Information Technology Reference
In-Depth Information
k
m
∑
∏
ξ
α
P
(
t
)
=
(
1
+
ln(
)
)(
W
(
t
)
V
(
t
)
)
ω
j
i
ij
i
(6)
i
=
1
i
=
k
+
1
Assuming that totally
m
constraints (
1
≤
i
≤
m
) are considered, when
k+1
≤
i
≤
m,
ω
i
(binary variable: 0 or 1) are restrictive constraints such as water body, slope etc, which
may include local, regional and
global levels with equal weight.
When
1
≤
i
≤
k
, they are non-restrictive constraints.
W
i
(t)
is the weight value of con-
straint
i
computed from eq.5. For proximity variables like the distance to major road,
here a negative exponential function is employed to calculate
V
ij
(t)
. Urban models
based on economic theory
[14]
, and discrete choice theory
[15]
had made widespread
uses of the negative exponential function.
V
ij
(t)=e
-
φ
dij
0<V
ij
(t)<1
(7)
d
ij
is the value of proximity variable
i
at cell
j.
φ is the density gradient for quanti-
fying its spatial influence. Usually, 0<φ<1, and φ varies with factor
i
. Eq.7 is actually
to standardise non-restrictive variables.
In order to generate the patterns that are closer to reality, a stochastic disturbance is
introduced as (1+ln(ξ)
α
)
[16]
. ξ is a random variable within [0∼1]. α is a parameter
controlling the size or strength of the stochastic perturbation.
P(t)
represents the po-
tential or probability of development of cell
j
at time
t,
which is the major driving
force of local growth.
In our model, neighbourhood size is not universal globally and is locally param-
eterised, which varies with different projects. Neighbourhood effect i.e. 'action-at-
distance' is also represented as one or two non-restrictive variables in eq.6, which
indicate the spatial influences of developed cell (including both the new and the old)
on its surrounding sites.
(8)
P
j
(t) → P
j'
(t)
(9)
∆L(t )=L(t)-L(t-1), L(0)=0
Eq.8 builds a transition from
P
j
(t)
to
P
j'
(t),
which is to reorder from maximum to
minimum. ∆
L(t)
in eq.9 is the land development demand at the phase from
t-1
to
t
as
L(t)
is the accumulative amount of land development till time
t
.
