Simulating Dynamical Features of Escape Panic Dirk Helbing, Illes Farkas, and Tamas Vicsek...

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)?