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Tables of Contents for Transportation Network Analysis
Chapter/Section Title
Page #
Page Count
Preface
V
1 Introduction
1
16
1.1 Motivation and approach
1
1
1.2 Network representation
2
1
1.3 Modes of travel
3
1
1.4 Network equilibrium
3
2
1.5 Generalised costs
5
1
1.6 Demand curves
6
1
1.7 Link cost functions
6
4
1.8 Supply curves
10
2
1.9 Intermodal equilibrium
12
2
1.10 User benefit and surplus
14
1
1.11 Time dependency
15
1
1.12 Structure of the book
15
2
2 Transportation Networks
17
24
2.1 Introduction
17
1
2.2 Network terminology
17
2
2.3 Transportation network types
19
2
2.4 Flow and cost variables
21
1
2.5 Incidence matrices
22
2
2.6 Conservation relationships
24
1
2.7 Shortest path algorithms
25
4
2.8 Path enumeration and column generation
29
1
2.9 Link choice probabilities
29
4
2.10 Utility maximisation and expected minimum cost
33
1
2.11 Network capacity
34
1
2.12 Space-time networks
34
3
2.13 Network equilibrium
37
3
2.14 Concluding remarks
40
1
3 Optimality
41
26
3.1 Introduction
41
1
3.2 Kinds of variable
41
1
3.3 Matrix operations
42
3
3.4 Objective functions
45
2
3.5 Constraints
47
2
3.6 Optimality conditions
49
2
3.7 Dual variables
51
3
3.8 Lagrangian equation
54
2
3.9 Sensitivities
56
3
3.10 Method of successive averages
59
1
3.11 Iterative balancing
59
2
3.12 Summary
61
4
3.13 Notation
65
2
4 Cost Functions
67
16
4.1 Introduction
67
1
4.2 Traffic representation
67
1
4.3 Link costs
68
4
4.4 Junction costs
72
6
4.5 Priority junctions
78
1
4.6 Signal controlled junctions
78
4
4.7 Discussion
82
1
5 Deterministic User Equilibrium Assignment
83
30
5.1 Introduction
83
3
5.2 Existence and uniqueness
86
3
5.3 Solution algorithms
89
6
5.4 Sensitivity
95
5
5.5 Most likely path flows
100
2
5.6 Elastic demand
102
6
5.7 Time-dependent networks
108
3
5.8 Discussion
111
2
6 Stochastic User Equilibrium Assignment
113
36
6.1 Introduction
113
2
6.2 Existence and uniqueness
115
3
6.3 A general equivalent optimisation problem
118
2
6.4 Logit assignment
120
13
6.5 Probit assignment
133
1
6.6 Sensitivity
134
4
6.7 Elastic demand
138
2
6.8 Space-time networks
140
8
6.9 Discussion
148
1
7 Trip Table Estimation
149
30
7.1 Introduction
149
1
7.2 Maximum entropy
150
1
7.3 An generalised least squares
155
1
7.4 Bi-level programming
156
4
7.5 Linear path flow estimation
160
4
7.6 Log-linear path flow estimation
164
6
7.7 Time-dependent methods
170
6
7.8 Conclusions
176
3
8 Network Reliability
179
14
8.1 Introduction
179
1
8.2 Connectivity
179
1
8.3 Structure function
180
3
8.4 Structure function and reliability value
183
2
8.5 Exact methods
185
1
8.6 Heuristic methods
186
5
8.7 Travel time reliability
191
1
8.8 Future challenges
192
1
9 Network Design
193
12
9.1 Introduction
193
2
9.2 Objective function
195
1
9.3 Bi-Level programming
196
1
9.4 Sensitivities
197
2
9.5 Numerical example
199
5
9.6 Conclusions
204
1
10 Conclusions
205
4
10.1 Network equilibrium
205
1
10.2 Traffic assignment
206
1
10.3 Path flow estimation
207
1
10.4 Network reliability
208
1
10.5 Network design
208
1
References
209
6
Index
215