I tried to build a model of the complex choreography of all those people
walking to "middle points".
But... it doesnt work with the rule #1 :
"Chose A & B ; Walk to the middle point between A ans B ; then stop"
All points crash together.
Prooof : When every point stops, lets draw the smallest circle aroud them.
Two (or more) points are on the edge of the circle. So they cannot be -
mathematicaly - middle poionts of any AB line.
But... people are not points ! Poeple use rule #2, I presume :
"Chose A & B ; Walk so that you see A and B on the two sides of your vsion
angle + equal distance" (So, in the triangle ACB, AC = CB and angle ACB is
ca. 150° and not 180°)
This rule seems to imply that the system can work only if nb of people > 12.
Cordialement
Jean-Louis Cordonnier
36, rue Lavisse
66000 Perpignan (France)
33 4 68 63 87 04
From: "Jean-Louis Cordonnier" <jlcord@wanadoo.fr>
demonstrations of complex behaviour
-
"Jean-Louis Cordonnier"
- Junior Member
- Posts: 2
- Joined: Fri Mar 29, 2002 3:39 am
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John Sterman
- Senior Member
- Posts: 117
- Joined: Fri Mar 29, 2002 3:39 am
demonstrations of complex behaviour
There has been some discussion of how to model the classroom
demonstration in which people in a group all move to a point
equidistant from two others.
While not exactly the same, the type of model called for is similar
to models of crowds moving through different spaces. A particularly
interesting and important application of such models is the study of
"escape panics" - that is, what happens when a crowd of people all
try to escape from a room or space through narrow doors. These
situations arise in fires, in riots, at football (soccer) games, at
rock concerts, etc. Typically, each person attempts to get out
first, leading to the common outcome of bunching, congestion, and
trampling at the exits, reducing the total outflow and increasing
casualties far above the level that would occur if people took turns.
There is an obvious positive feedback loop here: more congestion,
more panic and still more congestion as people desperately try to get
out ahead of others. The outcome is a classic example of
dysfunctional collective behavior arising from simple, individually
self-interested decision rules: your attempt to get out as fast as
possible raises the exit time for all, usually including yourself.
An elegant model of this phenomenon is presented in
Helbing, Farkas, and Vicsek, 2000, Simulating dynamical features of
escape panic, Nature 407, 487 - 490 (2000).
The paper is available on line at
http://www.nature.com/cgi-taf/DynaPage. ... 813A377F9E
John Sterman
From: John Sterman <jsterman@MIT.EDU>
demonstration in which people in a group all move to a point
equidistant from two others.
While not exactly the same, the type of model called for is similar
to models of crowds moving through different spaces. A particularly
interesting and important application of such models is the study of
"escape panics" - that is, what happens when a crowd of people all
try to escape from a room or space through narrow doors. These
situations arise in fires, in riots, at football (soccer) games, at
rock concerts, etc. Typically, each person attempts to get out
first, leading to the common outcome of bunching, congestion, and
trampling at the exits, reducing the total outflow and increasing
casualties far above the level that would occur if people took turns.
There is an obvious positive feedback loop here: more congestion,
more panic and still more congestion as people desperately try to get
out ahead of others. The outcome is a classic example of
dysfunctional collective behavior arising from simple, individually
self-interested decision rules: your attempt to get out as fast as
possible raises the exit time for all, usually including yourself.
An elegant model of this phenomenon is presented in
Helbing, Farkas, and Vicsek, 2000, Simulating dynamical features of
escape panic, Nature 407, 487 - 490 (2000).
The paper is available on line at
http://www.nature.com/cgi-taf/DynaPage. ... 813A377F9E
John Sterman
From: John Sterman <jsterman@MIT.EDU>