Modelling and optimisation of flows on networks: Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009]
Gespeichert in:
| Weitere Verfasser: | |
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| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
Springer
2013
|
| Schriftenreihe: | Lecture notes in mathematics
2062 : CIME Foundation subseries |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | XIV, 497 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642321593 9783642321597 |
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| 245 | 1 | 0 | |a Modelling and optimisation of flows on networks |b Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009] |c Luigi Ambrosio ..., Enrique Zuazua. Ed.: Benedetto Piccoli ... |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XIV, 497 S. |b graph. Darst. |c 235 mm x 155 mm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in mathematics |v 2062 : CIME Foundation subseries | |
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| 689 | 0 | 0 | |a Netzwerkfluss |0 (DE-588)4126130-6 |D s |
| 689 | 0 | 1 | |a Mathematisches Modell |0 (DE-588)4114528-8 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Ambrosio, Luigi |d 1963- |e Sonstige |0 (DE-588)133791408 |4 oth | |
| 700 | 1 | |a Piccoli, Benedetto |d 1968- |0 (DE-588)173402178 |4 edt | |
| 700 | 1 | |a Zuazua, Enrique |e Sonstige |4 oth | |
| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |z 978-3-642-32160-3 |
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| 943 | 1 | |a oai:aleph.bib-bvb.de:BVB01-025496590 | |
Datensatz im Suchindex
| _version_ | 1809404177774804992 |
|---|---|
| adam_text |
Contents
A User's Guide to Optimal Transport
. 1
Luigi Ambrosio
and Nicola
Gigli
1
Introduction
. 1
2
The Optimal Transport Problem
. 3
2.1
Monge
and Kantorovich Formulations of the
Optimal Transport Problem
. 3
2.2
Necessary and Sufficient Optimality Conditions
. 7
2.3
The Dual Problem
. 13
2.4
Existence of Optimal Maps
. 16
2.5
Bibliographical Notes
. 26
3
The
Wasserstein
Distance W2
. 28
3.1
X Polish Space
. 29
3.2
X Geodesic Space
. 37
3.3
X Riemannian Manifold
. 47
3.4
Bibliographical Notes
. 58
4
Gradient Flows
. 59
4.1
Hilbertian Theory of Gradient Flows
. 59
4.2
The Theory of Gradient Flows in a Metric Setting
. 61
4.3
Applications to the
Wasserstein
Case
. 81
4.4
Bibliographical Notes
. 92
5
Geometric and Functional Inequalities
. 93
5.1
Brunn-Minkowski Inequality
. 94
5.2
Isoperimetric Inequality
. 94
5.3
Sobolev Inequality
. 95
5.4
Bibliographical Notes
. 96
6
Variants of the
Wasserstein
Distance
. 97
6.1
Branched Optimal Transportation
. 97
6.2
Different Action Functional
. 99
6.3
An Extension to Measures with Unequal Mass
. 100
6.4
Bibliographical Notes
. 102
7
More on the Structure of (@>2(M),W2)
. 103
7.1
"Duality" Between the
Wasserstein
and the
Arnold Manifolds
. 103
7.2
On the Notion of Tangent Space
. 106
7.3
Second Order Calculus
. 107
7.4
Bibliographical Notes
. 130
8
Ricci
Curvature Bounds
. 131
8.1
Convergence of Metric Measure Spaces
. 134
8.2
Weak
Ricci
Curvature Bounds: Definition and
Properties
. 137
8.3
Bibliographical Notes
. 150
References
. 152
Hyperbolic Conservation Laws: An Illustrated Tutorial
. 157
Alberto
Bressan
1
Conservation Laws
. 158
1.1
The Scalar Conservation Law
. 158
1.2
Strictly Hyperbolic Systems
. 160
1.3
Linear Systems
. 161
1.4
Nonlinear Effects
. 163
1.5
Loss of Regularity
. 164
1.6
Wave Interactions
. 166
2
Weak Solutions
. 167
2.1
Rankine-Hugoniot Conditions
. 168
2.2
Construction of Shock Curves
. 172
2.3
Admissibility Conditions
. 173
3
The Riemann Problem
. 179
3.1
Some Examples
. 179
3.2
A Class of Hyperbolic Systems
. 182
3.3
Elementary Waves
. 184
3.4
General Solution of the Riemann Problem
. 187
3.5
The Riemann Problem for the p-System
. 190
3.6
Error and Interaction Estimates
. 194
4
Global Solutions to the Cauchy Problem
. 196
4.1
Front Tracking Approximations
. 197
4.2
Bounds on the Total Variation
. 200
4.3
Convergence to a Limit Solution
. 203
5
The
Glimm
Scheme
. 205
6
Continuous Dependence on the Initial Data
. 210
6.1
Unique Solutions to the Scalar Conservation Law
. 211
6.2
Linear Hyperbolic Systems
. 212
6.3
Nonlinear Systems
. 213
7
Uniqueness of Solutions
. 216
7.1
An Error Estimate for Front Tracking Approximations
. 217
7.2
Characterization of Semigroup Trajectories
. 218
7.3
Uniqueness Theorems
. 221
8
The Vanishing Viscosity Approach
. 223
8.1
Local Decomposition by Traveling Waves
. 226
8.2
Evolution of Gradient Components
. 230
8.3
Lyapunov Functionals
. 231
8.4
Continuous Dependence on the Initial Data
. 236
8.5
The Semigroup of Vanishing Viscosity Limit Solutions
. 237
9
Extensions and Open Problems
. 238
9.1
Compactness Theorems
. 239
9.2
An Elementary Error Estimate
. 240
9.3
The Center Manifold Theorem
. 241
References
. 243
Derivation of Non-local Macroscopic Traffic Equations and
Consistent Traffic Pressures from Microscopic Car-Following Models
_ 247
Dirk Helbing
1
Introduction
. 247
2
The Gradient Expansion Approach
. 248
3
The Linear Interpolation Approach
. 250
4
An Approach Reminding of Smooth Particle
Hydrodynamics
. 253
4.1
Derivation of the Continuity Equation
. 253
4.2
Derivation of the Macroscopic Velocity Equation
. 255
4.3
Discussion of the Non-locality
. 260
4.4
Comparison with Other Macroscopic Traffic Models
. 260
5
Summary, Discussion, and Conclusions
. 266
References
. 268
On the Controversy Around Daganzo's Requiem for and
Aw-Rascle's Resurrection of Second-Order Traffic Flow Models
. 271
Dirk Helbing and Anders Johansson
1
Introduction
. 272
2
Summary of the Controversy Regarding
Second-Order Traffic Flow Models
. 273
3
Linear Instability of Macroscopic Traffic Models
. 275
3.1
Derivation of the Instability Condition
. 278
3.2
Characteristic Speeds, Phase, and Group Velocities
. 279
4
Discussion
. 281
4.1
Characteristic Speeds in the Aw-Rascle Model
. 281
4.2
Payne's Traffic Model
. 282
4.3
Characteristic Speeds Vs. Vehicle Speeds
. 284
5
Linear Instability and Characteristic Speeds
of the Optimal Velocity Model
. 286
6
Summary, Conclusions, and Outlook
. 289
Appendix
1
Hyperbolic Sets of Partial Differential Equations
and Characteristic Speeds
. 291
Appendix
2
Stability Analysis for Macroscopic Traffic Models
. 293
Appendix 3
Derivation of Formula
(19). 294
Appendix
4
Meaning of the Group Velocity
. 296
Appendix
5
Linear Stability Analysis of the Optimal Velocity Model
. 297
Appendix
6
Correspondence of the Optimal Velocity Model with
the Macroscopic Payne Model
. 299
References
. 300
Theoretical vs. Empirical Classification and Prediction of
Congested Traffic States
. 303
Dirk Helbing, Martin
Treiber, Arne
Resting, and Martin
Schönhof
1
Introduction
. 303
2
On the Definition of Traffic Phases
. 306
3
Congested Traffic States
. 307
4
Derivation and Explanation of the Phase Diagram
of Traffic States
. 309
4.1
Transition to Congested Traffic for Small Bottlenecks
_ 313
4.2
Conditions for Different Kinds of Congested
Traffic After the Breakdown of Traffic Flow
. 315
5
Combinations of On- and Off-Ramps
. 318
6
Other Phase Diagrams and Universality Classes of Models
. 321
7
Empirical Phase Diagram
. 324
7.1
Reply to Criticisms of Phase Diagrams for
Traffic Models with a Fundamental Diagram
. 325
7.2
On the Validity of Traffic Models
. 326
8
Summary, Conclusions, and Outlook
. 328
Appendix
1
Modeling of Source and Sink Terms (In- and Outflows)
. 329
Appendix
2
Parameter Dependence of the Instability Thresholds
in the Intelligent Driver Model
. 330
References
. 331
Self-Organized Network Flows
. 335
Dirk Helbing, Jan Siegmeier, and Stefan
Lämmer
1
Introduction
. 335
2
Flows in Networks
. 336
2.1
Flow Conservation Laws
. 337
2.2
Two Views on Traffic Jams
. 339
3
Treatment of Merging, Diverging and Intersection Points
. 344
3.1
Diverging Flows: One Inflow and Several Outflows
. 345
3.2
Merging Flows: Two Inflows and One Outflow
. 345
3.3
A Side Road Merging with a Main Road
. 346
3.4
Intersection-Free Designs of Road Networks
. 347
3.5
Two Inflows and Two Outflows
. 348
3.6
Inefficiencies Due to Coordination Problems
. 350
4
Towards a Self-Organized Traffic Light Control
. 351
5
Summary and Outlook
. 353
References
. 354
Operation Regimes and Slower-is-Faster-Effect in
the Control
of Traffic Intersections
. 357
Dirk Helbing and
Amin Mazloumian
1
Introduction
. 357
1.1
Paradoxical Behavior of Transport Systems
. 358
2
Specification of the Traffic System Under Consideration
. 359
3
Consideration of Traffic Flows
. 362
4
Travel-Time-Oriented Signal Operation
. 364
4.1
The Optimize-One-Phase Approach
. 365
4.2
Transformation to Dimensionless Variables
and Parameters
. 368
4.3
Control Strategies and Slower-is-Faster Effect
. 371
4.4
Operation Regimes for Periodic Operation
. 372
4.5
Minimization of Vehicle Queues
. 375
4.6
Complexity of Traffic Light Control
. 375
5
Optimize-Multiple-Phases Approach
. 376
5.1
Combined Flow-and-Delay Time Optimization
. 377
6
Summary, Discussion, and Outlook
. 383
6.1
Self-Organized Traffic Light Control
. 385
Appendix
1
Considering the Price of Stopping Vehicles
. 387
Appendix
2
More Than Two Traffic Phases
. 389
Appendix
3
Limited Forecast Time Horizon
. 391
References
. 392
Modeling and Optimization of Scalar Flows on Networks
. 395
Simone Göttlich
and Axel
Klar
1
Introduction
. 395
2
Traffic Flow Networks
. 397
2.1
Network Models Based on Scalar Partial
Differential Equations
. 397
2.2
Simplified Dynamics on the Network
. 410
2.3
Optimization
. 415
2.4
Summary
. 436
3
Modeling Supply Networks
. 437
3.1
Network Models Based on Scalar Conservation Laws
_ 437
3.2
Optimization Problems
. 442
3.3
Numerical Results
. 451
3.4
Summary
. 459
References
. 459
Control and Stabilization of Waves on 1-d Networks
. 463
Enrique Zuazua
1
Introduction and Main Results
. 464
2
The Wave Equation on a Network
. 468
3
Main Results on Observability and Controllability
. 474
3.1
Summary of Known Results
. 474
3.2
The Weighted Observability Inequality
. 477
4
Stabilization
. 478
4.1
Problem Formulation
. 478
4.2
Observability for the Damped System
. 482
4.3
The Interpolation Inequality
. 484
4.4
The Main Result
. 486
5
Further Comments and Open Problems
. 487
References
. 491 |
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| series2 | Lecture notes in mathematics |
| spelling | Modelling and optimisation of flows on networks Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009] Luigi Ambrosio ..., Enrique Zuazua. Ed.: Benedetto Piccoli ... Berlin [u.a.] Springer 2013 XIV, 497 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Lecture notes in mathematics 2062 : CIME Foundation subseries Netzwerkfluss (DE-588)4126130-6 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf (DE-588)1071861417 Konferenzschrift gnd-content Netzwerkfluss (DE-588)4126130-6 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Ambrosio, Luigi 1963- Sonstige (DE-588)133791408 oth Piccoli, Benedetto 1968- (DE-588)173402178 edt Zuazua, Enrique Sonstige oth Erscheint auch als Online-Ausgabe 978-3-642-32160-3 Lecture notes in mathematics 2062 : CIME Foundation subseries (DE-604)BV000676446 2062 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4068535&prov=M&dok%5Fvar=1&dok%5Fext=htm Inhaltstext Digitalisierung UB Passau application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025496590&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Modelling and optimisation of flows on networks Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009] Lecture notes in mathematics Netzwerkfluss (DE-588)4126130-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4126130-6 (DE-588)4114528-8 (DE-588)1071861417 |
| title | Modelling and optimisation of flows on networks Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009] |
| title_auth | Modelling and optimisation of flows on networks Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009] |
| title_exact_search | Modelling and optimisation of flows on networks Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009] |
| title_full | Modelling and optimisation of flows on networks Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009] Luigi Ambrosio ..., Enrique Zuazua. Ed.: Benedetto Piccoli ... |
| title_fullStr | Modelling and optimisation of flows on networks Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009] Luigi Ambrosio ..., Enrique Zuazua. Ed.: Benedetto Piccoli ... |
| title_full_unstemmed | Modelling and optimisation of flows on networks Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009] Luigi Ambrosio ..., Enrique Zuazua. Ed.: Benedetto Piccoli ... |
| title_short | Modelling and optimisation of flows on networks |
| title_sort | modelling and optimisation of flows on networks cetraro italy 2009 cime course on modelling and optimisation of flows on networks held in cetraro in the summer of 2009 |
| title_sub | Cetraro, Italy 2009 [CIME course on modelling and optimisation of flows on networks held in Cetraro in the summer of 2009] |
| topic | Netzwerkfluss (DE-588)4126130-6 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | Netzwerkfluss Mathematisches Modell Konferenzschrift |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4068535&prov=M&dok%5Fvar=1&dok%5Fext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025496590&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000676446 |
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