Geography Reference
In-Depth Information
where
q
.x
k
x
i
/
2
C
y
k
y
j
2
=V
m
q
x
k
x
j
2
C
.y
k
y
i
/
2
D
C
t
k
(12.35)
t
j
t
i
t
k
>0
T
k
D
(12.36)
0
else
Based on the consumer welfare theory that maximizing consumer surplus
(Wilson
1976
), the benefit from location (
x
k
,
y
k
) can be calculated as (Miller
1999
):
(
0
D
0orT
k
0
if
a
k
exp
h
˛
ln T
k
t
k
i
B
k
D
(12.37)
ˇ
ln a
k
C
else
and an additive accessibility provided by the choice set
k
2
[1,
n
] can be measure as
(Miller
1999
):
n
X
AM
D
B
k
(12.38)
k
D
1
However, this additive accessibility measure ignores the probability of choosing
each option in the choice set, and may misestimate the actual benefits that can
be provided to the individual. In order to solve this issue, we can incorporate the
visit probability developed in Sect.
12.3.1
, and define an accessibility measure for
expected/potential benefits:
B
k
P
.x
k
;y
k
/
ˇ
ˇ
ˇ
t
k
n
X
AM
D
(12.39)
k
D
1
where
P
((
x
k
,
y
k
)
j
t
k
) is the probability to visit location (
x
k
,
y
k
) at time
t
k
.Whatever
the actual method used to calculate the visit probability, it should always satisfy
the unity property given in Eq.
12.14
. As a result, the accessibility calculated
using Eq.
12.39
can avoid overestimation by assigning probabilities to each loca-
tional benefit. These probabilities can be estimated using the stochastic simulation
techniques discussed earlier in this chapter, modified to account for the varying
attractiveness of the activity locations.
12.4.2
Accessibility Cost
Although the space-time prism is an effective measure of potential benefits from
accessibility, there has been little attention paid to the cost of accessibility. When
applying prism measures in accessibility analysis, there is an implicit assumption
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