Breakdown in Traffic Networks: Fundamentals of Transportation Science

671 Pages·2017·25.238 MB·English

by  Boris S. Kerner (auth.)

Boris S. Kerner
Breakdown
in Traffi c
Networks
Fundamentals of Transportation
Science
Breakdown in Traffic Networks
Boris S. Kerner
Breakdown in Traffic
Networks
Fundamentals of Transportation Science
123
BorisS.Kerner
PhysicsofTransportandTraffic
UniversityDuisburg-Essen
Duisburg,Germany
ISBN978-3-662-54471-6 ISBN978-3-662-54473-0 (eBook)
DOI10.1007/978-3-662-54473-0
LibraryofCongressControlNumber:2017941004
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Preface
Traffic breakdownis a transition from free flow to congested traffic in a traffic or
transportationnetwork.Trafficbreakdownoccursusuallyatnetworkbottlenecks.
Users of traffic andtransportationnetworksexpectthat throughthe application
oftrafficcontrol,dynamictrafficassignment,cooperativedrivingsystems, aswell
as other intelligent transportation systems (ITS), traffic breakdown in a network
canbeprevented.Thisisbecausecongestedtrafficresultingfromtrafficbreakdown
causes a considerableincrease in traveltime, fuelconsumption,CO2 emission, as
well as other travel costs. Therefore, any traffic and transportation theory applied
forthedevelopmentofautomaticdrivingvehiclesandreliablemethodsofdynamic
trafficassignmentandcontrolshouldbeconsistentwithempiricalfeaturesoftraffic
breakdownatanetworkbottleneck.
The most important empirical feature of traffic breakdown in a network is the
nucleation nature of traffic breakdown found in real field traffic data. The term
nucleation nature of traffic breakdown means that traffic breakdown occurs in a
metastablefreeflow.Themetastabilityoffreeflowisasfollows.Therecanbemany
speed(density,flowrate)disturbancesinfreeflow.Amplitudesofthedisturbances
can be very different. When a disturbance occurs randomly whose amplitude is
largerthanacriticalone,thentrafficbreakdownoccurs.Suchadisturbanceresulting
inthebreakdowniscallednucleusforthebreakdown.Otherwise,ifthedisturbance
amplitude is smaller than the critical one, the disturbance decays; as a result, no
trafficbreakdownoccurs.
The nucleation nature of traffic breakdown at a network bottleneck is an
empiricalfundamentaloftransportationscience.
Unfortunately, generally accepted classical traffic and transportation theories,
which have had a great impact on the understanding of many empirical traffic
phenomena, have nevertheless failed by their applications in the real world.
Even several decades of a very intensive effort to improve and validate network
v
vi Preface
optimization and control models based on the classical traffic and transportation
theorieshavehadnosuccess.Indeed,therecanbenoexamplesfoundwhereonline
implementationsofthenetworkoptimizationmodelsbasedontheseclassicaltraffic
andtransportationtheoriescouldreducecongestioninrealtrafficandtransportation
networks.Inparticular,inthebook,wewillshowthatapplicationsoftheclassical
approachesfordynamictrafficassignmentintrafficnetworks,whicharerelatedto
thestateoftheartintrafficandtransportationresearch,deterioratethetrafficsystem
whileprovokingheavytrafficcongestioninurbannetworks.
This failure of classical traffic and transportation theories can be explained as
follows:Theclassicaltrafficandtransportationtheoriesarenotconsistentwiththe
nucleation nature of traffic breakdown. The nucleation nature of empirical traffic
breakdown was understood only during last 20 years. In contrast, the generally
acceptedfundamentalsandmethodologiesoftrafficandtransportationtheorywere
introducedinthe1950s–1960s.Thus,thescientistswhoseideasledtotheclassical
trafficandtransportationtheoriescouldnotknowtheempiricalnucleationnatureof
trafficbreakdown.Respectively,theauthorintroducedthethree-phasetraffictheory
andthebreakdownminimization(BM)principle.
The three-phase theory is the theoretical fundamental of transportation sci-
encethatexplainstheempiricalnucleationnatureoftrafficbreakdown.
TheBMprincipleisthetheoreticalfundamentaloftransportationsciencethat
permitstomaximizethenetworkthroughputpreventingtrafficbreakdownin
thenetwork.
The classical traffic and transportationtheories that failed by their applications
intherealworldarecurrentlythemethodologiesofteachingprogramsinmostuni-
versitiesandthesubjectofpublicationsinmosttransportationresearchjournalsand
scientificconferences.Consequently,someofbook’sobjectivesareasfollows:
1. Weprovetheempiricalnucleationnatureoftrafficbreakdowninnetworks.
2. Wediscusstheoriginofthefailureofclassicaltrafficandtransportationtheories.
3. Weshowthatthethree-phasetheoryisincommensurablewiththeclassicaltraffic
theories.
4. Weexplainthatstandarddynamictrafficassignmentthatisthestateoftheartin
transportationresearchprovokesheavytrafficcongestioninnetworks.
5. WeshowthatapplicationsoftheBMprincipleresultinthemaximizationofthe
networkthroughputwhileensuringthatnobreakdowncanoccurinthenetwork.
Stuttgart,Germany BorisS.Kerner
December2016
Acknowledgments
I thank Michael Schreckenberg, Dietrich Wolf, Florian Knorr, and Gerhard Her-
manns of the University Duisburg-Essen as well as my former colleagues at
the Daimler Company, in particular, Hubert Rehborn, Peter Häussermann, Harald
Brunini, Ralf-Guido Herrtwich, Ralf Lamberti, Peter Konhäuser, Martin Schilke,
MatthiasSchulze,PeterEbel,ViktorFriesen,MarioAleksic´,JochenPalmer,Micha
Koller,PeterHemmerle,GerhardNöcker,WinfriedKronjäger,andAndreasHiller
fortheirsupport,discussions,andadvice.
IthankRuiJiangformanyusefuldiscussionsandcommentstothebook.Ithank
CraigDavisformanyusefulcommentstothethree-phasetheoryusedinthisbook.
IthankalsoJun-fangTianforfruitfuldiscussionsofthebooktitle.
ParticularthanksaretoSergeyKlenov,HubertRehborn,andMichaKollerwho
havereadthebookandmademanyusefulcomments.
I thank our partnersfor their supportin the projects“UR:BAN—Urban Space:
User oriented assistance systems and network management” and “MEC-View—
ObjectdetectionforautomateddrivingbasedonMobileEdgeComputing,”funded
bytheGermanFederalMinistryofEconomicAffairsandEnergy.
I thank authorities of the State of Hessen (Germany) for providing real field
traffic data measured on German freeways as well as Ralf-Peter Schäfer, Oliver
Kannenberg,StefanLorkowski,andNikolausWitteforprovidinganonymizedGPS
probe data of the TomTom Company. I thank also Heiko Böhme, Timo Finke,
and Nicolas Gath for providing real field detector data measured in Düsseldorf
(Germany).
I amgratefultoSergeyKlenovforhishelpwithnumericalsimulationsandthe
preparationofillustrationsforthebook.
Finally,Ithankmywife,TatianaKerner,forherhelpandunderstanding.
vii
Contents
1 Introduction—The Reason for Paradigm Shift
inTransportationScience.................................................. 1
1.1 DefinitionsofFreeandCongestedTrafficinEmpiricalData ..... 2
1.2 Bottlenecks .......................................................... 5
1.3 DefinitionsofSynchronizedFlowandWideMovingJam
PhasesinEmpiricalDataforCongestedTraffic ................... 6
1.4 TrafficBreakdown .................................................. 9
1.5 EmpiricalPhaseTransitionsinTrafficFlow ....................... 9
1.6 EmpiricalFundamentalofTransportationScience ................ 12
1.7 TheOriginofFailureofClassicalTrafficandTransportation
Theories ............................................................. 17
1.7.1 NatureofStochasticHighwayCapacity ................. 17
1.7.2 DescriptionofTrafficBreakdownwithClassical
TrafficFlowModels ...................................... 18
1.7.3 DeteriorationofTrafficSystemThroughStandard
DynamicTrafficAssignmentinNetworks .............. 21
1.7.4 Failure of Applications of Intelligent
TransportationSystems(ITS)BasedonClassical
TrafficTheories ........................................... 23
1.8 ClassicalIdeasofTransportationScienceandNucleation
NatureofEmpiricalTrafficBreakdown ........................... 25
1.9 Three-PhaseTrafficTheory ........................................ 25
1.10 Infinite Number of Stochastic Highway Capacities
inThree-PhaseTheory .............................................. 29
1.11 BreakdownMinimization(BM)Principle ......................... 30
1.12 Mathematical Three-Phase Traffic Flow Models
andITS-ApplicationsofThree-PhaseTheory ..................... 31
1.13 CriticismofThree-PhaseTrafficTheory .......................... 36
1.14 Incommensurabilityof Three-Phase Traffic Theory
andClassicalTrafficTheories ...................................... 39
1.15 ObjectivesoftheBook .............................................. 40
ix
x Contents
1.16 Book’sStructure .................................................... 42
References.................................................................... 44
2 AchievementsofEmpiricalStudiesofTrafficBreakdownat
HighwayBottlenecks....................................................... 73
2.1 Introduction.......................................................... 73
2.2 EmpiricalFeaturesofTrafficBreakdown .......................... 74
2.2.1 TrafficBreakdown—TransitionfromFree to
SynchronizedFlowatHighwayBottleneck ............. 74
2.2.2 Time-DependenceofFlowRateDuringEmpirical
TrafficBreakdownatHighwayBottleneck .............. 75
2.3 StochasticBehaviorandProbabilityofTrafficBreakdown
atHighwayBottleneck .............................................. 77
2.4 Conclusions ......................................................... 80
References.................................................................... 81
3 Nucleation Nature of Traffic Breakdown—Empirical
FundamentalofTransportationScience................................. 87
3.1 Introduction.......................................................... 87
3.2 Definitionsof EmpiricalSpontaneousand Empirical
InducedTrafficBreakdownsatHighwayBottlenecks ............ 88
3.3 ExplanationofTerm“Nucleus”forTrafficBreakdown ........... 92
3.4 NucleationofEmpiricalSpontaneousTrafficBreakdownat
HighwayBottlenecks ............................................... 94
3.4.1 WavesinEmpiricalFreeFlow ........................... 94
3.4.2 EmpiricalNucleationofTrafficBreakdownat
On-RampBottleneck...................................... 96
3.4.3 EmpiricalNucleationofTrafficBreakdownat
Off-RampBottleneck ..................................... 96
3.4.4 EmpiricalPermanentSpeed Disturbance at
HighwayBottleneckandNucleationofTraffic
Breakdown ................................................ 100
3.4.5 EmpiricalTwo-Dimensional(2D)Asymmetric
SpatiotemporalStructureofNucleiforTraffic
Breakdown ................................................ 104
3.5 WavesinFreeFlowandEmpiricalSpontaneousTraffic
BreakdowninFlowWithoutTrucks ............................... 107
3.6 Induced Traffic Breakdown—Empirical Proof
ofNucleationNatureofEmpiricalTrafficBreakdown ............ 107
3.6.1 Sources of Nucleus for Empirical Traffic
Breakdown ................................................ 108
3.6.2 InducedTrafficBreakdownasOneofDifferent
ConsequencesofSpilloverinRealTraffic .............. 116
3.7 EmpiricalNucleation Nature of Traffic Breakdown
asOriginoftheInfinityofHighwayCapacities ................... 117
Contents xi
3.8 Conclusions.......................................................... 120
References.................................................................... 121
4 FailureofGenerallyAcceptedClassicalTrafficFlowTheories....... 123
4.1 Introduction.......................................................... 123
4.2 FundamentalDiagramofTrafficFlow ............................. 125
4.2.1 EmpiricalFeaturesofFundamentalDiagramof
TrafficFlow................................................ 125
4.2.2 ApplicationofFundamentalDiagramforTraffic
FlowModelling............................................ 128
4.3 Traffic Breakdown at Bottleneck in
Lighthill-Whitham-Richards(LWR)Model ....................... 128
4.3.1 BasicAssumptionofLWRModel ....................... 128
4.3.2 AchievementsofLWRTheoryinDescriptionof
TrafficBreakdown ........................................ 129
4.3.3 Failure of LWR Theory in Explanation
of Empirical Nucleation Nature of Traffic
Breakdown ................................................ 131
4.4 DescriptionofTrafficBreakdownwithGeneralMotors
(GM)ModelClass .................................................. 134
4.4.1 ClassicalTrafficFlowInstability:GrowingWave
ofLocalSpeedReductioninTrafficFlowDue
toOver-DecelerationEffect .............................. 134
4.4.2 “Boomerang”Effect ...................................... 136
4.4.3 MovingJamEmergenceatBottleneck .................. 139
4.5 Achievements of Generally Accepted Classical
TrafficModels ....................................................... 140
4.5.1 Metastability of Free Flow with Respect to
MovingJamEmergenceandLineJ ..................... 141
4.5.2 DriverBehavioralAssumptions .......................... 147
4.6 Summaryof Achievementsof Classical Traffic Flow
Models ............................................................... 148
4.7 WhyAreGenerallyAcceptedClassicalTwo-PhaseTraffic
FlowModelsInconsistentwithFeaturesofRealTraffic? ......... 149
4.8 ModelValidationwithEmpiricalData ............................. 151
4.9 Applicationsof Classical Traffic Flow Theoriesfor
DevelopmentofIntelligentTransportationsystems(ITS)......... 154
4.9.1 SimulationsofITSPerformance.......................... 154
4.9.2 On-RampMetering ....................................... 156
4.9.3 EffectofAutomaticDrivingonTrafficFlow ............ 157
4.10 ClassicalUnderstandingofStochasticHighwayCapacity ........ 159
4.11 StrictBeliefinClassicalTheoriesasReasonforDefective
AnalysisofEmpiricalTrafficPhenomena ......................... 163
4.11.1 APossibleOriginofFailureofClassicalTraffic
FlowModels .............................................. 163