eds) Crowd Dynamics, Volume 1. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-05129-7_9

Download citation

Publish with us

Policies and ethics

Search

Navigation