Dynamics and Stochasticity in Transportation Systems : Tools for Transportation Network Modelling

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. 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 Dynamics and Stochasticity in Transportation Systems: Solutions for Transportation Network Modeling breaks new ground on the topics, providing consistent and comprehensive coverage of steady state equilibrium and dynamic assignment within a common strategy. The book details the most recent advances in network assignment, including day-to-day and within-day dynamics, providing a solid foundation to help transportation planners solve transient overload and other problems. Users will find a book that fills the gap in knowledge with its description on how to use and employ the latest dynamic network models for evaluation of traffic and transport demand interventions. This book demystifies the many different dynamic traffic assignment approaches and requires no previous knowledge on the part of the reader. All results are fully described and proven, thus eliminating the need to seek out other references. The skills described will appeal to transportation professionals, researchers and graduate students alike. Presents a consistent and comprehensive theory on steady state equilibrium assignment and day-to-day dynamic assignment models within a common framework Describes and solves modeling calculations in detail, with no need to reference other sources Includes numerical and graphical examples, text boxes and summaries at the end of each chapter to help readers better understand theoretical components Includes primary mathematical tools necessary for each dynamic model, easing comprehension "Dynamics and Stochasticity in Transportation Systems: Solutions for Transportation Network Modeling breaks new ground on the topics, providing consistent and comprehensive coverage of steady state equilibrium and dynamic assignment within a common strategy. The book details the most recent advances in network assignment, including day-to-day and within-day dynamics, providing a solid foundation to help transportation planners solve transient overload and other problems. Users will find a book that fills the gap in knowledge with its description on how to use and employ the latest dynamic network models for evaluation of traffic and transport demand interventions. This book demystifies the many different dynamic traffic assignment approaches and requires no previous knowledge on the part of the reader. All results are fully described and proven, thus eliminating the need to seek out other references. The skills described will appeal to transportation professionals, researchers and graduate students alike."-- Publisher's website