Since hunting gathering era human brains have evolved to be more sensitive to var-
iations in space and/or time of the surrounding environment rather than regularity
and uniformity; (mostly unconscious) representations of location over space and
evolution over time allowed human beings to survive in challenging conditions. This
is still the case: a pedestrian wishing to cross a urban street tries to anticipate evo-
lution over time of the locations of the surrounding vehicles.
Developing a (mathematical) model of real systems, as common in modern
applied sciences, is a more conscious way to follow that ancestral attitude.
Author(s): Giulio Erberto Cantarella, David Paul Watling, Stefano de Luca, Roberta Di Pace
Publisher: Elsevier
Year: 2020
Language: English
Pages: 345
Cover......Page 1
Dynamics and
Stochasticity in
Transportation
Systems:
Tools for Transportation
Network Modelling
......Page 3
Copyright......Page 4
Contributors......Page 5
Preface......Page 6
Purpose of this book......Page 8
Contribution of this book......Page 12
Traffic analysis......Page 13
Transportation systems analysis......Page 14
Transportation supply analysis......Page 15
Traffic control......Page 16
Transportation systems control and design......Page 17
Major findings......Page 18
References......Page 19
Acknowledgements......Page 20
1
Introduction......Page 21
Basic elements of graph and network theory......Page 24
Graphs and networks in transportation system analysis......Page 28
Time modelling: Dynamic models......Page 29
Uncertainty modelling: Stochastic models......Page 32
Founding conceptual equations......Page 33
Further readings......Page 34
References......Page 35
2
Assignment to uncongested networks......Page 36
Basic notations and definitions......Page 37
Basic assignment models......Page 42
Supply model......Page 43
Demand model......Page 44
Parking choice behaviour......Page 47
Independent route formulations......Page 48
Multi class assignment......Page 51
Supply model......Page 52
Demand model......Page 53
Reduction to the standard form......Page 54
Multi-vehicle and multi-mode assignment......Page 55
Arc flow function and arc feasible set......Page 56
Remarks......Page 59
References......Page 60
3
Assignment to congested networks: User equilibrium-Fixed points......Page 61
Basic equations......Page 62
Supply models......Page 64
Demand models......Page 68
Fixed-point models for equilibrium assignment......Page 70
Two equation assignment models......Page 72
Existence and basic uniqueness analysis......Page 74
Basic uniqueness conditions......Page 75
Solution algorithms and convergence analysis......Page 77
Advanced uniqueness and convergence analysis......Page 78
Further readings......Page 87
Remarks......Page 88
Convergence of MSA algorithms through a corollary of Blum's theorem for compact sets......Page 92
Convergence of the MSA-FA algorithm......Page 93
Convergence of the MSA-CA algorithm......Page 95
References......Page 96
4
Assignment to congested networks: Day-to-day dynamics-Deterministic processes......Page 98
Basic equations for simple DP models......Page 100
Supply models for simple DP models......Page 102
Demand models for simple DP models......Page 107
Simple DP models......Page 110
Two equation assignment models......Page 111
Fixed point states......Page 114
Solution issues and convergence analysis......Page 117
Dissipativeness analysis......Page 120
Dissipativeness of DP-ES/ES......Page 121
Dissipativeness of DP-MA/ES......Page 122
Dissipativeness of DP-OEAMs......Page 123
Local stability analysis......Page 124
Local stability condition......Page 127
Local stability condition for arc cost functions with symmetric Jacobian......Page 130
Local stability condition for arc cost functions with symm. positive semi-definite Jacobian......Page 131
Local bifurcation analysis......Page 132
Basic equations for general models......Page 134
Supply models for general DP models......Page 135
Demand models for general DP models......Page 136
Two equation assignment models......Page 140
OEAMs......Page 141
Fixed-point states of general deterministic processes......Page 142
General fixed-point existence conditions......Page 144
General fixed-point uniqueness conditions......Page 145
Major findings......Page 146
Remarks......Page 147
Appendix A: Dissipativeness of DP-MA/ES (adapted from Cantarella and Watling, 2016)......Page 148
Appendix B: Local stability conditions for of DP-ES/ES......Page 151
Local stability conditions for of DP-ES/ES......Page 152
Appendix C: DP with today states depending on itself (adapted from Cantarella and Watling, 2016)......Page 156
References......Page 158
Further reading......Page 159
5
Assignment to congested networks: Day-to-day dynamics-Stochastic processes......Page 160
Basic equations for SP models......Page 162
Supply models for SP......Page 165
Demand models for SP models......Page 168
General SP models......Page 172
General two equation assignment models......Page 173
Ergodic sets of stochastic processes......Page 175
Regularity conditions-Invariant distribution existence and uniqueness conditions......Page 176
Solution issues and convergence analysis......Page 178
Major findings......Page 182
Further readings......Page 183
Further reading......Page 184
6
Assignment to transportation networks: Within-day dynamics......Page 185
Basic equations......Page 187
Supply models......Page 188
Demand model......Page 195
Assignment......Page 197
Uncongested networks......Page 198
Congested networks: Day-to-day dynamics-Dynamic process models......Page 199
References......Page 200
Further reading......Page 201
7
Conclusion......Page 202
Remarks......Page 204
Further reading......Page 205
A short history of this book......Page 206
A final comment......Page 208
Appendix A: Discrete choice modelling with application to route and departure time choice......Page 209
Random utility theory for modelling travellers choice......Page 212
Choice set definition......Page 213
Specification of the systematic utility......Page 215
Distribution of perceived utility and choice functions......Page 218
Homoscedastic and correlated perceived utilities......Page 221
Heteroscedastic and correlated perceived utilities......Page 223
Calibration and validation of a choice model......Page 225
Analysis on utility parameters......Page 226
Test and indicators based on Log-Likelihood value......Page 227
Analysis of clearness of predictions......Page 229
Random utility models for route choice......Page 230
Formalisation of an interpretative framework......Page 231
Trip behaviour and alternatives in route choice modelling......Page 232
Holding choice in route choice modelling......Page 234
Multinomial Logit and Logit-based model......Page 235
Multinomial Weibit model......Page 236
Multinomial Probit model......Page 237
Multinomial Gammit model......Page 239
Updating choices in route choice modelling......Page 240
Switching choices in route choice modelling......Page 241
Diversion choices in route choice modelling......Page 244
Explicit model of adaptation to information......Page 245
Implicit model of adaptation to information......Page 246
Explicit model of the cognitive process to acquire and use the information......Page 248
Random utility models for departure time and route choice modelling......Page 250
Fuzzy utility models for modelling travellers choice......Page 252
Distribution of perceived utility and choice functions......Page 254
Neural network for modelling travellers choice......Page 256
Specification and calibration of a neural network model......Page 260
Major findings......Page 263
Further readings......Page 264
Mathematical properties of random or deterministic utility models......Page 265
Fuzzy and crisp sets......Page 270
Uncertain numbers......Page 271
References......Page 273
Further reading......Page 277
Appendix B: Traffic flow theory......Page 278
Basic TFT......Page 279
Running links......Page 280
Queuing links......Page 282
Running links......Page 283
Queuing links-Deterministic models......Page 287
Queuing links-Stochastic models......Page 290
M/M/1 systems......Page 291
Running links......Page 292
Queuing links......Page 294
Point based models......Page 295
Propagation of density variations......Page 296
Shock waves......Page 297
Payne model......Page 298
Kerner and Konhäuser model [KK model]......Page 299
Continuous time discrete space macroscopic models......Page 300
Running links......Page 301
Wave models......Page 302
Newell model......Page 303
Running links......Page 306
Network equations......Page 308
Discrete time discrete space macroscopic models......Page 309
Finite difference models......Page 310
The cell transmission model......Page 311
Network equations......Page 312
Mesoscopic models......Page 314
Traffic analysis and flow forecasting mesoscopic dynamic [TRAFFMED]......Page 315
Network equations......Page 318
Microscopic models......Page 319
Gazis-Herman-Rothery (GHR) model......Page 321
Stability in microscopic models......Page 322
Link between microscopic and macroscopic models......Page 324
Wiedemanns model......Page 325
Nagel-Schreckenberg model......Page 328
Further readings......Page 329
Queuing in macroscopic models......Page 332
Dispersion in macroscopic models......Page 333
References......Page 334
Further reading......Page 337
Index......Page 338
Back cover......Page 345
