Simulating Dynamical Features of Escape Panic

1
Simulating Dynamical Features of Escape Panic

• Dirk Helbing, Illes Farkas, and Tamas Vicsek
• Presentation by
• Andrew Goodman

2
The Problem

• Crowd stampedes can be deadly
• People act in uncoordinated and dangerous ways
  when panicking
• It is difficult to obtain real data on crowd
  panics

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The Solution

• Model people as self-driven particles
• Model physical and socio-psychological influences
  on peoples movement as forces
• Simulate crowd panics and see what happens

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Acceleration of Simulated People

• vi0(t) desired speed
• ei0(t) desired direction
• vi(t) actual velocity
• ti characteristic time
• mi mass

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Forces from Other People

• Force from other peoples bodies being in the way
• Force of friction preventing people from sliding
• Psychological force of tendency to avoid each
  other
• Sum of forces of person j on person i is fij

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Total Force of Other People

• Aiexp(rij dij)/Binij is psychological force
• rij is the sum of the peoples radii
• dij is the distance between their centers of mass
• nij is the normalized vector from j to i
• Ai and Bi are constants

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Physical Forces

• kg(rij dij)nij is the force from other bodies
• ?g(rij dij)?vtijtij is the force of sliding
  friction
• g(x) is 0 if the people dont touch and x if they
  do touch
• tij is the tangential direction
• ?vtij is the tangential velocity difference
• k and ? are constants

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Forces from Walls

• Forces from walls are calculated in basically the
  same way as forces from other people

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Values Used for Constants and Parameters

• Values chosen to match flows of people through an
  opening under non-panic conditions
• People are modeled as the same except for their
  radius
• Insufficient data on actual panic situations to
  analyze the algorithm quantitatively

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Simulation of Clogging
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Simulation of Clogging

• As desired speed increases beyond 1.5m s-1, it
  takes more time for people to leave
• As desired speed increases, the outflow of people
  becomes irregular
• Arch shaped clogging occurs around the doorway

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Widening Can Create Crowding
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Mass Behavior

• Panicking people tend to exhibit herding behavior
• Herding simulated using panic parameter p

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Effects of Herding
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Injured People Block Exit
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A Column Can Increase Outflow
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Findings

• Bottlenecks cause clogging
• Asymmetrically placed columns around exits can
  reduce clogging and prevent build up of fatal
  pressures
• A mixture of herding and individual behavior is
  ideal

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Some Questions

• Are parameters based on non-panic situations
  correct for panic situations?
• How can we get quantitative data about panic
  situations to test simulations?
• What happens when injured people are allowed to
  fall over (and possibly be trampled)?