Geography Reference
In-Depth Information
where
Z
ij
(
t
) is the spatial extent of all accessible locations at time
t
2
[
t
i
,
t
j
]
,P
((
x
,
y
)
j
t
)
is the probability for location (
x
,
y
) to be visited, and
P
t
(
v
j
(
x
,
y
)) is the velocity
profile at that location. The accessibility-related environmental cost calculated in
this framework can be combined with the benefits accessibility measures, and
used to develop a benefit-cost framework for evaluation within the sustainable
transportation paradigm.
12.5
Conclusion
The potential of space-time prism in analyzing individual's potential mobility and
accessibility has been widely acknowledged and applied in transportation science,
urban planning, public health and other human sciences. A space-time prism
captures all locations that can be reached in space and time given the origin and
destination locations, the earliest departure time from the origin, the latest arrival
time at destination, the maximum allowed travel velocity and the minimum time
required for activities participation. The boundary of the prism is the envelope of all
accessible locations, and has been recognized and proven as an effective measure
of individual mobility and accessibility to the environment and opportunities in that
environment.
However, little attention has been paid to the prism interior and its mobility-
related properties. Visit probabilities and velocity distributions are two properties
that should not be expected to be uniform distributed throughout the prism interior.
This chapter analyzes these properties of the prism interior and the implications of
these properties for measuring accessibility benefits and costs. Based on discrete
space and time, we modify the classic undirected random walk theory to consider
constraints imposed by the requirement to be at the second anchor by a specified
time. We develop a framework for directed movements in continuous time and space
using Brownian Bridges techniques. We also consider uniform and non-uniform
velocity distributions, the latter based on temporal constraints and visit probability
distributions. To illustrate the potentials of estimating the properties of the prism
interior, we provide two examples: (1) a modified utility-based accessibility benefit
measure that considers the visit probabilities; and (2) a new measure for the potential
environmental costs of accessibility based on the visit probability and velocity
distribution.
Novel insights into the internal structure of the space-time prism can improve
not only the theoretical understanding of the space-time prism, but also the
practical applications of it. By introducing the visit probability, existing prism-based
accessibility measures can be modified to avoid the overestimate of individual acces-
sibilities and location opportunities. In addition, the velocity distribution along with
the visit probability at each accessible location enables us to estimate the potential
environment costs to facilitate mobility at that location (e.g. energy consumption
and waste emissions). The environment cost challenges the fundamental assumption
that greater accessibility is an unmitigated benefit to individuals and society, and
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