Information Technology Reference
In-Depth Information
700
680
660
640
620
600
580
560
540
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
λ
Fig. 4.
The time needed to evacuate a room as a function of
λ
.Low
λ
means people
do not consider other directions than the favorite one. The plot shows that by increas-
ing the directions considered and thus slowing the mean velocity to the door, higher
throughput is achieved. The plot is the result of single runs with all individuals on one
side of wall with a door of size 3.
To create a su
?
ciently diverse crowd, the parameter
ξ
is initially randomly
chosen for each individual. For the sake of convenience, we would like to generate
this diversity using a continuous parameter
λ ∈
[0
,∞
[ which describes the mean
behavior of the crowd. We therefore use a discretized power-law distribution,
namely we compute
ξ
= [(4
x
1
λ
)], where
x ∈
[0
,
1] is a random variable uniformly
distributed.
With this method,
ξ
will take integer values between 0 and 3. The probability
that
ξ
=
l
is given by
P
(
ξ
=
)=
P
(
≤
4
x
1
/λ
<
+1)
4
λ
λ
+1
4
=
P
≤ x<
+1
4
λ
4
λ
=
−
(4)
These probabilities result in a mean value of
ξ
=3
−
3
λ
+2
λ
+1
4
λ
When
λ →
0,
ξ
is always equal to 0 which means no individual ever considers
any other cell but its favorite direction; with a value of
λ
=1
.
0, values of
ξ
are
equiprobable with
ξ
=3
/
2. For higher values of
λ
the density of individuals
with
ξ
= 3 increases. Again the actual value of
ξ
is probably situation dependent
and should vary dynamically.
