A utility threshold model of herding–panic behavior in evacuation under emergencies based on complex network theory

Abstract

Casualties during crowd evacuation in many unexpected events are closely related to panic behaviors. In this paper the evacuation crowd system is abstracted into a dynamic complex network composed of three types of people, namely calm people, panic people, and herding people, as well as their interactions. The mathematical model of these interactions is established based on complex network theory. Further, the evolution of herding people to panic people is interpreted by a specific concept of “herding–panic threshold,” as well as its utility threshold model, in which the own characteristics of herding people and the external pressure from the surrounding crowd are comprehensively considered. To verify the rationality of some assumption in the utility threshold model, a questionnaire survey about the evacuation psychological behaviors is carried out. Through theoretical analysis and simulation, the influence of some key parameters on the herding–panic behavior is discussed in detail, via analyzing the change of panic rate. Some safety measures to control herding–panic in evacuation are also suggested.

Keywords

Crowd evacuation complex network herding–panic behavior utility threshold psychological behavior survey

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References

Nilsson

Johansson

Social influence during the initial phase of a fire evacuation-analysis of evacuation experiments in a cinema theatre. Fire Safe J 2009; 44: 71–79.

Kinateder

Social influence in emergency situations - studies in virtual reality. PhD Thesis, University of Wurzburg, GER, 2013.

Bryan

. Human behavior and fire. In: Cote

(ed.) Fire protection handbook. Vol.1. 19th ed. Quincy, MA: National Fire Protection Association, 2003, pp.4.3–4.32.

Hewstone

Martin

Social influence. In: Hewstone

Ströbe

Jonas

(eds) Introduction to social psychology. 4th ed.London: Blackwell Publishing, 2008.

Fahy

Proulx

Aiman

‘Panic’ and human behaviour in fire. NRC Publications Archive, NRCC-51384. A version of this document is published in: Proceedings of the 4th International Symposium on Human Behaviour in Fire, Cambridge, UK, July 13 2009, pp. 387–398. http://nparc.cisti-icist.nrc-cnrc.gc.ca/eng/view/object/?id=b23d49c3-226d-4cfa-890b-a3465d1493ad.

Shields

Proulx

The science of human behavior: past research endeavour, current developments and fashioning a research agenda. Fire Safe Sci 2000; 6: 95–113.

Helbing

Farkas

Vicsek

Simulating dynamical features of escape panic. Nature 2000; 407: 487–490.

Rita

Proulx

Aiman

Panic or not in fire: clarifying the misconception. Fire Mater 2012; 36: 328–338.

Germain

. Tinsel and tears: a complete list of the dead, reprint, “The Italian Hall Disaster, Calumet, Michigan”, Genealogia.fi, http://www.genealogia.fi/emi/emi3d31e.htm (1984, accessed 4 January 2011).

10.

Xue

Wei

Tian

. Opinion formation and propagation induced by pedestrian flow. Pedestrian Evac Dynam 2010; 2: 371–379.

11.

Illera

Fink

Hinneberg

. NO PANIC: escape and panic in buildings–architectural basic research in the context of security and safety research. Pedestrian Evac Dynam 2010; 3: 733–742.

12.

Bosta

SA.

Crowd management based on scientific research to prevent crowd panic and disasters. Pedestrian Evac Dynam 2011; 15: 741–746.

13.

Dias

Sarvi

Shiwakoti

. Investigating collective escape behaviours in complex situations. Safe Sci 2013; 60: 87–94.

14.

Zou

Xie

Wang

. Evacuation of pedestrians with two motion modes for panic system. Plos One 2016; 11:1-13–13.

15.

Wang

Sun

. Qualitative simulation of the panic spread in large-scale evacuation. Simul-T Soc Mod Sim 2012; 88: 1465–1474.

16.

Ben-Akiva

Lerman

. Discrete choice analysis: theory and application to travel demand. Cambridge, MA: The MIT Press, 1985.

17.

Watts

Strogatz

SH.

Collective dynamics of small-world networks. Nature 1998; 393: 440–442.

18.

Barabási

Réka

Emergence of scaling in random networks. Science 1999; 286: 509–512.

19.

Barabási

Bonabeau

. Scale-free networks. Sci Am 2003; 288: 50–59.

20.

Hong

Yang

Zio

. A novel dynamics model of fault propagation and equilibrium analysis in complex dynamical communication network. Appl Math Comput 2014; 247: 1021–1029.

21.

Kinney

Crucitti

Albert

. Modeling cascading failures in the north American power grid. Eur Phys J B 2005; 46: 101–107.

22.

Serrano

Boguñá

Topology of the world trade web. Phys Rev E 2003; 68: 634-646.

23.

Piqueira

JRC

Araujo

. A modified epidemiological model for computer viruses. Appl Math Comput 2009; 213: 355–360.

24.

Wang

Chen

Complex networks theory and its application. Beijing: Tsinghua University Press, 2006, pp.1–100.

25.

Wang

Cao

Bao

. A novel local-world evolving network model for power grid. Acta Phys Sin Ch Ed 2009; 58: 3597–3602.

26.

Newman

MEJ

. Networks: an introduction. Oxford, UK: Oxford University Press, 2010.

27.

Karsai

Juhász

Iglói

Nonequilibrium phase transitions and finite-size scaling in weighted scale-free networks. Phys Rev E 2006; 73: 1–6.

28.

Janssen

Jager

Simulating market dynamics: interactions between consumer psychology and social networks. Artif Life 2003; 9: 343–356.

29.

Lovreglio

Borri

dell’Olio

. A discrete choice model based on random utilities for exit choice in emergency evacuations. Safe Sci 2014; 62: 418–426.

30.

López-Pintado

Diffusion in complex social networks. Games Econ Behav 2008; 62: 573–590.

31.

Nakamura

Expected utility with a threshold function. Lect Notes Econ Math Syst 1987; 286: 170–179.

32.

Aven

Reniers

. How to define and interpret a probability in a risk and safety setting. Safe Sci 2013; 51: 223–231.