Geoscience Reference
In-Depth Information
Table 15.3
Path definitions, target times, optimal path flows, optimal path time deviations, and
optimal lagrange multipliers for the numerical example
Path definition
x
p
*
z
p
*
ˉ
p
*
T
kp
P
R
1
: set of paths corresponding to demand
point
R
1
p
1
¼
(1, 5,
7, 9,13,15)
65
13.95 53.66 321.99
p
2
¼
(1, 5,
7, 9,13,16)
64
5.28 39.23 235.39
p
3
¼
(1, 5,
7,10,13,15)
61
0.00 19.32 115.90
p
4
¼
(1, 5,
7,10,13,16)
60
0.00
4.83
28.99
p
5
¼
(2, 6,
8,11,14,18)
61
0.06 18.67 112.03
p
6
¼
(2, 6,
8,12,14,18)
64.5
6.79 43.12 258.75
p
7
¼
(3, 9,13,15)
62
0.00 56.66 339.99
p
8
¼
(3, 9,13,16)
61
0.00 42.23 253.39
p
9
¼
(3,10,13,15)
58
0.00 22.34 134.05
p
10
¼
(3,10,13,16)
57
0.00
7.84
47.03
p
11
¼
(4,11,14,18)
59
0.00 20.71 124.24
p
12
¼
(4,12,14,18)
62.5
0.00 45.24 271.46
P
R
2
: set of paths corresponding to demand
point
R
2
p
13
¼
(1, 5,
7, 9,13,17)
63
0.00 13.87
83.25
p
14
¼
(1, 5,
7,10,13,17)
59
0.00
0.00
0.00
p
15
¼
(2, 6,
8,11,14,19)
59
0.13
0.00
0.00
p
16
¼
(2, 6, 8,11,14,
20)
60
0.04
0.00
0.00
p
17
¼
(2, 6,
8,12,14,19)
62.5
5.55 19.91 119.44
p
18
¼
(2, 6, 8,12,14,
20)
63.5
7.45 22.40 134.43
p
19
¼
(3, 9,13,17)
60
0.00 16.90 101.41
p
20
¼
(3,10,13,17)
56
0.00
0.00
0.00
p
21
¼
(4,11,14,19)
57
0.00
0.00
0.00
p
22
¼
(4,11,14, 20)
58
0.00
0.00
0.00
p
23
¼
(4,12,14,19)
60.5
0.00 21.96 131.77
p
23
¼
(4,12,14, 20)
61.5
0.00 24.48 146.85
0
@
1
A
,
ʳ
R
1
ðÞ¼
3
X
p∈P
R
1
ʳ
R
2
ðÞ¼
3
X
p∈P
R
2
z
p
z
p
:
The Euler method (cf. (
15.31
)-(
15.33
)) for the solution of variational inequality
(
15.24
) was implemented in FORTRAN on a PC at the University of Massachusetts
