Geoscience Reference
In-Depth Information
TABLE 8.8
Input Variables and Notation for Durham Spatial Interaction Model
Symbol
Notation
Description
V
1
O
i
Origin flow total
V
2
D
i
Destination flow total
V
3
O
j
Inverse destination flow total
V
4
D
j
Inverse origin flow total
V
5
C
ij
Distance measure
V
6
X
ij
Intervening opportunity which is the percentage of intervening
destinations between each trip pair
V
7
Z
ij
Competing destination which is the sum of
D
j
divided by
distance from alternative destinations
V
8
I
ij
Intrazonal trip flag identifies when a trip starts and finishes in the
same zone
TABLE 8.9
Mathematical Functions for
Durham Spatial Interaction Model
Symbol
Description
+
Addition
−
Subtraction
*
Multiplication
/
Division
^
Power
abs
Absolute
sqrt
Square root
log
Natural logarithm
exp
Exponential
<
Less than
>
Great than
sin
Sine
cos
Cosine
Equation 8.8 - Initial volume-based GP solution
−
V
5
−
1
.
82
VV
182
.
182
.
−
182
.
182 65
.
TVVVVV
=
12
+ +− +
3342
.
VVV
VV
+
2
1 26
2
1
1 5
14
V
2
−
V
5
−
182
.
VV
V
(
)
65
167
.
182
.
×+++
VV
334
.
V
log.
167
+−
V
3
V
2
6
2
6
6
2
VV VV
V
VV
(
)
+
(8.8)
2
×
V
167
.
−
2
V VVV
+
log
182
.
−
139
.
−
182
.
+
+
6
6
1
4
5
15
2
2
22
25
