Transcript crowdSimulation

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)?