Geography Reference
In-Depth Information
Fig. 12.3
Available time
interval [t
min
,t
max
]atan
accessible location
q
x
x
j
2
C
y
y
j
2
V
m
t
max
D
t
j
(12.6)
where
t
min
is the earliest time an individual can reach that location from origin and
t
max
is the latest time s/he has to leave that location in order to reach destination on
time. An opportunity is accessible to the individual only if it is located within the
PPA and its own available time [
t
start
,
t
end
] (e.g. opening hours of the grocery store)
intersects the time available at that location [
t
min
,
t
max
] to a sufficient degree, that is,
no less than the minimum required time for activity participation
t
s
(Fig.
12.3
):
t
.x; y/
D
min .t
end
;t
max
/
max .t
start
;t
min
/
t
s
(12.7)
In the real world, an individual's movements are often confined by the geometry
and velocity limits allowed by transport networks (Miller
1991
). Kuijpers and
Othman (
2009
) extend the two definitions above to define the
network time prism
(NTP). Given a road network
RN
, the NTP at any instant time
t
2
(
t
i
,
t
j
) can be
defined mathematically as:
n
.x; y/
ˇ
ˇ
ˇ
RN
o
Z
ij
.t /
D
f
i
.t /
\
p
j
.t /
\
g
ij
\
(12.8)
n
.x; y/
ˇ
ˇ
ˇ
t
RN
..x
i
;y
i
/ ; .x; y//
t
t
i
o
f
i
.t /
D
(12.9)
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