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DATA-DRIVEN TRAFFIC ENGINEERING DATA-DRIVEN TRAFFIC ENGINEERING Understanding ofTrafficand Applicationsbased onThree-Phase TrafficTheory HUBERTREHBORN
MICHAKOLLER
STEFANKAUFMANN
Elsevier
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Aimofthebook Preciselymeasuredtrafficdatafromallroadshaverecentlybecomeubiquitousintransportationandtrafficsciences.Therefore,theempiricalandcomprehensivebasisfortheanalysisandunderstandingofallfeaturesoftrafficis availablenowadays.Wetrytoexplainthelargevarietyandcomplexityof measuredtrafficdataandthosefeaturesonfreewaysaswellasinurbanareas. Manytrafficapplicationswillbesupportedbasedontheavailabledata.
Almost20yearsaftertheinventionofthethree-phasetraffictheoryby BorisKerner,itistimetohaveacloselookatitsconsequencesfortransportationengineeringaswellasitspracticalapplications.Thisbookwillhelp transportationengineersandtechnicianstounderstandboththeapplications andapplicabilityofKerner’sthree-phasetraffictheoryinavarietyofscenarios.Itstartswithmeasurementsoftrafficphenomena,bothwithstationary loopdetectorsandwithconnectedvehicledata.Then,atheoreticalaswellas historicalexplanationofthethree-phasetraffictheoryfollows.Basedonthis theoreticalfundament,anumberofthetheories’conclusionsofferideasfor newapproachesintrafficcontrolaswellasnewvehicularapplicationssuch asdriverinformationanddriverassistance.Moderntrafficengineering methodsarecloselyrelatedtoinformationtechnologyandcomputerscience.Therefore,algorithmsandmethodswillbedescribedwiththeirapplicabilityassoftwareinbothcollectivetrafficmanagementandindividual vehicles.
Today,moreandmorepeoplehaveabandonedprintedmapsinvehicles forrouteguidance.Instead,electronicnavigationhasbecomestateoftheart inallvehicles.Congestedtrafficinfluencesthosenavigationsystemsand theirrelateddynamicroutechoices.BasedonKerner’sthree-phasetraffic theory,weareabletodefinetherequirementsandtestingmethodsfor high-qualitytrafficmessagesusedinnavigationsystems.
Expectedreaders Wehopeabroaderaudienceisinterestedinscientificexplanationsforthe emergence,propagation,anddissolutionoftrafficcongestion.Inaddition, theaspectsoftrafficphase-dependentfuelconsumption,theinfluenceof weatherontraffic,andaspectsofautomateddrivinginrealtrafficshould attractreaderswhenthesetopicsarediscussedtechnicallyinthescopeof thethree-phasetraffictheory.
Scopeandoutlineofthebook Empiricalmeasurementsindifferentcountriesandofdifferentkindsillustratethevarietyofcongestedphenomenaintraffic.AhistoryofKerner’s three-phasetraffictheorywillexplainsomehistoricstepsfromthefoundationsofthistraffictheoryanditsconsequencesuntiltoday.Startingfrom trafficmodelingintheearly1990,theintensiveworkwithempiricalmeasuredtrafficdataleadstoadeepunderstandingofthecomplexdynamicprocessesonfreeways.Additionalconsequencesofthethree-phasetraffic theory’sstatementshavebeenboththeproposalofpracticalapplications andtheinventionofimprovedtrafficmodels.
Thisbookwilloutlinethedevelopmentofthethree-phasetraffictheory aswellasexplaintherelevantmilestonesandsteps.Itstartswithahistorical viewontrafficmodelinginthree-phasetraffictheoryandproceedswith thefundamentsofthetheory.ThehistoryofthemodelsASDA/FOTO andsomeotherapplicationsaresummarizedfurtheron.Jamtailwarnings andonboardtrafficstatedetectionmethodsdescribeanapproachthat includesmoreprecisetrafficinformationinvehiclesystems.Thevehicles’ navigationsystemshavetointegratetrafficmessagesinaproperway,and thequalityofthosecongestionmessageshavetobeevaluatedinthescope ofKerner’stheory.
CHAPTER1 Introduction Everymorning,thecommutersinmanyurbanareasoftheworldsufferfrom timedelayscausedbytrafficcongestion.Thecongestionisregular,recurring,andpermanentatcertainlocationsoftheroadnetwork.Therefore, beginningfromabetterunderstandingoftheunderlyingphysicalprocesses intraffic,thewishforpreciseandreliabletrafficanalysisarisesformultiple trafficmanagementpurposes,bothcollective(e.g.,trafficcontrol)orindividual(e.g.,dynamicrouteguidanceinnavigationsystems).Toreachthese goals,empiricalcongestionpatternsmustfirstbeanalyzedandunderstood correctly.Thiscanbedoneonlyifsufficientmeasuredtrafficdataareavailable.Today,connectedvehiclessendingtheirpositiondata(i.e.,probevehicledata)areonekeyelementofcollectingtrafficdataoneachroadsegment throughoutthewholeroadnetwork.
Ourbookintroducesmanydifferentcongestedtrafficsituationsmeasuredwithconnectedvehiclefleetsanddiscussesseveralaspectsofpossible trafficapplications.Theinvestigatedvehiclefleetcontainsmorethanone millionvehiclesthathavegiventheirpositiondatatoimprovethequality ofthetrafficservice.Aswewillshowinthebook,about2%ofthetotalflow rateonaroadsectiongivesenoughinformationtoreconstructtherelated trafficsituationwithhigh-enoughquality:onathree-lanefreewaywith about6000vehiclesperhour,about120connectedvehiclesand/ordevices sendingtheirpositiondatatoacentralserverallowatrafficservicewith about500–1000mgranularityofthepositionsofanytrafficcongestion. Thecomplexityofthedifferentcongestedtrafficpatternsatdifferentbottlenecksisillustratedforseveralroadsectionsinseveralcountries.Themeasuredtrafficdatashowthevarietyinmanyheterogeneoussituationsthat emergeduetoourdrivingbehavior:theindividualbreakingandaccelerationleadtocollectiveeffectsthatcanpropagateseveralkilometersupstream. Inaddition,weinvestigateandanalyzemicroscopictrafficwiththehighest possibledetail:droneobservationsallowmeasuringthedrivingofeachindividualvehicleovertime(i.e.,inatimeintervalofabout20min)andspace (i.e.,about400mwithonecamera)simultaneously. Fig.1 illustratessucha dronemeasurementonafreewaysegment,observingallvehiclesbyacameraanddetectingallobjectsonthefreeway.
2 Data-driventrafficengineering
ThetheoreticalfoundationofthisworkisgivenbyBorisKerner’sthreephasetraffictheory(seeWikipedia [1] andthebooks [2–4]).Trafficcanbe distinguishedintothreedistinctphases:(i)freeflow,(ii)synchronizedflow, and(iii)widemovingjam.Infree-flowingtraffic,eachdrivercanchoosehis individualspeedandcanovertakeonpurpose;insynchronizedflow,there arealmostnopossibilitiestoovertakeandthespeedhasatendencytobe synchronizedamongthedifferentlanesofthesamedrivingdirection;and inthewidemovingjamphase,thevehicleshavecometoanearstandstill andthetrafficflowisinterrupted.Thetrafficbreakdownisassociatedwith aphasetransitionfromfreetosynchronizedflow.Insidethesynchronized flowregion,duetodriverbehaviorwidemovingjamscanprobablyemerge thatthenpropagatefurtherupstreamwithavelocityof 15km/hon average.
Thebookwillfollowtheprincipleofdiscussingalldata-drivenfactsand featuresbasedonmeasuredtrafficdataonly.Manyvarioustrafficcongestions onfreewaysandinurbanareasarepresentedin Chapter2:time-space diagramsofmeasuredfleetdatafromconnectedvehiclesillustratethecomplexityoftrafficcongestion. Chapters3 (dedicatedtothehistoryofthe three-phasetraffictheoryandcongestedtrafficpatternsonfreeways)and 4 (discussingcongestioninurbanareaswithsignalizedintersections)try togiveacomprehensiveoverviewofallkeyelementsofthethree-phase traffictheoryastheyarerelevantforunderstandingallempiricalexamples.
Snapshotofcameraobservationandobjectdetectionprovidedbyadrone measurementofafreewaysegment.
Fig.1
Thisbackgroundgivesthefoundationofthedifferentapplicationsintransportation;withoutthisbackgroundwecannotdistinguishbetweenpossible andimpossibleapplicationsandwhysomeapplicationsarepossiblewhile othersfailcompletely.
Chapter5 withapplicationsintransportationbeginswithareviewofthe ASDA/FOTOmodelsdevelopedbasedonthethree-phasetraffictheory andimplementedinsoftwaremodules.Wewillshowinadditionthedependencyofthetrafficparametersontheweatherconditions.
Whatthenfollowsisageneralstatisticalanalysisofthedatafromalarge fleetofconnectedvehicles:whatarethemobilityparameterssuchasaverage triptimes,speeds,etc.,andtherefore,howdopeopleusevehiclesinsome differentcountries?Inaddition,whatistheroutechoicebehavioriftraffic informationisusedinnavigationsystems?Dopeoplefollowadvice?Also,in whichtrafficsituationscanatimedelaybesavedwithalternativeroutesin theoccurrenceoftrafficcongestiononthemainroad?Andhowmuchtime canbesaved?
Ifenoughandprecisevehicledataareavailableonaroad,anactivejam tailwarningwillbecomefeasible.Thisannouncessuchaneventinadvance toeachdriver:thepositionovertimeof,forexample,awidemovingjam withasuddenbreakdownfromfreeflowtoacompletestandstillcanbe reconstructedwithin500–1000maccuracy.
Furthermore,detailedmeasurementsinvehiclesallowdiscussingtraffic phasedependentfuelconsumption:duetodecelerationandaccelerationin congestedtraffic,thefuel/energyconsumptionincreases.Wecanrevealfactorsofincreasedaverageconsumptionindependencyoftherelated trafficphase.
Automateddrivingisoneoftherelevantresearchtopicsoftheautomotiveindustryanditcomeswithhighexpectationsforourmobility.Wewill concentratethetechnicaldiscussionofonespecificdifficultexampleforan automatedvehicle:whatarethetimegapsinrealtrafficandhowcansuchan automatedvehiclemergeontoahighwaythroughanon-ramp?
Forvehiclemanufacturerswithembeddednavigationsystemscompetingwithmobiledevicesregardingapplicationsandfeatures,oneremaining possiblefieldofvehicularapplicationisthevehicleitself.Themanufacturer canusethedynamicinformationofthetrafficserviceinthevehicleby,for example,usingupcomingcongestionaheadtotriggerthebehaviorofacontrolunit(e.g.,withabreakingassistsystem)inacertainway.Asanother example,anupcomingjamfrontcanbeusedtoactivelyreducethevehicle speedadvisedtothedriver.
Finally, Chapter5 willdiscusssomeexamplesandaspectsoftrafficservicesfornavigationsystemsandillustratesomeexamplesofcomplextraffic situations.
Allthetheoreticalworkandthetrafficdataanalysisworkhavebeensupportedbyseveralcolleagueswhomwewanttothank:BorisKernerandSergeyKlenovfortheirsupportonalltheoreticalandapplicationquestions; JochenPalmerforhisalgorithmicworkonASDA/FOTOwithprobevehicledata;PeterHemmerleforhisworkwithurbantrafficdataanddrone experiments;MarkusAuerforhisanalysisofthemobilitydataofthevehicle fleet;Sven-EricMolzahnforhisinvestigationofjamtailwarningapplications;andYildirimD € ulgarforhisanalysisoftimegapsofvehiclesandthe preparationofdiagramsforfleetdata.Thisbookwouldnotbepossible withoutsomefundedpublicresearchprojectsoverseveralyears(e.g., “MECView—ObjectdetectionforautonomousdrivingbasedonMobile EdgeComputing”and“LUKAS—Localmodelforcooperativeandautonomousdrivingincomplextrafficsituations”fundedbytheGermanFederal MinistryofEconomicAffairsandEnergy)aswellasthesupportofthe Mercedes-Benzresearchanddevelopmentfacilities.
References
[1]Anon, https://en.wikipedia.org/wiki/Three-phase_traffic_theory
[2] KernerBS.Thephysicsoftraffic.Berlin,NewYork:Springer;2004.
[3] KernerBS.Introductiontomoderntrafficflowtheoryandcontrol.Berlin,NewYork: Springer;2009.
[4] KernerBS.Breakdownintrafficnetworks:fundamentalsoftransportationscience.Berlin:Springer;2017.
CHAPTER2 Howtrafficdataaremeasured Westructurethedescriptionofthemostcommontechnologiesformeasuringtrafficdataonroadsintothreeseparatesections: Section2.1 describesthe historicallyandcurrentlystillwidelyusedmeasurementswithfixedinstalled sensorsintheroadnetwork.Trafficdatafrommovingobjectsintrafficflow, called“probevehicledata,”areincreasingnowadayswithconnectedvehiclesandothermobiledevices;thisisexplainedin Section2.2.Dueto recentlyavailabledronetechnologiesandobjectreconstruction,theaerial observationoftrafficflowisanewlyreinventedandinterestingapproach togetcomprehensivespatial-temporaltrafficdatasets(Section2.3).
2.1Loopdetectordata Empiricaltrafficmeasurementsaretodaystillverycommonlyperformed withfixedinductiveloopdetectorsinstalledonlanes,bothonfreeways andinurbannetworks.Typically,theyhavefixedmeasurementintervals of1minandaggregatetwotrafficflowvariables:(i)theaveragespeedof allpassingvehiclesinkilometresperhour,and(ii)thetrafficflowrate countedinvehiclesperhour.Infreeflowconditions,typicalflowrates ononefreewaylanegoupto2500vehiclesperhourandtheaveragespeed isapproximately100km/hormore.Fortrafficcontrolpurposes,thespeed andflowratebreakdownofthemeasuredvariablesisusedtoidentifycongestion.Inaddition,doubleloopsensorscandistinguishamongdifferent vehicletypessuchaslongvehicles,passengercars,andtrailers.
Anexamplefortypicalempiricalmeasurementswithalocalloopdetectorisillustratedin Fig.1.Onfreewaysegmentswithvariablemessagesigns (VMS),thecontrolofthespeedsshowntodriversisderivedfromdatameasuredbytheloopdetectorscoveringeachlane(oneofthemmeasuresbelow eachVMS). Fig.1Apresentstheschemeofthefreewayandthepositionsof loopdetectors.Incolour,twodifferentkindsofverycommonbreakdowns aremarked:(i)inaspeedandflowdiagram,thered(darkgreyinprintversion)markedtimeintervalischaracterizedbyasuddendropinbothspeed andflowmeasurements,and(ii)in Fig.1B–C,theyellow(lightgreyinprint
Data-DrivenTrafficEngineering
2021ElsevierInc. https://doi.org/10.1016/B978-0-12-819138-5.00003-2
6:43am 8:43am 10:43am 6:43am 8:43am 10:43am
: Breakdown of speed and flow rate
: Breakdown of speed only
Fig.1 (A)schemeofafreewaywithloopdetectors,(B)averagedvehiclespeedatthe leftlaneofdetectorD1,(C)flowrateattheleftlaneofdetectorD1. (AdaptedfromKerner BS,RehbornH.Experimentalpropertiesofphasetransitionsintrafficflow.PhysRevLett, 1997;79:4030.)
version)markedtimeintervalshowsadropinthevehiclespeedwhilethe flowrateremainsabove1200vehiclesperhour(fordetailsee[12]).
Adetailedpictureofloopdetectormeasurementsshowingeachindividuallaneisillustratedin Fig.2:themeasurementsforeachlaneofthefreeway indicatethehigherspeedontheleftlaneandthelowestspeedontheright lane(inGermanyduetotherightdrivinglawafterovertakingandlong vehiclesontherightlanes).Anuparrowshowsthetimemomentwhen attheloopdetector,thespeeddecreasesandbecomessimilarinalllanes (atdetectorsD1toD4). Fig.2Ashowsaclearsynchronizationofthevehicle speedsonthethreelanesafter7:16a.m.Incontrasttofreeflow,overtakingis thennolongerpossibleatthereducedspeedofabout60km/h.Froma driver’sperspective,thismightbecalledslowand/orqueuingtraffic.The correspondingflowrateatdetectorsD3andD4(Fig.2E)showshighvalues ofabout2400vehiclesperhour.Inaddition,theinvestigationoftheD2 on-rampmeasurementsrevealsabreakdownintheaveragespeedsonthe rampbetween7:12a.m.and9:12a.m.(Fig.2G)whileafterashort
D A (A)(B)(C) (km/h)
(D) (G)(H) (E)(F) Fig.2 (A)–(D)Vehiclespeedsatloopdetectorsfromafreewaysegmentshownin Fig.1Aforeachlane;(E,F)correspondingflowratesatD3,D4,andD2on-ramps;(G, H)D2on-rampmeasurementsforalargertimeinterval. (AdaptedfromKernerBS, RehbornH.Experimentalpropertiesofphasetransitionsintrafficflow.PhysRevLett, 1997;79:4030.)
breakdownintheflowrateatapprox.7:40a.m.(Fig.2F),theflowrateatthis on-rampremainsonahighlevelatabout500vehiclesperhourmerging ontothefreeway.
Inadditiontofreeways,loopdetectorsareusedinurbanareastomeasure vehiclespeedsandflowrates.AnexampleforanurbanroadinD € usseldorf, Germany,isgivenin Fig.3:630maheadofthetrafficsignal“TS,”thefixed detector“D”measuresaggregatedtrafficvariables.Similartothetimeintervalsmarkedin Fig.1B–C,thedropinvehiclespeedandflowratecanbe observedattheurbandetectoraswell(fordetailsee[11]).Between 7:45a.m.and9:15a.m.onApril10,2013(andfrom8:00a.m.to9:15a.m. onFeb.5,2013),thereisasignificantspeeddropwithalmostnodropin Time Time 7:16am 7:22am 7:12am 7:20am 7:28am 7:12am 7:20am 7:28am 7:38am 7:28am 7:34am 7:40am 7:17am 7:16am 7:16am 7:12am 7:20am 7:28am 7:12am 7:20am 7:28am 7:12am 7:20am 7:28am 7:12am 8:32am 9:52am 8:32am 9:52am 7:12am
9:00am 11:00am 7:00am 9:00am 11:00am 7:00am 9:00am 1 7:00am 9:00am 11:00am
: Breakdown of speed and flow rate
: Breakdown of speed only
Fig.3 (A)SchemeoftheurbanstreetVolklingerinD € usseldorf,Germany,withtraffic signal “TS” anddetector “D” atthebeginningofthesection;(B)twodayswith measurementsat “D” withvehiclespeedandflowrate. (AdaptedfromKernerBS, HemmerleP,KollerM,HermannsG,KlenovSL,RehbornH,etal.Empiricalsynchronized flowinoversaturatedcitytraffic.PhysRevE2014;90(3):032810.)
theflowratediagram.Onthecontrary,thespeeddropfrom9:50a.m.to 10:05a.m.onApril10,2013,isaccompaniedbyadropintheflowratevalues. Thetwotypesofbreakdownsarerelatedtotrafficcongestion.Independentoftheremainingflowrate,weasindividualdriverswoulddefinetraffic congestionasastateontheroadwherethefreeflowspeedcannotbe achievedanymoreandovertakingisalmostimpossible.OntypicalGerman freewaysegments,therewillbecongestedtrafficifthespeeddecreasesbelow about80km/h(if120km/hormoreisallowed)andontypicalGerman urbanstreetsifthespeeddecreasesbelowabout30km/h(if50km/his allowed).
2.2Probevehicledata Since2000,theGlobalPositioningSystem(GPS)hasallowedthelocalizationofportabledeviceswithanaccuracyofabout5–7m(e.g., [1]).Before thattime,duetoanartificialGaussiansignalcalledselectiveavailability,an accuracyofonlyabout100mforsatellitepositioningforcommercialuses waspossible.Sincethen,manydeviceshavebecomeequippedwithGPS sensorsandallowpermanentlocalizationwhiledrivingontheroads(socalled“matching”ofrawGPSpositiondatatoapositiononaspecificroad inadigitalmap).Overtime,moreandmoredevicesandvehicleshave becomeconnectedviaanIPconnectiontocentralservers.Withallthese ingredients—especiallytheuseofmobilesmartphonedevices—wecan measuretrafficcongestioneverywhereandatanytime.Theprobedata coverthewholeroadnetworkatanytime.
Basically,onevehicledrivesonaroad,hastoslowdowntoastandstill, anddrivessometimesbelowthefreeflowspeed.Peoplemightcallthis “stationarytraffic”or“slowtraffic”asbothreducedvelocitiesarecalled “congestion”(Fig.4).Ifonevehiclesenditspositiondataas“probes”to thetrafficcenter,itisimpossibletodetectthe(congested)trafficsituation. Butitisveryclearthatwithanincreasingamountofvehicles,thistraffic reconstructionbecomesbetterandbetter.
Inthefollowing,wewillshowmeasuredprobedatafromalargevehicle fleetdrivingondifferentroadsindifferentcountries.Aftersuccessfully
matchingtheGPSprobedataofthevehicles,wecanshowtime-spacediagrams,asin Fig.4 (bottom),fordifferentroadstretchesandtherelatedmeasuredGPSdataforeachtrafficsituation.Inthenextexamples,wesimply colourtheGPSdataaccordingtothefollowinglegend:(i)red(darkgrey inprintversion):0–25km/h,(ii)yellow(lightgreyinprintversion): 25–60km/h,and(iii)green(greyinprintversion): >60km/h.Thespeed valuesarecalculatedbasedonthepositiondatain5–10sintervals.Thegiven colourschemeisappropriateforfreeways.Forotherroadclassessuchas urbanroads,thevalueshavetobeadaptedtotheusualdrivenvelocities. WeshowexamplesfromfreewaysegmentsinGermanyandtheUnited Kingdom.Inallcasesbasedonthecolouring,theregionsoftrafficcongestioncanbequalitativelyidentified.Theanonymizeddataareobtainedfrom connectedvehiclesofalargefleetfromreal-worldcustomersdrivingonthe publicroadnetwork.ThesevehiclessendtheGPSlocationalongwitha timestampandsessionidentifiertoasecureback-endserver.ThedatacomprisetherawGPSlocationthat,aftermapmatching,representsatrajectory onthegivenroadsection.Dependingonthevehiclemodelandvariantcoding,thedatahasatypicalsamplingrateofeither5or10s.
Forallfollowingprobedataexamples,wewillusethesameschemeof datarepresentationillustratedin Fig.5:eachprobevehicleisillustratedas oneline.Thefleetdataforoneroadsectionarecolouredsimilarly:(i)all vehicletrajectoriesshowingspeedsabove80km/harerepresentedingreen, (ii)vehiclesdrivingbetween30km/hand80km/hareinyellow,and
v > 80 km/h 30 km/h < v < 80 km/h v < 30 km/h Ramps at intersections
Fig.5 Schemeofprobedataillustrationsintime-spacediagrams.Blackrectangular objectsindicatepossibleregionsoflowervehiclespeeds.
(iii)vehiclesdrivingslowerthan30km/honafreewaysegmentareshownin red.Foreachprobedatadiagram,theroadinfrastructureisshowntothe rightofthediagramandindicatesthenumberoflanesandon-andoff-ramps aswellasintersections.Theblackboxesinthediagramof Fig.5 ontheleft sideindicatetheregionsofcongestion(withlowerspeeds),whichwillbe explainedlaterinmoredetail.
2.2.1Propagatingcongestion Inthefollowing,wetakealookatdatameasuredonhighwayA81inGermanyfromHeilbronntoStuttgartonNov.13,2016(aSunday).In Fig.6, weconsiderthetrafficfrom10:00a.m.to10:00a.m.Mostofthetimethe vehiclesonthisstretchofroadaregoingfasterthan60km/h,whichis markedasgreenlinesin Fig.6.Onereasonforthisisthatthedataarefrom aSunday,whichismostlylesscongestedthanaworkingday.However,in thetimeintervalfrom5:00a.m.to7:00a.m.between20and30km,apatternwithslowlydrivingvehicleswasobserved;itisshownin Fig.7.At 30km,thereisanoff-rampfollowedbyanon-ramp.Atthevehicletrajectoriesplottedin Fig.7,onecanseethatthetrafficcongestiondispersesafter thelocationoftheoff-/on-rampat30km.Moreover,weseethatatraffic patterncausedbyvehiclesdrivingslowerthan25km/h,whichismarkedin red(tinywavylinesinprintversion)in Fig.7,ismovingbackwardinspace. Thewidthandgradientofthered(tinywavylinesinprintversion)pattern seemtobeconstantwhilemovingbackward.
Fig.6 GPSprobevehicledataforNov.13,2016forhighwayA81fromHeilbronnto Stuttgart(Germany).
“Mundelsheim” Junction “Ilsfeld”
Fig.7 GPSprobevehicledataforNov.13,2016forhighwayA81fromHeilbronnto Stuttgart(Germany).
InothercountriessuchastheUnitedKingdom,similartrafficpatterns canbediscovered(see Fig.8).Inthisexamplethered-markedarea(tiny wavylinesinprintversion)existsformorethan1handpropagatesmore than20kmbackward. Fig.9 showsthatmultiplesuchpropagatingareas canoccurwithinashorttime,forexample,fiveareasinlessthan1h.
2.2.2Localizedcongestion In Fig.10,weconsiderdatameasuredonhighwayA4inParis(France)on Oct.10,2016,(Monday).Weseethatapartfromtheareabetween4kmand 7km,thevehiclesaregoingfastwithspeedsofatleast60km/h.Between
M4, 25th Oct, 2016
Ramps Junction “M25” 4:30pm 5:30pm 6:30pm 7:30pm 8:30pm
Fig.8 GPSprobevehicledataforOct.25,2016,forhighwayM4neartheintersection withM25inLondon,theUnitedKingdom.
UK M4, 15th Nov, 2016
Fig.9 GPSprobevehicledataforOct.25,2016,forhighwayM4intheUnitedKingdom.
France A4, 30th Oct, 2016
Fig.10 GPSprobevehicledataforOct.10,2016forhighwayA4inParis(France).
4kmand6.2km,mostofthevehiclesaregoingslowerthan60km/h.At 6.2km,thereseemstobeafixedspotafterwhichthevehiclesareaccelerating.Actually,thereisanoff-rampataround6.2km.However,inthementionedareathereareonlytinyred(tinywavylinesinprintversion)regions, whichmeansthatthevastmajorityofthevehiclesaregoingfasterthan 25km/h. Fig.11 illustratesacongestedpatternintheUKatfreewayM3, whichislocalizedatthejunctionwithfreewayM5.Alocalizedstructure isstableformorethan3h,withthereducedspeedsindicatedinyellow.
Fig.12 showsanothersimilartrafficpatternmeasuredonhighwayA5in Hessen(Germany)onOct.31,2016.
“A86”
UK M3, 27th Oct, 2016
Fig.11 GPSprobevehicledataforOct.27,2016forhighwayM3inLondon(United Kingdom). A5-North, 31st Oct, 2016
Junction “A66” 3:00pm 4:00pm 5:00pm 6:00pm 7:00pm Time
Fig.12 GPSprobevehicledataforOct.31,2016forhighwayA5inHessen(Germany).
2.2.3Localizedandpropagatingcongestion:Ageneraltraffic pattern
Thedatashownin Fig.13 weremeasuredonhighwayA81fromHerrenbergtoB € oblingen/Sindelfingen(Germany)onOct.27,2016(Thursday). Weseeagainthatataround15.7km,thereisafixedspotafterwhichthe slowlydrivingvehiclesareaccelerating.Theinfrastructure-basedreasonis theG€auTunnelwithoutanyon-andoff-ramp,butwithaspeedlimit andatunnelentrance.Themaindifferencewith Fig.10 isthatin Fig.13,vehiclesaregoingveryslowlyatsomepartsthataremarkedin red(greywavylinesinprintversion).Thepatternsfollowingfromlowspeed areverysimilartothepatternfoundin Fig.7.Thesepatternsarealsomoving
A81, General Pattern, 27th Oct, 2016
Bottleneck “Gäu-Tunnel”
Fig.13 GPSprobevehicledataforOct.27,2016forhighwayA81fromHerrenbergto B € oblingen/Sindelfingen(Germany).
backwardinspace.In Fig.14,anothersimilartrafficpatternisshownthatis largerintimeandspace.ItwasmeasuredonhighwayA81fromHeilbronn toStuttgart(Germany)onNov.10,2016(Thursday).
2.2.4Localizedcongestion:Completefreewayblockage (“Megajam”) In Fig.15,wetakealookatdatameasuredonhighwayA8fromKirchheim unterTecktoStuttgart(Germany)onOct.27,2016(aThursday).At around12.9km,weseeafixedspot,afterwhichtheslowlydrivingvehicles
A8, General Pattern, 10th Nov, 2016
Junction “Weinsberg” 6:00am 7:00am 8:00am 9:00am 10:00am
Fig.14 GPSprobevehicledataforNov.10,2016forhighwayA81fromHeilbronnto Stuttgart(Germany).
A8 Mega-Jam 27th, Oct, 2016
8:00pm9:00pm 10:00pm 11:00pm
Fig.15 GPSprobevehicledataforOct.27,2016forhighwayA8fromKirchheimunter TecktoStuttgart(Germany).
areacceleratingandtrafficcongestiondispersesrapidly.Furthermore,wesee thatthefirstvehiclesstartgoingslowerat7:45a.m.at12.9km.Thespeed slowsdownunder25km/h,whichisveryslowonahighway;thisismarked inred(wavylinesinprintversion)inthefigure.Itisalsoimportanttosee thattherearealmostnopartsofthevehicletrajectoriesinwhichthespeedis between25km/hand60km/h;thisismarkedinyellow(smallportion aroundwavylinesinprintversion)inthefigures.Itseemsthatsomething happenedat7:45a.m.atroadlocation12.9km,afterwhichallvehicles hadtoslowdownrapidlyorevenstop.Itcouldbeacaraccidentthatcaused thehugetrafficcongestionbetween7:45a.m.and11:15a.m.Anothersimilarpatternisshownin Fig.16 fordatameasuredonhighwayA81from Leonberg/StuttgarttoHeilbronn(Germany)onNov.6,2016(Sunday).
2.2.5Inducedcongestion:Propagatingstructures Inalltheexamplesshownbefore,thetrafficbreakdownoccursatonelocation,andwecandefinethisasspontaneouscongestion(emergence).Inadditiontotheselocalizedphenomena,apropagatingcongestedstructurecan induceatrafficbreakdownatanupstreambottleneck,asweillustratein somefurtherexamples.Forthese,themeasuredspeedsofthevehiclesbelow 20km/harecolouredinredwhilethosebetween20and80km/harein yellowandthoseabove80km/hareingreen.
In Fig.17,apropagatingyellow(lightgreyregioninprintversion)structureemergesat7:55a.m.at4.5kmandpropagatesuntiltheon-rampat
A81 Mega-Jam, 6th Oct, 2016
4:30pm 5:30pm6:30pm 7:30pm Time
Junction “Pleidelsheim”
Fig.16 GPSprobevehicledataforOct.6,2016forhighwayA81fromLeonberg/ StuttgarttoHeilbronn(Germany).
A5-South 27th November, 2017
Intersection “Westkreuz Frankfurt”
Intersection “Nordwestkreuz Frankfurt” On-ramp On-ramp On-ramp 7:50am 8:00am 8:10am 8:20am 8:30am
Fig.17 GPSprobevehicledataforNov.27,2017forhighwayA5SouthnearFrankfurt (Germany).
3.5km.After8h,congestedtrafficwithreducedspeedsbetween20and 80km/hremainsstableformorethanthenext30min.
In Fig.18,twopropagatingstructuresinred(wavylinesinprintversion) arevisibleonall7kmoftheillustratedroadsection.Thesecondstructure inducesslowertrafficatthebottleneck,whichispotentiallytheendingofa roadgrade.Theslowtrafficremainsforalmostthenexthourlocalizedatthis kindofbottleneck.
ThethirdexampleofinducedcongestionisshownforInterstate90in Chicago:slow-movingtrafficpropagatesfrom22kmupstreamandinduces at19km(anintersectionofI-90)slow-movingcongestion.Thiscongestion
A5-North, 16th Nov, 2017
End of road grade of 3.9%
Begin of road grade of 3.9% Intersection “Friedberg” “Rastplatz Schäferborn”
Fig.18 GPSprobevehicledataforNov.16,2017forhighwayA5NorthnearFrankfurt (Germany).
Intersection between I-90 and “Harlem Ave” Intersection between I-90 and “N Cumberland Ave”
Intersection between I-90 and I-94
Fig.19 GPSprobevehicledataforApril8,2019,atInterstate90(West)inChicago(data providedbyHERE.Urbanfreewaywithmanyintersectionsandramps).
remainsformorethan2hatthebottlenecklocation.Theprobedateforthis examplehavebeenprovidedbyHEREfortheUSmarket(Fig.19).
2.2.6Similarandheterogeneouscongestedtrafficpatterns
Wewillnowtakeacloserlookatasequenceofdatameasuredonmotorway M11inLondon.ThedataweremeasuredfromOct.25,2016(aWednesday)toNov.16,2016(aWednesday)inthetimeintervalbetween6:00a.m. and12:00a.m.Weseethatthetrafficpatternsontheweekdaysaresimilarto eachother,whereasthetrafficpatternontheweekendsdiffersfromthe weekday.Onweekdays,theusualcongestedtrafficpatternsareobserved
atthepeakhoursinthetimeintervalof7:00a.m.to10:00a.m.frompeople goingtowork.Asexpected,ontheweekendsthetrafficislessandthereisno trafficcongestionobserved(Fig.20).
Additionally,congestedtrafficpatternsona33kmstretchoffreewayA5 illustrateboththevarietyandsimilarityofthepatterns.Onweekdays,the congestionstartsalmostsimultaneouslyatbottlenecksatthetwojunctions WalldorfandBruchsalatabout6:30a.m.,withthecongestionremaining untilapproximately9:00a.m.Onaglobalview,thewidthandduration
6:00am 9:00am 12:00pm
6:00am 9:00am 12:00pm
6:00am 9:00am 12:00pm
Monday, 31th Oct. Fri, 11th Nov Monday, 7th Nov.
6:00am 9:00am 12:00pm 6:00am 9:00am 12:00pm6:00am 9:00am 12:00pm 6:00am 9:00am 12:00pm 6:00am 9:00am 12:00pm 6:00am 9:00am 12:00pm 6:00am 9:00am 12:00pm
Junction “M25” Tuesday, 1st Nov. Tuesday, 8th Nov. Wed., 2nd Nov. Wed., 9th. Nov. Thu., 3rd. Nov.
10th Nov.
Junction “M25”
Junction “M25” Junction “M25” Junction “M25” Fri., 4th Nov.
Fig.20 TwoweeksofcongestedpatternsintheUKatfreewayM11;similarityon weekdayswithcongestionalwaysbeginningat7a.m.
areverysimilar,butlookingintothedetailssomedifferencesarevisible.As oneexample,onsomedaysthreepropagatingstructuresfromtheWalldorf junctionpropagateuntiltheBruchsaljunction(Nov.2and9,2016).Onone day,(Nov.8,2016),twostructurespropagateupstream,butonsomedays thereisonlyonepropagatingstructure(Nov.7,10,14,and16,2016).On someweekdays,nostructurepropagatesupstreamuptobottleneckB(Nov. 11and15,2016)(Fig.21).
2.2.7Complexempiricaltrafficpatterns Incomplexroadnetworksonlongersections,alwaysatseveralbottlenecks, alargevarietyofcongestedpatternsexist,emerge,anddissolveinparallel. Thefollowingexamplesillustratethiscomplexityofcongestedtraffic patterns
Fig.22 showsthehighwaysectionA8comingfromKirchheim,passing thecityofStuttgartgoingtowardPforzheim.Markedonthesidearebottlenecksthatinfluencethetrafficheavily.Foronce,onecanseetheusual congestedtrafficpatternsatpeakhoursfrompeoplegoing(6:30a.m.until 10:00a.m.)toworkandleavingforhome(4:00p.m.until8:00p.m.)at KreuzStuttgart,whichisamajorintersectiononthishighway.AtthebottleneckEsslingen,twolargecongestionsevolvedafteranaccident.
In Fig.23,themap-matchedrawGPSdataareshownfortheM4going towardLondon’scitycenter.AswiththeA8sectioninGermany,themajor jamsarehappeningduringthepeakhourswherepeoplearegoingtoand leavingwork.Similartrafficpatternsareobserved.Itisclearthatwithmore data,theprecisenessofthetrafficreconstructionincreases.ThefiguressupportaqualitativejudgementthatwithapproximatelyoneGPSprobeper minute(i.e.,about60connectedvehiclesperhour,whichisabouta1%penetrationrateofthetotaltrafficflowforathree-lanefreewaywith6000vehicles/hinpeaktimes),onaveragethequalityissufficientforatrafficservice.
2.2.8Trafficpatternsinurbanareas Inthefollowing,wewillconsideranurbanareawithaspeedlimitof50km/ h.ThedataweremeasuredonNov.9,2016,foranurbanroadsectionin Boblingen.Inurbanareas,wesimplycolourthevehicletrajectoriesaccordingtothefollowinglegend:(i)red:0–10km/h,(ii)yellow:10–35km/h, and(iii)green: >35km/h.Amaindifferenceoftheemergenceoftraffic congestionbetweenurbanareasandhighwaysisthatusuallytrafficsignals causetrafficcongestioninurbanareas,whereasonhighways,bottlenecks
