Geography Reference
In-Depth Information
nonuniform throughout the prism interior. The framework developed for the planar
space can also be modified for the network space considering travel time within
road network. This theoretical foundation can not only provide novel theoretical
insights into the space-time prism, but also refine the prism as a measure of potential
mobility. The next section provides two example applications to demonstrate the
potentials of these novel insights derived from looking inside the space-time prism.
12.4
Implications of Insights from Inside the Prism
12.4.1
Accessibility Benefit Measures
In general, accessibility is a term that describes the degree to which facilities,
services, or opportunities are available to people. In transportation planning and
research, accessibility plays a significant role in evaluating current infrastructure
and supporting political and planning decisions on future strategies. The space-
time prism is an elegant and sensitive accessibility measure: it captures individual
differences in scheduling constraints, the available locations and timing of activities,
and the ability of the transportation system in meeting an individual's mobility and
accessibility needs (Hägerstrand
1970
).
Miller (
1999
) develops an analytical framework and computational procedures
to derive accessibility benefit measures that are consistent with the rigorous Weibull
(
1976
) axiomatic approach to the measurement of accessibility. This framework
reconciles three complementary approaches to accessibility: (1) the constraints-
oriented approach implemented by Hägerstrand's space-time prism; (2) the gravity-
based approach that weights location's attractiveness against its required travel
cost; and (3) a benefits measure based on the microeconomic theory of consumer
surplus. In this section, we introduce and modify this space-time accessibility
benefit measure by including visit probabilities in the first approach.
Considering the generic utility function (Burns
1979
; Miller
1999
)
u
.a; T; t /
D
a
˛
T
ˇ
exp .
t/
(12.33)
where
a
indicates the attractiveness of the activity location,
T
is the time available
for activity participation,
t
is required travel time from the first anchor to the activity
location and subsequently to the second anchor, and ˛, ˇ,and are parameters.
Assume that an individual cannot leave a fixed activity location (
x
i
,
y
i
) until
t
i
and has to participate in another activity at location (
x
j
,
y
j
)by
t
j
, the utility of
participating an activity at location (
x
k
,
y
k
) can be calculated by modifying Eq.
12.33
and the analytical prism with no stationary activity time (see Eqs.
12.1
,
12.2
,
12.3
,
and
12.4
and
t
s
D
0):
u
.a
k
;T
k
;t
k
/
D
a
k
T
k
exp
.
t
k
/
(12.34)
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