Information Technology Reference
In-Depth Information
where
F
labels the favorite direction and
j
=
F, F ±
1
, .., F ± ξ
. Note that
directions
F
+
i
and
F − i
are considered in a random order to avoid a
systematic bias in case of an equal score.
Lets first consider the probability of moving: it is constructed such that the
number of people allowed to move is on average
ρ
0
or less. A possible interpre-
tation for this rule is that only people at the boundary of the area of cell are
able to move.
2000
µ
1900
1800
1700
1600
1500
1400
1300
1200
1100
50
100
150
200
250
300
350
400
450
500
iteration
Fig. 2.
A measure of total mobility in a crowd for the three cases shown in
fig. 1:(crosses) no lanes
λ
≈
0
,η
≈
2
, (circles) dense lanes
λ
≈
1
,η
≈
2
,(line) sparse
lanes
λ
≈
0
,η
≈
1. Note that the maximum value of the total mobility is 2500, i.e. the
total number of individuals.
Once an individual is allowed to move, the choice of the destination cell is
mainly governed by the agreement between the mobility at a given cell
µ
(
r
+
c
j
,t
)
and the direction
c
j
needed to reached the cell which is given by the first term
of eq. (3). This reflects the need to find mobility in a dense crowd. On the other
hand, the mobility found at
r
+
c
j
should not completely outweigh the fact
that an individual possesses a favorite direction
c
F
. Hence the presence of the
second term in eq. (3) which measures the agreement between the considered
direction
c
j
and the favorite direction
c
F
. Therefore, movement towards a cell
which opposes
c
F
is only possible if high mobility compensates backtracking.
The
η
factor is a parameter which determines whether the crowd will gen-
erally prefer mobility or their final destination. A value of
η
=1
/
2 means both
scalar products have equal weight. In the present model this is a free parameter.
