Simulating Dynamical Features of Escape Panic

Dirk Helbing, Illes Farkas, and Tamas Vicsek

Presentation by

Andrew Goodman

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

The Solution

• Model people as self-driven particles

• Model physical and socio-psychological influences on people’s movement as forces

• Simulate crowd panics and see what happens

Acceleration of Simulated People

• vi0(t) = desired speed

• ei0(t) = desired direction

• vi(t) = actual velocity

• τi = characteristic time

• mi = mass

Forces from Other People

• Force from other people’s 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

Total Force of Other People

• Aiexp[(rij – dij)/Bi]nij is psychological “force”

• rij is the sum of the people’s radii

• dij is the distance between their centers of mass

• nij is the normalized vector from j to i

• Ai and Bi are constants

Physical Forces

• kg(rij – dij)nij is the force from other bodies

• κg(rij – dij)Δvtijtij is the force of sliding

friction

• g(x) is 0 if the people don’t touch and x if they do touch

• tij is the tangential direction

• Δvtij is the tangential velocity difference

• k and κ are constants

Forces from Walls

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

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

Simulation of Clogging

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

Widening Can Create Crowding

Mass Behavior

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

Effects of Herding

Injured People Block Exit

A Column Can Increase Outflow

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

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)?