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Table 2 Results for the 5-link network for different link tolls

From: A smoothing approach for solving transportation problem with road toll pricing and capacity expansions

Link flow

1

3

5

\(\boldsymbol{\tau_{1\cdots{5}}}\)

\(x_{1}\)

1.514

1.381

1.274

1.282

\(x_{2}\)

2.875

2.282

1.169

2.108

\(x_{3}\)

0.00

0.00

0.00

0.00

\(x_{4}\)

1.514

1.381

1.274

1.282

\(x_{5}\)

2.875

2.875

1.169

2.108

\(y_{1}\)

0.000

0.000

0.000

0.000

\(y_{5}\)

1.875

1.282

0.169

1.108

\(q_{14}\)

4.390

3.662

2.442

3.390

\({F_{\mathrm{max}}}\)

178.303

144.662

110.568

140.699

Net benefit

1,250.7

1,151.8

1,099.7

1,153.9