Geoscience Reference
In-Depth Information
Derivation of Mode Choice and Composite Cost Functions
Assuming zonal passenger and commodity shipments by mode
x
ij
mw
are positive,
the following model may be obtained from Eq. (
17.13
):
h
i
exp
x
mw
ij
x
ij
exp
a
m
g
m
m
a
m
mw
ij
¼
ʸ
ij
1
:
0
ʴ
8
mwij
,
i
6¼
j
ð
17
:
16
Þ
By substituting Eq. (
17.16
) into Eq. (
17.3
), we obtain:
h
i
X
X
x
mw
ij
x
mw
ij
x
ij
exp
a
m
g
m
m
ij
a
m
mw
ij
¼
¼
ʸ
1
:
0
exp
ʴ
ð
17
:
17
Þ
w
w
Therefore,
1
exp
a
m
g
m
ð
1
:
0
Þ ¼
X
ð
17
:
18
Þ
a
m
mw
ij
exp
ʴ
w
2
3
mw
ij
a
m
exp
ʴ
4
5
8
x
mw
ij
x
ij
¼
mwij
,
i
6¼
j
ð
17
:
19
Þ
X
a
m
mw
ij
exp
ʴ
w
Equation (
17.19
) becomes a typical transportation mode choice equation based
on the probability of choosing mode
w
among all available modes.
Interregional Interaction Functions
Again assuming that
x
ij
m
>
0, from Eqs. (
17.3
) and (17.15) and we obtain:
"
!
exp
g
m
#
8
exp
g
m
X
i
X
s
d
ij
x
ij
¼
X
i
n
a
snm
i
m
j
exp
n
ʼ
1
:
0
ʼ
mij
"
#
a
m
ln
X
w
1
definingd
ij
¼
a
m
mw
ij
exp
ʴ
ð
17
:
20
Þ
By defining the following balancing factors,
!
g
m
X
i
X
s
m
i
n
a
snm
i
ʲ
¼
exp
n
ʼ
1
:
0
8
m
,
i
ð
17
:
21
Þ
