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

3. 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

4. Acceleration of Simulated People v i 0 (t) = desired speed e i 0 (t) = desired direction v i (t) = actual velocity τ i = characteristic time m i = mass

5. 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 f ij

6. Total Force of Other People A i exp[(r ij – d ij )/B i ]n ij is psychological “force” r ij is the sum of the people’s radii d ij is the distance between their centers of mass n ij is the normalized vector from j to i A i and B i are constants

7. Physical Forces kg(r ij – d ij )n ij is the force from other bodies κg(r ij – d ij )Δv t ij t ij is the force of sliding friction g(x) is 0 if the people don’t touch and x if they do touch t ij is the tangential direction Δv t ij is the tangential velocity difference k and κ are constants

8. Forces from Walls Forces from walls are calculated in basically the same way as forces from other people

9. 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

10. Simulation of Clogging

11. 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

12. Widening Can Create Crowding

13. Mass Behavior Panicking people tend to exhibit herding behavior Herding simulated using “panic parameter” p

14. Effects of Herding

15. Injured People Block Exit

16. A Column Can Increase Outflow

17. 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

18. 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)?