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Simulating dynamical features of escape panic


One of the most disastrous forms of collective human behaviour is the kind of crowd stampede induced by panic, often leading to fatalities as people are crushed or trampled. Sometimes this behaviour is triggered in life-threatening situations such as fires in crowded buildings1,2; at other times, stampedes can arise during the rush for seats3,4 or seemingly without cause. Although engineers are finding ways to alleviate the scale of such disasters, their frequency seems to be increasing with the number and size of mass events2,5. But systematic studies of panic behaviour6,7,8,9 and quantitative theories capable of predicting such crowd dynamics5,10,11,12 are rare. Here we use a model of pedestrian behaviour to investigate the mechanisms of (and preconditions for) panic and jamming by uncoordinated motion in crowds. Our simulations suggest practical ways to prevent dangerous crowd pressures. Moreover, we find an optimal strategy for escape from a smoke-filled room, involving a mixture of individualistic behaviour and collective ‘herding’ instinct.

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Figure 1: Simulation of pedestrians moving with identical desired velocity v0i = v0 towards the 1-m-wide exit of a room of size 15 m × 15 m.
Figure 2: Simulation of an escape route with a wider area.
Figure 3: Simulation of N = 90 pedestrians trying to escape a smoky room of area A = 15 m × 15 m (grey) through two invisible doors of 1.5 m width.

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  1. Keating, J. P. The myth of panic. Fire J. 57–61, 147 (May 1982).

  2. Elliott, D. & Smith, D. Football stadia disasters in the United Kingdom: learning from tragedy? Ind. Environ. Crisis Q. 7(3), 205–229 (1993).

    Article  Google Scholar 

  3. Jacobs, B. D. & 't Hart, P. in Hazard Management and Emergency Planning (eds Parker, D. J. & Handmer, J. W.) Ch. 10 (James & James Science, London, 1992).

    Google Scholar 

  4. Johnson, N. R. Panic at “The Who Concert Stampede”: an empirical assessment. Soc. Problems 34(4), 362– 373 (1987).

    Article  Google Scholar 

  5. Smith, R. A. & Dickie, J. F. (eds) Engineering for Crowd Safety (Elsevier, Amsterdam, 1993).

    Google Scholar 

  6. Mintz, A. Non-adaptive group behavior. J. Abnormal Normal Social Psychol. 46, 150–159 ( 1951).

    Article  CAS  Google Scholar 

  7. Kelley, H. H., Condry, J. C. Jr, Dahlke, A. E. & Hill, A. H. Collective behavior in a simulated panic situation. J. Exp. Social Psychol. 1, 20–54 (1965).

    Article  Google Scholar 

  8. Quarantelli, E. The behavior of panic participants. Sociol. Social Res. 41, 187–194 (1957).

    Google Scholar 

  9. Brown, R. Social Psychology (Free, New York, 1965).

    Google Scholar 

  10. Drager, K. H. et al. in Proc. 1992 Emergency Management and Engineering Conf. (ed. Drager, K. H.) 101–108 (Society for Computer Simulation, Orlando, Florida, 1992).

    Google Scholar 

  11. Ebihara, M., Ohtsuki, A. & Iwaki, H. A model for simulating human behavior during emergency evacuation based on classificatory reasoning and certainty value handling. Microcomput. Civil Eng. 7, 63– 71 (1992).

    Article  Google Scholar 

  12. Still, G. K. New computer system can predict human behaviour response to building fires. Fire 84, 40–41 (1993).

    Google Scholar 

  13. Predtetschenski, W. M. & Milinski, A. I. Personenströme in Gebäuden–Berechnungsmethoden für die Projektierung (Müller, Köln-Braunsfeld, 1971).

    Google Scholar 

  14. Weidmann, U. Transporttechnik der Fußgänger (Institut für Verkehrsplanung, Transporttechnik, Straßen- und Eisenbahnbau (IVT), ETH Zürich, 1993).

    Google Scholar 

  15. Helbing, D., Farkas, I. J. & Vicsek, T. Freezing by heating in a driven mesoscopic system. Phys. Rev. Lett. 84, 1240–1243 (2000).

    Article  ADS  CAS  Google Scholar 

  16. Helbing, D. & Mulnár, P. Social force model for pedestrian dynamics. Phys. Rev. E 51, 4282– 4286 (1995).

    Article  ADS  CAS  Google Scholar 

  17. Ristow, G. H. & Herrmann, H. J. Density patterns in two-dimensional hoppers. Phys. Rev. E 50, R5– R8 (1994).

    Article  ADS  Google Scholar 

  18. Wolf, D. E. & Grassberger, P. (eds) Friction, Arching, Contact Dynamics (World Scientific, Singapore, 1997).

    Book  Google Scholar 

  19. Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I. & Schochet, O. Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75, 1226–1229 (1995).

    Article  ADS  MathSciNet  CAS  Google Scholar 

  20. Kelley, H. H. & Thibaut, J. W. in The Handbook of Social Psychology Vol. 4 (eds Lindzey, G. & Aronson, E.) (Addison-Wesley, Reading, Massachusetts, 1969).

    Google Scholar 

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D.H. thanks the German Research Foundation (DFG) for financial support by a Heisenberg scholarship. T.V. and I.F. are grateful for partial support by OTKA and FKFP.

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Correspondence to Dirk Helbing.

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Helbing, D., Farkas, I. & Vicsek, T. Simulating dynamical features of escape panic. Nature 407, 487–490 (2000).

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