Geography Reference
In-Depth Information
f
e
Œ
t
s
;t
e
i
;
v
..x;y/;t;s.e
i
;t//
Z
l
e
Z
t
0
max
l
t
0
D
..x;y/;s.e
i
;t //
dldt
(7.7)
t
0
min
l
s
..
x;y
/
;s
.
e
i
;t
//
C
v
.x; y/ ; t
i
.1
C
s.e
i
;t//t
l
t
i
C
t
..
x
C
x;y
C
y
/
;s
.
e
i
;t
//
D
l
t
i
(7.8)
Equations
7.6
,
7.7
,and
7.8
describe a dynamic transportation network-based
prism incorporating the congestion index. Equation
7.8
represents the set of space-
time points constrained by the congestion index, which reflects the influence of the
congestion index on travel time.
7.3
Critical Links and Activity Opportunities
Unlike the network structure analysis approach used for critical links in transporta-
tion, this chapter uses the frequency of taxi trajectories on links to identify critical
links for activity scheduling because taxi drivers usually choose high-utility (low-
cost and fast) routes in an urban environment. In other word, the critical links with
higher frequency are easier and more convenient for travelers to follow when they
carry out their activities. This chapter introduces several definitions related to critical
links and opportunities.
Let EUN denote the number of taxi trajectories using an edge within a time
period [
t
s
,
t
e
], which is defined as follows:
EUN .e;Œt
s
;t
e
/
D
X
i
X
.i;e;t/; t
s
< t < t
e
(7.9)
t
subject to:
0 if taxi i did not pass link e at time t
1otherwise
.i;e; t/
D
(7.10)
Equation
7.10
represents the individual frequency value derived from the situa-
tion that taxi
i
either passed over link
e
at time
t
or not. Figure
7.2
illustrates the
number of taxi trajectories using an edge in a dynamic transportation network. The
thick black lines highlight the critical links of taxi trajectories in this network during
a specific time period.
The critical index of a link
e
in a space-time environment is denoted as CI, which
is defined as:
EUN
.e; Œt
s
;t
e
/
max UN
.e
i
;Œt
s
;t
e
/
;e
i
CI .e; Œt
s
;t
e
/
D
2
E
(7.11)
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