Geography Reference
In-Depth Information
subject to:
Z
t
e
D
Length
l
s
;l
e
v
..x; y/ ; t / dt
(7.3)
t
s
.
x;y
/
C
v
.x; y/ ; t
i
t
l
t
i
C
t
.
x
C
x;y
C
y
/
D
l
t
i
(7.4)
8
<
X
n
1
n
v
i
;
if a moving car has passed
v
.x; y/
D
(7.5)
:
i
D
1
v
;
otherwise
Equations (
7.1
)and(
7.2
) represent a time-varying network-based prism and a
time-varying accessible vertical area derived from edge
e
i
,where
t
0
s
,
t
0
e
,
t
0
min
,and
t
0
max
are time- and location-dependent variables and
v
((
x
,
y
),
t
) is an instantaneous travel
speed at location (
x
,
y
) at time
t
. Equation (
7.3
) defines the condition that the total
travel distance is covered within a time interval [
t
0
s
,
t
0
e
].
l
(
x
,
y
)
is a space-time point in
3D space.
Length
(
l
0
s
,
l
0
e
) denotes the accessible length of edge
e
i
in TVNBP. Equation
(
7.4
) illustrates the dynamic motion process from point l
t
i
.x;y/
to point l
t
i
C
.x
C
x;y
C
y/
along edge
e
i
,where
t
is a variable indicating a small time slice. Equation (
7.5
)
defines the travel speed used to evaluation the congestion index. This speed is the
average of the speed values in all trajectories in which there are some moving cars
passing over edge
e
i
. If no moving cars are present, the speed on edge
e
i
is the
average value of the speeds on all transportation links with the same road function
and hierarchical position as edge
e
i
. Figure
7.1
illustrates a time-varying network-
based prism as represented by lines (Fig.
7.1
a) and three-dimensional polygons
(Fig.
7.1
b).
The TVNBP can be extended by considering the influence of the congestion
index as follows:
TVNBP
0
.O;D;T/
D
X
e
i
2
f
e
Œ
t
s
;t
e
i
;
v
..x; y/ ; t; s .e
i
;t//
(7.6)
E
Fig. 7.1
Time-varying network-based prism
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