Traffic flow on networks: conservation laws models
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Springfield, Mo.
American Inst. of Math. Sciences
2006
|
| Series: | AIMS series on applied mathematics
1 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 243 S. graph. Darst. |
| ISBN: | 1601330006 9781601330000 |
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| 245 | 1 | 0 | |a Traffic flow on networks |b conservation laws models |c Mauro Garavallo and Benedetto Piccoli |
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| adam_text | AIMS SERIES ON APPLIED MATHEMATICS VOLUME 1 TRAFFIC FLOW ON NETWORKS
CONSERVATION LAWS MODELS MAURO GARAVELLO AND BENEDETTO PICCOLI
TECHNISCHE INFORMATIONSBIBLIOTHEK UNIVERSITATSBIBLIOTHEK HANNOVER AIMS
AMERICAN INSTITUTE OF MATHEMATICAL SCIENCES CONTENTS 1 INTRODUCTION 1
1.1 BOOK CHAPTERS 7 2 CONSERVATION LAWS 9 2.1 BASIC DEFINITIONS 9 2.2
WEAK SOLUTIONS 10 2.3 ENTROPY ADMISSIBLE SOLUTIONS 16 2.3.1 SCALAR CASE
16 2.4 RIEMANN PROBLEM 17 2.4.1 THE NON-CONVEX SCALAR CASE 23 2.5
FUNCTIONS WITH BOUNDED VARIATION 26 2.5.1 BV FUNCTIONS IN RN 30 2.6
WAVE-FRONT TRACKING AND EXISTENCE OF SOLUTIONS 32 2.6.1 THE SCALAR CASE
32 2.6.2 THE SYSTEM CASE 37 2.7 UNIQUENESS AND CONTINUOUS DEPENDENCE 38
2.8 EXERCISES 43 2.9 BIBLIOGRAPHICAL NOTE 44 3 MACROSCOPIC TRAFFIC
MODELS 47 3.1 LIGHTHILL-WHITHAM-RICHARDS MODEL 47 3.1.1 DERIVATION OF
THE EQUATION 48 3.1.2 FUNDAMENTAL DIAGRAMS 48 3.1.3 RIEMANN PROBLEMS 49
3.1.4 THE NOT STRICTLY CONCAVE CASE 52 3.1.5 LIGHTHILL-WHITHAM-RICHARDS
MODEL WITH VISCOSITY 53 3.2 PAYNE-WHITHAM MODEL 55 3.3 DRAWBACKS OF
SECOND ORDER MODELS 56 3.4 AW-RASCLE MODEL 57 3.4.1 CHARACTERISTIC
FIELDS 58 3.4.2 DOMAINS OF INVARIANCE 58 XIV CONTENTS 3.5 THIRD ORDER
MODELS 60 3.6 HYPERBOLIC PHASE TRANSITION MODEL 61 3.6.1 THE RIEMARM
PROBLEM 62 3.7 A MULTILANE MODEL 64 3.8 A MULTIPOPULATION MODEL 66 3.8.1
THE CASE N = 2 68 3.9 EXERCISES 69 3.10 BIBLIOGRAPHICAL NOTE 70 4
NETWORKS 71 4.1 BASIC DEFINITIONS AND ASSUMPTIONS 71 4.2 RIEMANN SOLVERS
72 4.3 WAVE-FRONT TRACKING 74 4.3.1 THE SCALAR CASE 74 4.3.2 RICH
SYSTEMS 80 4.4 A CASE STUDY FOR RIEMANN SOLVERS 81 4.4.1 CONSTRUCTION OF
RIEMANN SOLVERS 86 4.4.2 CASE OFX SINGLETON 91 4.4.3 ESTIMATES OF FLUX
VARIATION 92 4.5 EXERCISES 93 4.6 OPEN PROBLEMS 94 5
LIGHTHIU-WHITHAM-RICHARDS MODEL ON NETWORKS 95 5.1 BASIC DEFINITIONS AND
ASSUMPTIONS 95 5.2 THE RIEMANN PROBLEM AT JUNCTIONS 99 5.2.1 THE CASEN^M
100 5.2.2 THE CASE OF N ^ 2 INCOMING ROADS AND M * 1 OUTGOING ROAD 103
5.2.3 DEMAND-SUPPLY OF LEBACQUE 106 5.3 INTERACTION ESTIMATES 106 5.3.1
ESTIMATES ON THE NUMBER OF WAVES AND INTERACTIONS . .. 107 5.3.2
ESTIMATES ON FLUX TOTAL VARIATION 109 5.4 LIPSCHITZ CONTINUOUS
DEPENDENCE ILL 5.5 TIME DEPENDENT TRAFFIC 115 5.6 TOTAL VARIATION OF THE
FLUXES 117 5.7 TOTAL VARIATION OF THE DENSITIES 118 5.8 EXERCISES 119
5.9 BIBLIOGRAPHICAL NOTE 121 A.L TECHNICAL RESULTS 122 A.2 LIPSCHITZ
DEPENDENCE IN A SPECIAL CASE 130 6 AW-RASCLE MODEL ON NETWORKS 133 6.1
BASIC DEFINITIONS AND ASSUMPTIONS 133 6.2 RIEMANN PROBLEMS AT JUNCTIONS
134 6.2.1 (AR-1): MAXIMIZE THE SPEED 141 CONTENTS XV 6.2.2 (AR-2):
MAXIMIZE THE DENSITY 144 6.2.3 (AR-3): MINIMIZE THE TOTAL VARIATION 146
6.3 STABILITY OF SOLUTIONS TO RIEMANN PROBLEMS AT JUNCTIONS 147 6.3.1
(AR-1): MAXIMIZE THE SPEED 148 6.3.2 (AR-2): MAXIMIZE THE DENSITY 151
6.3.3 (AR-3): MINIMIZE THE TOTAL VARIATION 153 6.4 EXISTENCE OF
SOLUTIONS TO A CAUCHY PROBLEM 155 6.5 OPEN PROBLEMS 158 6.6
BIBLIOGRAPHICAL NOTE 158 7 SOURCE DESTINATION MODEL 161 7.1 BASIC
DEFINITIONS 161 7.1.1 TRAFFIC DISTRIBUTION AT JUNCTIONS 162 7.1.2
EVOLUTION EQUATIONS FOR TRAFFIC-TYPE FUNCTIONS 164 7.1.3 ADMISSIBLE
NETWORKS AND SOLUTIONS 165 7.2 THE RIEMANN PROBLEM 166 7.2.1 JUNCTIONS
WITH TWO INCOMING AND TWO OUTGOING ROADS . 170 7.3 WAVE-FRONT TRACKING
ALGORITHM 173 7.4 BASIC ESTIMATES OF INTERACTIONS 173 7.4.1 INTERACTIONS
OF TYPE T2 175 7.4.2 INTERACTIONS OF TYPE T4 178 7.4.3 INTERACTIONS OF
TYPE T5 180 7.5 PERTURBATIONS OF AN EQUILIBRIUM 183 7.6 OPEN PROBLEMS
184 7.7 BIBLIOGRAPHICAL NOTE 185 8 AN EXAMPLE OF TRAFFIC REGULATION:
CIRCLES VS LIGHTS 187 8.1 FLUX CONTROL FOR TRAFFIC LIGHTS 188 8.1.1
NOTATIONS AND POSITION OF THE CONTROL PROBLEM 188 8.1.2 ANALYSIS OF
BACKWARD SHOCK WAVES ON THE INCOMING R.OADS 189 8.1.3 ASYMPTOTIC REGIME
FOR THE OUTGOING ROADS 190 8.2 SINGLE LANE TRAFFIC CIRCLE WITH LOW
TRAFFIC 191 8.3 SINGLE LANE TRAFFIC CIRCLE WITH HEAVY TRAFFIC 193 8.4
MULTI LANE TRAFFIC CIRCLE WITH NO INTERACTION 197 8.5 TRAFFIC LIGHT VS
TRAFFIC CIRCLE 198 8.5.1 LOW TRAFFIC 199 8.5.2 HEAVY TRAFFIC 199 8.5.3
COMPARISON 200 9 TELECOMMUNICATION NETWORKS (BY C. D APICE AND R. MANZO)
201 9.1 INTRODUCTION 201 9.2 PACKETS LOSS AND VELOCITY FUNCTIONS ON
TRANSMISSION LINES ... 203 9.3 RIEMANN SOLVER AT NODES 206 XVI CONTENTS
9.4 ESTIMATES ON DENSITY VARIATION 210 9.5 UNIQUENESS AND LIPSCHITZ
CONTINUOUS DEPENDENCE 215 10 NUMERICS ON NETWORKS 217 10.1 NUMERICAL
APPROXIMATION 217 10.1.1 GODUNOV SCHEME 217 10.1.2 KINETIC METHOD FOR A
BOUNDARY VALUE PROBLEM 218 10.1.3 BOUNDARY CONDITIONS AND CONDITIONS AT
JUNCTIONS 221 10.2 EXAMPLES . 224 10.2.1 BOTTLENECK 224 10.2.2 TRAFFIC
CIRCLE 225 10.3 TESTS 225 10.3.1 BOTTLENECK 226 10.3.2 TRAFFIC CIRCLE
229 REFERENCES 235 INDEX 241
|
| adam_txt |
AIMS SERIES ON APPLIED MATHEMATICS VOLUME 1 TRAFFIC FLOW ON NETWORKS
CONSERVATION LAWS MODELS MAURO GARAVELLO AND BENEDETTO PICCOLI
TECHNISCHE INFORMATIONSBIBLIOTHEK UNIVERSITATSBIBLIOTHEK HANNOVER AIMS
AMERICAN INSTITUTE OF MATHEMATICAL SCIENCES CONTENTS 1 INTRODUCTION 1
1.1 BOOK CHAPTERS 7 2 CONSERVATION LAWS 9 2.1 BASIC DEFINITIONS 9 2.2
WEAK SOLUTIONS 10 2.3 ENTROPY ADMISSIBLE SOLUTIONS 16 2.3.1 SCALAR CASE
16 2.4 RIEMANN PROBLEM 17 2.4.1 THE NON-CONVEX SCALAR CASE 23 2.5
FUNCTIONS WITH BOUNDED VARIATION 26 2.5.1 BV FUNCTIONS IN RN 30 2.6
WAVE-FRONT TRACKING AND EXISTENCE OF SOLUTIONS 32 2.6.1 THE SCALAR CASE
32 2.6.2 THE SYSTEM CASE 37 2.7 UNIQUENESS AND CONTINUOUS DEPENDENCE 38
2.8 EXERCISES 43 2.9 BIBLIOGRAPHICAL NOTE 44 3 MACROSCOPIC TRAFFIC
MODELS 47 3.1 LIGHTHILL-WHITHAM-RICHARDS MODEL 47 3.1.1 DERIVATION OF
THE EQUATION 48 3.1.2 FUNDAMENTAL DIAGRAMS 48 3.1.3 RIEMANN PROBLEMS 49
3.1.4 THE NOT STRICTLY CONCAVE CASE 52 3.1.5 LIGHTHILL-WHITHAM-RICHARDS
MODEL WITH VISCOSITY 53 3.2 PAYNE-WHITHAM MODEL 55 3.3 DRAWBACKS OF
SECOND ORDER MODELS 56 3.4 AW-RASCLE MODEL 57 3.4.1 CHARACTERISTIC
FIELDS 58 3.4.2 DOMAINS OF INVARIANCE 58 XIV CONTENTS 3.5 THIRD ORDER
MODELS 60 3.6 HYPERBOLIC PHASE TRANSITION MODEL 61 3.6.1 THE RIEMARM
PROBLEM 62 3.7 A MULTILANE MODEL 64 3.8 A MULTIPOPULATION MODEL 66 3.8.1
THE CASE N = 2 68 3.9 EXERCISES 69 3.10 BIBLIOGRAPHICAL NOTE 70 4
NETWORKS 71 4.1 BASIC DEFINITIONS AND ASSUMPTIONS 71 4.2 RIEMANN SOLVERS
72 4.3 WAVE-FRONT TRACKING 74 4.3.1 THE SCALAR CASE 74 4.3.2 RICH
SYSTEMS 80 4.4 A CASE STUDY FOR RIEMANN SOLVERS 81 4.4.1 CONSTRUCTION OF
RIEMANN SOLVERS 86 4.4.2 CASE OFX SINGLETON 91 4.4.3 ESTIMATES OF FLUX
VARIATION 92 4.5 EXERCISES 93 4.6 OPEN PROBLEMS 94 5
LIGHTHIU-WHITHAM-RICHARDS MODEL ON NETWORKS 95 5.1 BASIC DEFINITIONS AND
ASSUMPTIONS 95 5.2 THE RIEMANN PROBLEM AT JUNCTIONS 99 5.2.1 THE CASEN^M
100 5.2.2 THE CASE OF N ^ 2 INCOMING ROADS AND M * 1 OUTGOING ROAD 103
5.2.3 DEMAND-SUPPLY OF LEBACQUE 106 5.3 INTERACTION ESTIMATES 106 5.3.1
ESTIMATES ON THE NUMBER OF WAVES AND INTERACTIONS . . 107 5.3.2
ESTIMATES ON FLUX TOTAL VARIATION 109 5.4 LIPSCHITZ CONTINUOUS
DEPENDENCE ILL 5.5 TIME DEPENDENT TRAFFIC 115 5.6 TOTAL VARIATION OF THE
FLUXES 117 5.7 TOTAL VARIATION OF THE DENSITIES 118 5.8 EXERCISES 119
5.9 BIBLIOGRAPHICAL NOTE 121 A.L TECHNICAL RESULTS 122 A.2 LIPSCHITZ
DEPENDENCE IN A SPECIAL CASE 130 6 AW-RASCLE MODEL ON NETWORKS 133 6.1
BASIC DEFINITIONS AND ASSUMPTIONS 133 6.2 RIEMANN PROBLEMS AT JUNCTIONS
134 6.2.1 (AR-1): MAXIMIZE THE SPEED 141 CONTENTS XV 6.2.2 (AR-2):
MAXIMIZE THE DENSITY 144 6.2.3 (AR-3): MINIMIZE THE TOTAL VARIATION 146
6.3 STABILITY OF SOLUTIONS TO RIEMANN PROBLEMS AT JUNCTIONS 147 6.3.1
(AR-1): MAXIMIZE THE SPEED 148 6.3.2 (AR-2): MAXIMIZE THE DENSITY 151
6.3.3 (AR-3): MINIMIZE THE TOTAL VARIATION 153 6.4 EXISTENCE OF
SOLUTIONS TO A CAUCHY PROBLEM 155 6.5 OPEN PROBLEMS 158 6.6
BIBLIOGRAPHICAL NOTE 158 7 SOURCE DESTINATION MODEL 161 7.1 BASIC
DEFINITIONS 161 7.1.1 TRAFFIC DISTRIBUTION AT JUNCTIONS 162 7.1.2
EVOLUTION EQUATIONS FOR TRAFFIC-TYPE FUNCTIONS 164 7.1.3 ADMISSIBLE
NETWORKS AND SOLUTIONS 165 7.2 THE RIEMANN PROBLEM 166 7.2.1 JUNCTIONS
WITH TWO INCOMING AND TWO OUTGOING ROADS . 170 7.3 WAVE-FRONT TRACKING
ALGORITHM 173 7.4 BASIC ESTIMATES OF INTERACTIONS 173 7.4.1 INTERACTIONS
OF TYPE T2 175 7.4.2 INTERACTIONS OF TYPE T4 178 7.4.3 INTERACTIONS OF
TYPE T5 180 7.5 PERTURBATIONS OF AN EQUILIBRIUM 183 7.6 OPEN PROBLEMS
184 7.7 BIBLIOGRAPHICAL NOTE 185 8 AN EXAMPLE OF TRAFFIC REGULATION:
CIRCLES VS LIGHTS 187 8.1 FLUX CONTROL FOR TRAFFIC LIGHTS 188 8.1.1
NOTATIONS AND POSITION OF THE CONTROL PROBLEM 188 8.1.2 ANALYSIS OF
BACKWARD SHOCK WAVES ON THE INCOMING R.OADS 189 8.1.3 ASYMPTOTIC REGIME
FOR THE OUTGOING ROADS 190 8.2 SINGLE LANE TRAFFIC CIRCLE WITH LOW
TRAFFIC 191 8.3 SINGLE LANE TRAFFIC CIRCLE WITH HEAVY TRAFFIC 193 8.4
MULTI LANE TRAFFIC CIRCLE WITH NO INTERACTION 197 8.5 TRAFFIC LIGHT VS
TRAFFIC CIRCLE 198 8.5.1 LOW TRAFFIC 199 8.5.2 HEAVY TRAFFIC 199 8.5.3
COMPARISON 200 9 TELECOMMUNICATION NETWORKS (BY C. D'APICE AND R. MANZO)
201 9.1 INTRODUCTION 201 9.2 PACKETS LOSS AND VELOCITY FUNCTIONS ON
TRANSMISSION LINES . 203 9.3 RIEMANN SOLVER AT NODES 206 XVI CONTENTS
9.4 ESTIMATES ON DENSITY VARIATION 210 9.5 UNIQUENESS AND LIPSCHITZ
CONTINUOUS DEPENDENCE 215 10 NUMERICS ON NETWORKS 217 10.1 NUMERICAL
APPROXIMATION 217 10.1.1 GODUNOV SCHEME 217 10.1.2 KINETIC METHOD FOR A
BOUNDARY VALUE PROBLEM 218 10.1.3 BOUNDARY CONDITIONS AND CONDITIONS AT
JUNCTIONS 221 10.2 EXAMPLES '. 224 10.2.1 BOTTLENECK 224 10.2.2 TRAFFIC
CIRCLE 225 10.3 TESTS 225 10.3.1 BOTTLENECK 226 10.3.2 TRAFFIC CIRCLE
229 REFERENCES 235 INDEX 241 |
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| index_date | 2024-07-02T15:18:28Z |
| indexdate | 2024-07-09T20:42:05Z |
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| series | AIMS series on applied mathematics |
| series2 | AIMS series on applied mathematics |
| spelling | Garavello, Mauro Verfasser aut Traffic flow on networks conservation laws models Mauro Garavallo and Benedetto Piccoli Springfield, Mo. American Inst. of Math. Sciences 2006 XVI, 243 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier AIMS series on applied mathematics 1 Mathematisches Modell Conservation laws (Mathematics) Traffic flow Mathematical models Verkehrsnetz (DE-588)4062953-3 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Verkehrsablauf (DE-588)4062902-8 gnd rswk-swf Verkehrsnetz (DE-588)4062953-3 s Verkehrsablauf (DE-588)4062902-8 s Mathematisches Modell (DE-588)4114528-8 s DE-604 Piccoli, Benedetto Verfasser aut AIMS series on applied mathematics 1 (DE-604)BV023094684 1 GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014918600&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Garavello, Mauro Piccoli, Benedetto Traffic flow on networks conservation laws models AIMS series on applied mathematics Mathematisches Modell Conservation laws (Mathematics) Traffic flow Mathematical models Verkehrsnetz (DE-588)4062953-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Verkehrsablauf (DE-588)4062902-8 gnd |
| subject_GND | (DE-588)4062953-3 (DE-588)4114528-8 (DE-588)4062902-8 |
| title | Traffic flow on networks conservation laws models |
| title_auth | Traffic flow on networks conservation laws models |
| title_exact_search | Traffic flow on networks conservation laws models |
| title_exact_search_txtP | Traffic flow on networks conservation laws models |
| title_full | Traffic flow on networks conservation laws models Mauro Garavallo and Benedetto Piccoli |
| title_fullStr | Traffic flow on networks conservation laws models Mauro Garavallo and Benedetto Piccoli |
| title_full_unstemmed | Traffic flow on networks conservation laws models Mauro Garavallo and Benedetto Piccoli |
| title_short | Traffic flow on networks |
| title_sort | traffic flow on networks conservation laws models |
| title_sub | conservation laws models |
| topic | Mathematisches Modell Conservation laws (Mathematics) Traffic flow Mathematical models Verkehrsnetz (DE-588)4062953-3 gnd Mathematisches Modell (DE-588)4114528-8 gnd Verkehrsablauf (DE-588)4062902-8 gnd |
| topic_facet | Mathematisches Modell Conservation laws (Mathematics) Traffic flow Mathematical models Verkehrsnetz Verkehrsablauf |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=014918600&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV023094684 |
| work_keys_str_mv | AT garavellomauro trafficflowonnetworksconservationlawsmodels AT piccolibenedetto trafficflowonnetworksconservationlawsmodels |