EmpiricalStudyofTrafcFeaturesataFreewayLaneDropRobertL.Bertini,M.ASCE,1andMonicaT.Leal2 Abstract: TrafcwasstudiedupstreamanddownstreamofabottleneckthatarosenearafreewaylanedropnearLondon,U.K.using archivedhigh-resolutionloopdetectordata.Thebottleneck'slocationandmeandischargeowswerereproduciblefromdaytoday. Further,itisshownthatthebottleneck'sdischargeowwasabout10%lowerthantheprevailingowobservedpriortoqueueformation. Uponbottleneckactivation,owreductionsoccurringsequentiallyintimeandspacemarkedthepassageofthebackward-movingshock. Meanshockvelocitiesrangedbetween4.8and6.4km/h ~ 3and4mph ! astheytraveledupstreamfromthebottleneck.Duringbottleneck discharge,oscillationsaroseinthequeueandpropagatedupstreamatnearlyconstantspeedsof17.619.2km/h ~ 11mph ! .Flows measuredatlocationsdownstreamofthebottleneckwerenotaffectedbytheseoscillations.Thesendingswerecorroboratedusingdata fromafreewaylanedropinMinneapolis,Minn.Theanalysistoolsusedforthisstudywerecurvesofcumulativevehiclecount,timemean speedandoccupancyversustime.Thesecurveswereconstructedusingdatafromneighboringfreewayloopdetectorsandweretransformedinordertoprovidethemeasurementresolutionnecessarytoobservethetransitionsbetweenfreelyowingandqueuedconditions andtoidentifyimportanttrafcfeatures. DOI: 10.1061/ ~ ASCE ! 0733-947X ~ 2005 ! 131:6 ~ 397 ! CEDatabasesubjectheadings: Empiricalequations;Trafcpatterns;Interstatehighways;UnitedKingdom;Minnesota. IntroductionUnderstandingtrafcbehavioratfreewaybottlenecksprovidesa foundationforunderstandinghowafreewaysystemoperates.A bottleneckisapointonthenetworkupstreamofwhichonends aqueueanddownstreamofwhichonendsfreelyowingtrafc. Bottleneckscanbestatic ~ e.g.,atunnelentrance ! ordynamic ~ e.g.,anincidentoraslowmovingvehicle ! inspaceandtime.A bottleneckisconsideredactivewhenitmeetstheconditionsdescribedaboveandisdeactivatedwhenthereisadecreaseindemandorwhenthereisaspilloverfromadownstreambottleneck ~ Daganzo1997 ! .Bottlenecksareimportantcomponentsoffreewaysystems,sincethequeuesthatdevelopuponbottleneckactivationmaypropagateforseveralmiles,causingdelayandpotentiallyblockingofframpsandaccesstootherfacilities.Withthe implementationofnewtrafcsurveillancesystems,itispossible tostudyandunderstandfreewaybottlenecksofallkindsâ€“ includingmergesnearbusyonramps ~ e.g.,Bertini,1999;Cassidy andBertini1999b,a;BertiniandCassidy2002;Cassidyand Mauch2001;CassidyandRudjanakanoknad2002 ! ,divergesnear busyofframps ~ e.g.,Windover1998;Cassidyetal.2000;Muoz andDaganzo2002 ! ,lanedrops,andothercongurations.This studycontributestoagreaterunderstandingofbottlenecksarising inthevicinityoffreewaylanedrops,whicharevariantsoffreewaymergesassociatedwithonramps.LiteratureReviewTowardunderstandingthedetailsoftrafcowaroundlocations wheretrafcstreamsmerge,earlierstudieshaveexaminedtrafc conditionsbothupstreamanddownstreamoffreewaybottlenecks locatednearbusyonramps ~ Bertini1999;CassidyandBertini 1999b;a;BertiniandCassidy2002 ! .Bertini ~ 1999 ! alsodescribes otherpreviousstudiesthatwerelimitedbyavailabilityofdata onlyupstreamofactualbottlenecklocations.Inearlierstudies, oscillationswerealsofoundtopropagateupstreaminfreeway queuesatnearlyconstantspeeds ~ CassidyandMauch2001; Mauch2002;MauchandCassidy2002 ! .Theseoscillationsdid notaffectowsmeasureddownstreamofthelocationswhere queuesformed.Topromotethevisualidenticationoftimedependentfeaturesoftrafcstreams,thesepreviousstudiesused curvesofcumulativevehiclecountandcurvesofcumulativeoccupancyconstructedfromdatameasuredatneighboringfreeway loopdetectors ~ seeCassidyandWindover1995;CassidyandBertini1999b;afortutorialsontheuseofthesecumulativecurves ! . Theuseofthesecurvesprovidedthemeasurementresolutionnecessarytoobservetransitionsbetweenfreelyowingtoqueued conditionsandtoidentifyanumberofnotable,time-dependent trafcfeaturesofthebottlenecks. Cumulativecurvesofvehiclecount,timemeanspeedandoccupancywerealsousedinthisstudy,whichaddstoprevious ndingsbyreportingonobservationstakenduringvemorning peakperiodsbothupstreamanddownstreamofafreewaylane dropnearLondonandatafreewaylanedropinMinneapolis, Minn. ~ Leal2002 ! .FortheLondonsite,individualvehicleactuationtimes ~ tothenearestsecond ! andtimemeanspeedswere obtainedfrominductiveloopdetectorslocatedineachtravellane. 1AssociateProfessor,Dept.ofCivil&EnvironmentalEngineering, PortlandStateUniv.,P.O.Box751,Portland,OR97207-0751.E-mail: firstname.lastname@example.orgTransportationEngineeringAssistant,DKSAssociates,1400SW FifthAve.,Suite500,Portland,OR97201-5502.E-mail:mtl@ dksassociates.com Note.DiscussionopenuntilNovember1,2005.Separatediscussions mustbesubmittedforindividualpapers.Toextendtheclosingdateby onemonth,awrittenrequestmustbeledwiththeASCEManaging Editor.ThemanuscriptforthispaperwassubmittedforreviewandpossiblepublicationonAugust8,2003;approvedonSeptember9,2004. Thispaperispartofthe JournalofTransportationEngineering ,Vol. 131,No.6,June1,2005.ASCE,ISSN0733-947X/2005/6-397407/ $25.00.JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005/ 397
FortheMinnesotasite,owandoccupancydataat30sintervals wereobtainedfrominductiveloopdetectorsalsolocatedineach travellane.Throughtheuseofcumulativecurves,ithasbeen possibletoverifythatthebottlenecksbecameactive,guaranteeingthatvehiclesdischargedfromupstreamqueuesandwereunimpededbytrafcconditionsfromfurtherdownstream ~ Daganzo 1997 ! .Itwasalsopossibletoobservecertainbottleneckfeatures thatwerereproduciblefromdaytoday. First,somebackgroundwillbeprovided,followedbyadescriptionofthestudysitesandtheloopdetectordatausedforthis analysis.Next,detaileddescriptionsofthebottlenecks'locations anddischargefeatureswillbepresentedfor1representativeday ateachsite.Thisisfollowedbysummariesoffeaturesfoundto bereproducibleon4additionaldaysattheLondonsite.Finally, someconcludingcommentsareprovided.DataItisshownthatafreewaybottleneckarosenearafreewaylane drop ~ fromthreetotwolanes ! ontheM4motorwaynearLondon, U.K.Thebottleneck'slocationandaveragedischargeowwere reproduciblefromdaytoday.Further,itisshownthatthebottleneck'sdischargeowwasabout10%lowerthantheprevailing owobservedpriortoqueueformation.Itisalsoshownthat shockvelocitieswerenearlyconstantasthequeuepropagated upstreamfromthebottleneck.Duringbottleneckdischarge,oscillationsaroseintheupstreamqueue;theseoscillationspropagated upstreamatnearlyconstantspeeds.Theseoscillationswerenot observedinowsmeasureddownstreamofthebottlenecklocation.Thesendingswerecorroboratedusingdatafromafreeway lanedroponI-494inMinneapolis,Minn. Thetwofreewaysitesusedinthisstudywerethesegmentsof theM4MotorwaynearLondon,U.K.andtheI-494freewayin theMinneapolis,Minn.,illustratedinFig.1.Onthis4.1km ~ 2.5 mi ! segmentoftheM4,inductiveloopdetectorsspacedapproximatelyevery0.5km ~ 0.3mi ! recordedindividualvehicles'arrival times ~ tothenearestsecond ! andtheirtimemeanspeedsineach lane.Theloopdetectordatawereavailableintheirmostrawform andwerenotaggregatedoveranyarbitraryperiods.TheM4detectorswerelabeled1asshowninFig.1,andthelanedropis locatedatapproximatelyKilometer17.1 ~ Mile10.6 ! .Whenthese datawerecollectedin1998themotorwayspeedlimitwas 112km/h ~ 70mph ! upstreamofdetector9and80km/h ~ 50 mph ! downstreamofdetector9.Wenotethatin1999modicationstothemotorwaylanemarkingswereinstalled,creatingabus laneforusebybusesandtaxis ~ andasof2002,motorcyclesas well ! inthefast ~ right-hand ! lane ~ Reesetal.2000 ! .Thisdoesnot affectthepresentstudy'sndings.Onthe2.4km ~ 1.5mi ! segmentofI-494inMinneapolisshowninFig.1,thedetectorsrecordedcountsandoccupanciesineachlaneover30sintervals. Thedetectorswerelabeled1a4andthelanedropislocated betweenDetectors2and3. Thefollowingtwosectionsdescribethebottleneckfeatures observed ~ forsingledays ! ontheM4andonI-494.TheseobservationswerereproducedonfouradditionaldaysfortheLondon site,asdescribedinalatersection.ObservationsonM4MotorwayTrafcfeaturessurroundingthelanedropontheM4wereanalyzedusingdatafromMonday,November16,1998,reportedto beacloudydaywithnomeasurableprecipitation.Fig.2shows obliquecurvesofcumulativevehiclearrivalnumberversustime, N s x , t d ,constructedfromcountsmeasuredacrossalllanesatDetectors28andcollectedduringa30minperiod.Thesecurves wereconstructedbytakinglinearinterpolationsthroughtheindividualvehiclearrivaltimes,sothatacurve'sslopeattime t wouldbetheowpastlocation x atthattime.Thecountsforeach Fig.1. Sitemaps 398 /JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005
curvebegan s N =0 d relativetothepassageofahypotheticalreferencevehiclesoallcurvesdescribethesamecollectionofvehicles.Eachcurvewasshiftedhorizontallytotherightbythe averagefreeowtriptimefromitsrespective x toDetector8,the downstreammostdetectorinthegure.Anyresultingvertical displacementsaretheexcessvehicleaccumulationsbetweendetectorsduetovehicledelays ~ Newell1982,1993 ! . Inordertomagnifythecurves'features,anobliquecoordinate systemwasusedwhere N s x , t d wasreducedby q0s t t0d where q0wasanobliquescalingrateand t0wasthecurve'sstartingtime. OnecanvisualizethecurvesinFig.2asdepictingthedifference betweentheoriginal N s x , t d andalineofslope q0,whichmerely providesahighervisualresolutionofthesamedata.Thesame valueof q0wasusedforallcurvesandthereforedidnotaffectthe verticalseparations ~ CassidyandWindover1995 ! .Theuseofthis obliquecoordinatesystemisdescribedindetailinseveralreferences ~ CassidyandWindover1995;CassidyandBertini1999b ! . AsshowninFig.2,curvesforalldetectorswereinitiallysuperimposedindicatingfreelyowingtrafcthroughoutthisentire motorwaysection.ThecurvesforDetectors8and7remained nearlysuperimposedforthisentire30minperiod,indicatingthat trafccontinuedtoowfreelybetweenthesedetectors.Excess vehicleaccumulationsoccurredbetweenDetectors6and7subsequenttoowreductionsobservedatDetectors7and8at around6:44and6:45a.m.,respectively ~ despitethefactthatvehiclearrivaltimeswereavailabletothenearestsecond,timesare reportedtothenearestminutesoasnottoimplyanundueprecisionofmeasurement ! . ThedivergenceofthecurveatDetector6fromtheoneat Detector5 ~ at6:46a.m. ! markedthearrivalofabackwardmovingqueueatDetector6.TherewasapronouncedowreductionatDetector6thataccompaniedthisdivergence.Thepresence offreelyowingtrafcbetweenDetectors7and8accompanied byexcessvehicleaccumulationupstreamofDetector7revealed thatthebottleneckwaslocatedsomewherebetweenDetectors6 and7wherethetransitionfromthreelanestotwolanesoccurs. Fig.2alsomappedthepropagationofthequeueupstreamof Detector6.Asshowninthegure,areductioninowatDetector 5wasobservedat6:50a.m.,wherethecurveatDetector5deviatedfromtheupstreamcurves.ThisindicatedexcessvehicleaccumulationupstreamofDetector5.Additionaldeviationsoccurredinsequence,indicatingthatthequeueultimatelyarrivedat Detector2at7:01a.m..Fig.2hasmadeitpossibletodiagnose thebottleneck'slocation ~ betweenDetectors6and7 ! ,aswellas thetimeitbecameactive ~ around6:45a.m. ! .Tofurtherconrm thequeue'sarrivaltimeatDetector6atapproximately6:46a.m., theinsetinFig.2showsabarchartofthevarianceofthecounts recordedatDetector6,measuredove r3speriods.Inorderto amplifythisfeature,thevarianceisalsoplottedcumulativelyin thegure ~ seeBertini2003 ! ,usinganobliqueaxistomagnifythe detailsofthecurve.Thisshowsthatthevariancedropsatthe beginningofthequeuedischarge,whichisnotsurprisingsince vehiclesweredischargingfromaqueue. Toverifythearrivalofthebackward-movingqueueateach detector,cumulativecurvesoftimemeanspeed s V s x , t dd were constructedforeachdetector. V s x , t d wasthecumulativetime meanspeedmeasuredatdetector x bytime t .Aswiththe N s x , t d , piecewiselinearapproximationsto V s x , t d wereconstructed, wheretheslopeofthe V wasaspeedratemeasuredatlocation x attime t .Anobliquecoordinatesystemwasalsousedwhere V s x , t d wasreducedby V0s t t0d ,Similartotheuseof q0, V0was anobliquescalingrateand t0wasthecurve'sstartingtime.The V wereplottedusingthisobliqueaxistovisuallyidentifyperiodsof Fig.2. Transformed N s x , t d onM4 JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005/ 399
nearlyconstantaveragespeedandtimesmarkingchangesinaveragespeed. Fig.3containsobliquecurvesofcumulativevehiclespeed V s x , t d versustime,measuredatDetectors6and7.Asshownin thegure,asharpreductioninspeedwasseenatDetector7at around6:44a.m.,conrmingthearrivaloftheforward-moving waveatapproximatelythattime.The V s x , t d forDetector6revealsareductioninvelocitymeasuredatabout6:46a.m.,conrmingthequeue'sarrivalatthattime.Thegurealsoshows V s x , t d measuredinindividuallanesatDetectors6and7,toindicatethatspeedreductionsoccurredatslightlydifferenttimesin eachlane. Fig.3alsoshowsoblique V s x , t d forDetectors5,4,3,and2as measuredacrossalllanes.Thetimesmarkedbydropsinvelocity correspondedwiththetimesmarkedbyowreductionsinFig.2. Table1showstheshockspeedsrecordeduponbottleneckactivationforthisday.Asshown,theshock'supstreamvelocitywas between6.4and12.8km/h ~ 4and8mph ! .Notethatthewave betweenDetectors7and8wasadownstreammovingexpansion waveoflowerowandhighervelocity. Fig.3. Oblique V s x , t d onM4 400 /JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005
Inordertodeterminetheexactperiodduringwhichthisbottleneckremainedactive,Fig.4showsoblique N s x , t d forDetectors2 and8foralongerperiod.Asindicatedbythecontinuedvertical displacementbetweenthetwocurves,thequeuebetweenDetectors2and8persisteduntilaround9:07a.m.whenthe N s x , t d againbecamesuperimposed.Thisshowsthatvehiclesweretravelingunimpededbetweenthesedetectorsafterthistimeandthus indicatingqueuedissipation.TheinsetsinFig.4containoblique V s x , t d forDetectors2and8.Asshowninthelowerinset,aspeed increasewasobservedatDetector8aroundthetimethatthe queuedissipated.Queuedissipationoccurredseveralminutes afteradecreaseinowwasmeasuredatDetector2 ~ around8:48 a.m. ! signalingtheendofqueueingatthatlocation.Theupper insetveriesthetimingoftheendofqueueingatDetector2by showingthatanincreaseinspeedalsooccurredat8:48a.m. Figs.2and4haveveriedthebottleneck'slocation,thetimeit becameactive,andthetimethatitwasdeactivated.Fig.2also mapsthepassageofthebackward-movingqueue.Nowitispossibletoexaminetheactivebottleneck'squeuedischargefeatures indetail. CumulativecurvesatDetector8 ~ downstreamofthebottleneck ! wereusedtoexaminethebottleneck'sdischargefeatures. Fig.5showsoblique N s 8, t d and V s 8, t d .Inthegure,periodsof nearlyconstantowandspeedweremarkedwithsolidlines wheretheaverageowsareinvehicles/hourandtheaverage speedsareinkilometers/hour ~ mph ! .Theaveragedischargeow ismarkedwithadashedline.Fig.5showsthattheformationof theupstreamqueueat6:45a.m.wasmarkedbyareductionin N s x , t d accompaniedbyareductioninspeed.Sincethecurvesin Fig.5donotdisplayanyabruptreductionsinthe N s x , t d accompaniedbyreductionsinspeedbetween6:45and9:07a.m.,itis apparentthattherewasnodisruptionofactivebottleneckdischargecausedbyaqueuefromanywherefurtherdownstream. Turningtothebottleneck'sowfeaturesdisplayedinFig.5,it isshownthatbetween6:28a.m.andthebeginningofqueuedischarge ~ 6:45a.m. ! aowof3,690vehicles/hprevailedinthe two-lanesectiondownstreamofthebottleneck.Uponqueuedischarge,alowerowof3,470vehicles/hwasobserved,which prevailedforabout50min.Thiswasfollowedbyaseriesof sequencesofnearlyconstantowuntilqueuedissipation.This sequenceofowsdidnotdeviatesubstantiallyfromtheaverage dischargeowof3,300vehicles/h ~ markedbyadashedline ! , whichwas10.6%lowerthantheowthatprevailedpriorto bottleneckactivation.Thecause ~ s ! oftheseowchangesisnot knownandisthesubjectofongoingresearch.Thebottleneck's Table1. ShockCharacteristicsonM4 ~ November16,1998 ! Distance Meantraveltime ~ min:s ! Meanspeed Detectors ~ km !~ mi ! s km/h d ~ mph ! 7-80.500.310:24+75+47 6-50.500.313:4085 5-40.500.315:1964 4-30.500.313:5885 3-20.500.312:21138 Fig.4. Upstreamanddownstreamoblique N s x , t d onM4 JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005/ 401
dischargeowprevailedoveraperiodo f2h22 min.Thisconrmsthemeasurementofaowdropuponbottleneckactivation andthatthequeuedischargeowwasnearlyconstantonthisday. Trafcoscillationsinqueuedconditionsarecharacterizedby sharpincreasesinowfollowedbysharpreductionsinow.Toa motoristinthequeue,oscillationsappearasstopandgoorslow andgodrivingconditions ~ CassidyandMauch2001 ! .Fig.6illustratesoscillationsforabout45minofcongestedconditions usingoblique N s x , t d forDetectors18.Theverticaldistances betweentheoblique N s x , t d areproportionaltothedistances betweenthedetectorsalongthemotorway.Usingaprocedure fromMauchandCassidy ~ 2002 ! ,amoving10minaverageow wassubtractedfromeach N s x , t d : N s t d f N s t +5min d + N s t 5min dg /2,whichisshownas N N10inthegure.Therefore, theslopesoftheoblique N s x , t d inthisgurerepresentobserved owdeviationsfromaverageows ~ MauchandCassidy2002 ! . Asshown,theoscillationsonlyoccurredupstreamofthe bottleneck ~ Detectors16 ! andeachlastedforseveralminutes. Theoblique N s x , t d forthedetectorsdownstreamofthebottleneck remainedsmooth ~ Detectors7and8 ! .Thus,oscillationswerenot observedwheretrafcwasunqueued.Theamplitudeofeachoscillationwaslessthan70vehiclesasmeasuredacrossalllanesor about23vehiclesasmeasuredinindividuallanes,asshowninthe gure.Thelargestamplitudeof68vehiclesacrossalllanesor about22vehiclesperlanewasobservedatDetector1.Other ndingsreportedslightlyloweramplitudesoflessthan50vehicles ~ MauchandCassidy2002 ! . Thepeaksoftheoscillationswereconnectedbydashedlines, wheretheslopeofthedashedlinewastheupstreamvelocityof theoscillation.Theselinesappeartobeparallel,atanearlyconstantspeedofabout17.619.2km/h ~ 11mph ! ,independent ofthelocationwithinthequeue.MauchandCassidy ~ 2002 ! reportedsimilarspeedsofabout22.424.0km/h ~ 14mph ! .ObservationsonI-494inMinneapolisTrafcfeatureswereanalyzedontheI-494freewayusingdata fromWednesday,October27,1999.Fig.7showsobliquecurves ofcumulativevehiclearrivalnumberversustime, N s x , t d ,constructedfromcountsmeasuredacrossalllanesatDetectors14 andcollectedduringa50minperiodsurroundingactivationof thebottleneckbetweenDetectors2and3.TheDetector1curve containsthesumofcountsfromDetectors1aand1bandthe Detector4curveisthesumofcountsfromthemainline ~ two lanes ! plustheofframp. AsshowninFig.7,curvesforalldetectorswereinitiallysuperimposedindicatingfreelyowingtrafcthroughthewhole section.ThecurvesforDetectors3and4remainednearlysuperimposedforthisperiod,indicatingthattrafccontinuedtoow freelybetweenthesedetectors.Excessvehicleaccumulations wereseenbetweenDetectors2and3subsequenttoowreductionswhichwereobservedatDetectors3and4ataround6:35 a.m. ThedivergenceofthecurveatDetector2fromtheoneat detector3 ~ at6:35a.m. ! markedthearrivalofabackwardmovingqueueatDetector2.Toconrmthis,theleftinsetinFig. 7showsanobliquecurveofcumulativeoccupancyversustime T s x , t d forDetector2,wherecumulativeoccupancywasthetotal vehicletriptimemeasuredoverthedetectorsbytime t .Againfor thepurposeofmagnifyingdetails,the T s x , t d shownwasthedifferencebetweenthecumulativeoccupancyactuallymeasuredat Detector2 ~ acrossalllanes ! andaline T = b0t0,where b0wasan obliquescalingrateand t0wastheelapsedtimefromthebeginningofthecurve.Asharpincreaseinoccupancywasseenat around6:35a.m.,verifyingthearrivalofthequeue.Thepresence offreelyowingtrafcbetweenDetectors3and4,accompanied byexcessvehicleaccumulationupstreamofDetector2reveals Fig.5. Oblique N s x , t d and V s x , t d atdetector8onM4 402 /JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005
thatthebottleneckwaslocatedsomewherebetweenDetectors2 and3wherethetransitionfromthreelanestotwolanesoccurs.At about6:40a.m.therewasaowreductionaccompaniedbyan increaseinoccupancyatDetector1asshownintheright-hand insetinFig.7.Thisgurehasmadeitpossibletodiagnosethe bottleneck'slocation ~ betweenDetectors2and3 ! ,aswellasthe timeitbecameactive ~ around6:35a.m. ! . Table2showstheshockspeedmeasureduponbottleneckactivation.Asshown,theshockmovedupstreamataspeedof 12.8km/h ~ 8mph ! .Becausethedatawereaggregatedevery30s, andthewave'straveltimewaslessthan30s,itwasnotpossible tomeasuretheexpansionwave'svelocitybetweenDetectors3 and4. Inordertodeterminetheperiodduringwhichthisbottleneck remainedactive,Fig.8showsoblique N s x , t d forDetectors1and 4foralongerperiod.Asindicatedbythecontinuedverticaldisplacementbetweenthecurves,thequeuebetweenDetectors1and 4persisteduntilaround8:25a.m.whenthe N s x , t d againbecame superimposed.Thisshowsthatthevehiclesweretravelingunimpededbetweenthesedetectorsafterthistime.TheinsetsinFig.8 containobliquecurvesofcumulativeoccupancyatDetectors1 and4.Asshownintherightinset,anoccupancydecreasewas observedatDetector4aroundthetimethatthequeuedissipated. CompletequeuedissipationoccurredseveralminutesafteradecreaseinowatDetector1 ~ around8:10:30a.m. ! signaledthe endofqueueingatthatdetector.Theleftinsetveriesthetiming ofthequeuedissipationatDetector1byshowingthatadecrease inoccupancyalsooccurredaround8:10:30a.m.Figs.7and8 haveveriedthebottleneck'slocation,thetimeitbecameactive, andthetimethatitwasdeactivated. CumulativecurvesfromDetector4 ~ downstreamofthebottleneck ! wereusedtoexaminethebottleneck'sdischargefeatures. Fig.6. Oblique N N10ateachdetectoronM4 JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005/ 403
Fig.9showsobliquecurvesof N s 4, t d and T s 4, t d alsomeasured atDetector4.Inthegure,periodsofnearlyconstantowand occupancyareindicatedbysolidlineswheretheaverageows areinvehicles/hour.Theaveragedischargeowismarkedwitha dashedlineandisalsogiveninvehicles/hour.Fig.9showsthat theformationofanupstreamqueueat6:35a.m.wasmarkedbya reductionin N s x , t d accompaniedbyareductioninoccupancy. SincethecurvesinFig.9donotdisplayanyabruptreductionsin the N s x , t d accompaniedbyincreasesinoccupancybetween6:35 and7:40a.m.,itisapparentthattherewasnodisruptionofbottleneckdischargecausedbyaqueuefromanywherefurtherdownstream. TurningtothedischargefeaturesdisplayedinFig.9,itis shownthatbetween6:20a.m.andthebeginningofqueuedischarge ~ 6:35a.m. ! aowof5,040vehicles/hprevailedinthe two-lanesectiondownstreamofthebottleneck.Thiswasfollowedbyaseriesofsequencesofnearlyconstantowuntilqueue dissipation.Thissequenceofowsdoesnotdeviatemuchfrom theaveragedischargeowof4,370vehicles/h ~ markedbya dashedline ! ,whichwas12%lowerthantheowthatprevailed priortobottleneckactivation.Thisaveragedischargeowprevailedoveraperiodof1hand5min.ReproducingObservationsonM4Theanalysesdescribedintheprevioussectionswererepeated usingdatatakenfrom4additionaldaysontheM4motorway. Similartrafcconditionswerereproducedduringthe4days,but withsomeslightvariations.Onallvedays,thebottleneckarose betweenDetectors6and7.Table3reportsthesustainedow immediatelypriortoqueueformationandtheaveragedischarge ratethatprevailedsubsequenttobottleneckactivationforall5 days.Themean,standarddeviation,andcoefcientofvariation areidentiedfortheseows.Thedurationofqueuedischargeis alsodisplayed.Also,thetableshowsthepercentdifferencebetweenthehigherowpriortoqueuedischargeandthesustained averageowthatfollowed. Theowimmediatelypriortothequeuelastedforrelatively shortperiods,consistentwithotherstudies ~ e.g.,CassidyandBertini1999b;a;Bertini1999;BertiniandCassidy2002 ! .Atthis site,however,theseowsappearedtoberelativelyconsistent, withameanvalueof3,700vehicles/hmeasuredinthetwo-lane sectionatDetector8.Thismaybeatoddswithotherndings ~ e.g.,CassidyandBertini1999b;a;Bertini1999;Bertiniand Cassidy2002 ! thatrevealedpossibleinstabilitiesinthehigher owreportedpriortobottleneckactivation.Theaveragedischargeowwasalsoconsistentfromdaytoday,withamean valueof3,340vehicles/h.Thisowwassustainedformuch longerperiods,rangingfro m1h30minto almost5h.Thedrop inowobserveduponqueueformationwasalsoconsistentfrom daytoday.Onfourofthevedays,thispercentagedropwas between10and11%,whileonDecember2,1998thepercentage differencewasbetween6and7%. TheshockspeedswerealsoanalyzedforalldaysassummaTable2. ShockCharacteristicsonI-494 ~ October27,1999 ! Distance Meantraveltime ~ min:s ! Meanspeed Detectors ~ km !~ mi ! s km/h d ~ mph ! 2-11.00.635:00128 Fig.7. Transformed N s x , t d onI-494 404 /JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005
Fig.8. Upstreamanddownstreamoblique N s x , t d onI-494 Fig.9. Oblique N s x , t d and T s x , t d atdetector4onI-494 JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005/ 405
rizedinTable4.Themeanupstreamshockvelocitiesrangedbetween4.8and6.4km/h ~ 3and4mph ! .Therewereonlyslight differencesobservedbetweentheshockspeedsfromonemotorwaysectiontoanother.Thiswouldappeartoconrmthevalidity ofalinear q k relationforpredictingqueuepropagation ~ e.g., Newell1993;Windover1998 ! ,butconrmationofthisispartof ongoingresearch. Fig.10showsoblique V s x , t d forDetectors2and9fromDecember3,1998.Itisclearthatwhileaqueuewaspresentthe speeddroppedatbothdetectors,butthereductionatDetector2 waslargersincethespeedlimitwas112km/h ~ 70mph ! whileat Detector9thespeedlimitwas80km/h ~ 50mph ! .Thisspeed limitchangecouldcontributetotheobservationthatvehicle speedsatdownstreamdetectorsdidnotincreaseasrapidlyas Table3. SummaryofTrafcFeaturesonM4 FlowimmediatelypriortothequeueAveragedischargerate Percentdifference ~ % ! RateDurationRateDuration DateDay s vehicles/h d ~ h:min:s ! s vehicles/h d ~ h:min:s ! 16November1998Monday3,6900:17:503,3002:22:0610.6 18November1998Wednesday3,6900:14:453,3002:19:2510.6 30November1998Monday3,8400:08:073,4302:06:0910.7 2December1998Wednesday3,7500:11:573,5001:33:326.7 3December1998Thursday3,5100:13:123,1504:52:2210.3 Mean3,700â€“3,340â€“9.7 Standarddeviation121â€“135â€“â€“ Coefcientofvariation3.26â€“4.04â€“â€“ Table4. ShockCharacteristicsonM4 Detectors Distance Meanof5days Meantraveltime ~ min:s ! Meanspeed ~ km !~ mi ! s km/h d ~ mph ! 9-8a0.500.310:21+86+53 7-80.500.310:28+65+40 6-50.500.317:0343 5-40.500.315:2363 4-30.500.314:0974 3-20.500.315:4653a9-8wasmeasuredonDecember3,1998. Fig.10. Oblique V s x , t d atdetectors2and9onM4 406 /JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005
expected.Itappearsthatthevehiclesdidnotaccelerateveryrapidlyafterpassingthebottlenecklocationbecauseofthedropin speedlimitatDetector9.Thisaspectisthesubjectofongoing analysis.ConclusionsThisstudyanalyzedtrafcconditionsupstreamanddownstream oftwobottlenecksarisingnearfreewaylanedrops.Curvesof cumulativecount,timemeanspeedandoccupancyversustime wereusedinthisstudy.Suitablyconstructed,thesecurvesfacilitatedtheobservationoftrafcconditionsaroundthelanedrop bottlenecks.Ithasbeenshownthatbottlenecksaroseinthevicinityofthefreewaylanedropsinagenerallypredictableway. Flowsincreasedabovesomelevel,queuesformedandpropagated upstreamuntildemandreductionsledtoqueuedissipationlaterin themorning.TheLondonbottleneck'slocationwasreproducible fromdaytoday.Also,itwasshownthattheowscandrop substantiallyfollowingtheformationoftheupstreamqueues,followedbydischargeowsexhibitingnearlystationarypatterns. ThiscontradictsKerner ~ 2000 ! andKerner ~ 2002 ! ,whofound largevariationsindischargeowsdownstreamofbottleneckson aGermanhighway.Inthisstudy,thedropsinowwereaccompaniedbydropsinspeedandincreasesinoccupancy.Thehigher owspriortoqueueformationweresustainedforrelativelyshort periodsandthedischargeowsthatfollowedprevailedformuch longerperiods.Thevaluesofbothoftheseowsappearedtobe reproduciblefromdaytodayattheLondonsite.Thelongrun queuedischargeowsshouldbeconsideredtobethebottleneck capacitiessincedischargeowswerenearlyconstantandthey werereproduciblefromdaytoday. TheshockvelocitiesobservedontheM4weresomewhat slowerthanreportedelsewhereintheliterature.Towhatextent thiswasrelatedtodrivers'familiaritywiththeroadwaygeometry and/orthespeedlimitchangeatDetector9isthesubjectofongoingresearch.TheoscillationsontheM4arosewithinthequeue atthedetectorsupstreamofthebottleneck.Oscillationswerenot observedatlocationsdownstreamoftheheadofthequeue.Itwas observedthattheoscillationsdisplayedanearlyconstantupstreamspeed. Thisresearchwasonlyaninitialsteptowardunderstanding bottleneckbehaviorinrelationtolanedrops.Thus,furtheranalysesneedtobeconductedatthissiteinLondonaswellasatother lanedropsitesintheUnitedStates.AcknowledgmentsTheideaforthisstudywasoriginallypromptedbycorrespondencewithMr.StuartBeale,TelematicsGroup,Highways Agency,ExecutiveAgencyoftheDepartmentforTransport, UnitedKingdom.ThewritersgratefullyacknowledgeMr.Beale andMr.TimRees,ProjectManager,TransportResearchLaboratory,UnitedKingdom,forgenerouslysupplyingtheLondondata usedherein.TheauthorsalsothankProfessorDavidM.Levinson andLeiZhang,UniversityofMinnesotaandtheMinnesotaDepartmentofTransportation,forprovidingvaluabledatausedin thisstudy.RogerLindgren,OregonInstituteofTechnologyassistedwiththedatapreparation.Aportionofthisworkwas fundedbytheDepartmentofCivilandEnvironmentalEngineeringatPortlandStateUniversityandtheOregonEngineeringand TechnologyIndustryCouncil ~ ETIC ! .ReferencesBertini,R.L. ~ 1999 ! .Time-dependenttrafcowfeaturesatafreeway bottleneckdownstreamofamerge.PhDthesis,Univ.ofCaliforniaat Berkeley,Berkeley,Calif. Bertini,R.L. ~ 2003 ! .Towardthesystematicdiagnosisoffreewaybottleneckactivation. Proc.,IEEE6thAnnualConf.onIntelligentTransportationSystems ,Shanghai,China. Bertini,R.L.,andCassidy,M.J. ~ 2002 ! .Someobservedqueuedischargefeaturesatafreewaybottleneckdownstreamofamerge. Transp.Res.,PartA:PolicyPract. ,36A,683697. Cassidy,M.J.,Anani,S.B.,andHaigwood,J.M. ~ 2000 ! .Studyof freewaytrafcnearanofframp. CaliforniaPATHWorkingPaper , UCB-ITS-PWP-2000-10 ,Univ.ofCaliforniaatBerkeley,Berkeley, Calif. Cassidy,M.J.,andBertini,R.L. ~ 1999a ! .Observationsatafreeway bottleneck. Proc.,14thInternationalSymp.onTransportationand TrafcTheory,Jerusalem,Israel ,Pergamon,NewYork,107. Cassidy,M.J.,andBertini,R.L. ~ 1999b ! .Sometrafcfeaturesatfreewaybottlenecks. Transp.Res.,PartB:Methodol. ,33B,2542. Cassidy,M.J.,andMauch,M. ~ 2001 ! .Anobservedfeatureoflong freewaytrafcqueues. Transp.Res.,PartA:PolicyPract. ,35A, 149. Cassidy,M.J.andRudjanakanoknad,J. ~ 2002 ! .Studyoftrafcata freewaymergeandrolesforrampmetering. CaliforniaPATHWorkingPaper , UCB-ITS-PWP-2002-2 ,Univ.ofCalifornia,Berkeley, Calif. Cassidy,M.J.,andWindover,J.R. ~ 1995 ! .Methodologyforassessing thedynamicsoffreewaytrafcow. TransportationResearch Record , 1484 ,TransportationResearchBoard,Washington,D.C.,73 79. Daganzo,C.F. ~ 1997 ! . Fundamentalsoftransportationandtrafcoperations .Elsevier,NewYork. Kerner,B.S. ~ 2000 ! .Theoryofbreakdownphenomenonathighway bottlenecks. TransportationResearchRecord , 1710 ,Transportation ResearchBoard,Washington,D.C.,136. Kerner,B.S. ~ 2002 ! .Theoryofcongestedhighwaytrafc:empirical featuresandmethodsoftracingandprediction. Proc.,15thInternationalSymp.onTransportationandTrafcTheory,Adelaide,Australia ,Pergamon,NewYork,417439. Leal,M.T. ~ 2002 ! .Empiricalanalysisoftrafcowfeaturesofafreewaybottlenecksurroundingalanedrop.MSprojectthesis,Portland StateUniv.,Portland,Ore. Mauch,M. ~ 2002 ! .Analysesofstart-stopwavesincongestedfreeway trafc.PhDthesis,Univ.ofCaliforniaatBerkeley,Berkeley,Calif. Mauch,M.,andCassidy,M.J. ~ 2002 ! .Freewaytrafcoscillations:observationsandpredictions. Proc.,15thInternationalSymp.onTransportationandTrafcTheory,Adelaide,Australia ,Pergamon,New York,653673. Muoz,J.C.,andDaganzo,C.F. ~ 2002 ! .Thebottleneckmechanismof afreewaydiverge. Transp.Res.,PartA:PolicyPract. ,36A,483 505. Newell,G.F. ~ 1982 ! . Applicationsofqueueingtheory ,Chapmanand Hall,NewYork. Newell,G.F. ~ 1993 ! .Asimpliedtheoryofkinematicwavesinhighwaytrafc;I:GeneralTheory,II:Queueingatfreewaybottlenecks, III:Multi-destinationows. Transp.Res.,PartB:Methodol. ,27B ~ 4 ! ,281. Rees,T.,White,J.,andQuick,J. ~ 2000 ! . Monitoringofthebuslane:The rstyear .HighwayAgency,TRLLimited,London,U.K. Windover,J.R. ~ 1998 ! .Empiricalstudiesofthedynamicfeaturesof freewaytrafc.PhDthesis,Univ.ofCaliforniaatBerkeley,Berkeley,Calif.JOURNALOFTRANSPORTATIONENGINEERINGASCE/JUNE2005/ 407
1 CAPACITY CHANGE ANALYSIS AND ESTIMATION ON FLORIDA FREEWAYS By BRYAN ST. GEORGE A THESIS PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR TH E DEGREE OF MASTER OF ENGINEERING UNIVERSITY OF FLORIDA 2014
2 Â© 2014 Bryan St. George
3 To my Mom and Dad
4 ACKNOWLEDGEMENTS I would like to t hank my parents for supporting and encouraging me . I would also like to t hank you t o my friends for always sticking by me through the good times and the bad. Finally, thank you to the University of Florida, for six wonderful years.
5 TABLE OF CONTENTS P age ACKNOWLEDGEMENTS ................................ ................................ ............................... 4 LIST OF TABLES ................................ ................................ ................................ ............ 7 LIST OF FIGURES ................................ ................................ ................................ .......... 8 ABSTRACT ................................ ................................ ................................ ................... 10 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 11 2 LITERATURE REVIEW ................................ ................................ .......................... 13 Breakdown Definition ................................ ................................ .............................. 13 Capacity Definition ................................ ................................ ................................ .. 18 Capacity Drop ................................ ................................ ................................ ......... 25 Summary and Conclusions ................................ ................................ ..................... 33 3 METHODOLOGY ................................ ................................ ................................ ... 35 Overview of Methodology ................................ ................................ ....................... 35 Step 1 ................................ ................................ ................................ ..................... 35 Step 2 ................................ ................................ ................................ ..................... 36 Step 3 ................................ ................................ ................................ ..................... 37 Step 4 ................................ ................................ ................................ ..................... 37 Step 5 ................................ ................................ ................................ ..................... 38 4 DATA COLLECTION AND AN ALYSIS ................................ ................................ ... 39 Data Collection ................................ ................................ ................................ ....... 39 Site Description ................................ ................................ ................................ ....... 40 I 95 NB at Butl er Boulevard, Jacksonville, FL ................................ .................. 40 I 95 NB at University Boulevard, Jacksonville, FL ................................ ............ 41 SR 826 EB at NW 47 th Avenue, Miami, FL ................................ ....................... 42 I 4 EB at SR 408, Orlando, FL ................................ ................................ ......... 42 I 95 NB at NW 103 rd Street, Miami, FL ................................ ............................. 43 I 95 NB at Philips Highway, Jacksonville, FL ................................ .................... 43 I 4 EB at I 75, Tampa, FL ................................ ................................ ................. 44 I 95 NB at the Turnpike, Miami, FL ................................ ................................ ... 44 I 95 NB Between Baymeadows Rd and Butler Blvd, Jacksonville, FL .............. 45 I 4 WB at Lee Road, Orlando, FL ................................ ................................ ..... 45 Data Analysis ................................ ................................ ................................ .......... 46
6 5 MODEL DEVELOPMENT ................................ ................................ ....................... 56 Variable Testing ................................ ................................ ................................ ...... 56 Truck Percentages ................................ ................................ ........................... 56 Free Flow Speed ................................ ................................ .............................. 60 Number of Lanes ................................ ................................ .............................. 63 Bottleneck Type ................................ ................................ ................................ 66 Percentile Difference ................................ ................................ ........................ 69 Model Development ................................ ................................ ................................ 73 Breakdown Flow Definition ................................ ................................ ............... 74 5 Minute Flow Before Breakdown ................................ ................................ .... 76 15 Minute Flow Before Breakdown ................................ ................................ .. 78 Maximum 5 Minute Flow Before Breakdown ................................ .................... 80 Discharge Flow ................................ ................................ ................................ . 82 6 CONC LUSIONS AND RECOMMENDATIONS ................................ ....................... 85 Conclusions ................................ ................................ ................................ ............ 85 Recommendations ................................ ................................ ................................ .. 86 LIST OF REFERENCES ................................ ................................ ............................... 89 BIOGRAPHICAL SKETCH ................................ ................................ ............................ 91
7 LIST OF TABLES Table P age 2 1 Breakdow n summary ................................ ................................ .......................... 17 2 2 Capacity definition summary ................................ ................................ .............. 24 2 3 Capacity drop summary ................................ ................................ ...................... 30 2 4 Capacity drop model summary ................................ ................................ ........... 33 4 1 Selected urban freeway bottleneck locations ................................ ..................... 39 4 2 Capacity measure statistics fo r all sites ................................ .............................. 47 4 3 Actual difference statistics for all sites ................................ ................................ 50 4 4 Percentile difference statistics for all sites ................................ .......................... 52 5 1 Model development to predict capacity ................................ .............................. 73 5 2 Model development to predict actual difference and percentile difference ......... 74 5 3 Models related to the breakdown flow ................................ ................................ 75 5 4 Models related to the 5 minute flow before breakdown ................................ ...... 77 5 5 Models related to the 15 minute flow before breakdown ................................ .... 79 5 6 Models related to the maximum 5 minute flow before breakdown ...................... 81 5 7 Models related to the discharge flow ................................ ................................ .. 83
8 LIST OF FIGURES Figure P age 4 1 Schematic of I 95 NB at Butler Boulevard study secti on in Jacksonville, FL ...... 41 4 2 Schematic of I 95 NB at University Boulevard study section in Jacksonville, FL ................................ ................................ ................................ ....................... 41 4 3 Schematic of S R 826 EB at NW 47th Avenue study section in Miami, FL .......... 42 4 4 Schematic of the I 4 at SR 408 study section in Orlando ................................ ... 43 4 5 Schema tic of I 95 NB at NW 103 rd Street study section in Miami, FL ................. 43 4 6 Schematic of the I 95 NB at Philips Highway study section in Miami, FL ........... 44 4 7 Schematic of I 4 EB at I 75 study section in Tampa, FL ................................ ..... 44 4 8 Schematic of I .............. 45 4 9 Schematic of I 95 NB Between Baymeadows Road and Butler Boulevard study section in Jacksonville, FL ................................ ................................ ........ 45 4 10 Schematic of the I 4 WB at Lee Road study section in Orlando , FL ................... 46 5 1 Breakdown flow vs truck percentage for all sites ................................ ................ 57 5 2 5 min flow before breakdown vs truck percentage for all sites ........................... 57 5 3 15 min flow before breakdown vs truck percentage for all sites ......................... 58 5 4 Max 5 min flow in 15 min before breakdown vs truck pe rcentage for all sites .... 58 5 5 Discharge flow vs truck percentage for all sites ................................ .................. 59 5 6 Breakdown flow vs free low speed for all sit es ................................ ................... 60 5 7 5 min flow before breakdown vs free flow speed for all sites .............................. 61 5 8 15 min flow before breakdown vs free flow speed for all sites ............................ 61 5 9 Max 5 min flow in 15 min before breakdown vs free flow speed for all sites ...... 62 5 10 Discharge flow vs free flow sp eed for all sites ................................ .................... 62 5 11 Breakdown flow vs number of lanes for all sites ................................ ................. 63 5 12 5 min flow before breakdown vs number of lanes f or all sites ............................ 64
9 5 13 15 min flow before breakdown vs number of lanes for all sites .......................... 64 5 14 Max 5 min flow in 15 min before breakdo wn vs number of lanes for all sites ..... 65 5 15 Discharge flow vs number of lanes for all sites ................................ ................... 65 5 16 Breakdown flow vs bottleneck t ype for all sites ................................ ................... 66 5 17 5 min flow before breakdown vs bottleneck type for all sites .............................. 67 5 18 15 min flow before breakdown vs bot tleneck type for all sites ............................ 67 5 19 Max 5 min flow before breakdown vs bottleneck type for all sites ...................... 68 5 20 Discharge flow vs bott leneck type for all sites ................................ .................... 68 5 21 Percentile difference vs breakdown flow for all sites ................................ .......... 69 5 22 Breakdown flow percentile differen ce vs discharge flow for all sites ................... 70 5 23 Breakdown flow percentile change vs truck percentage for all sites ................... 71 5 24 Breakdown fl ow percentile change vs free flow speed for all sites ..................... 71 5 25 Breakdown flow percentile change vs number of lanes ................................ ...... 72
10 Abstract of Thesis Presented to the Graduat e School of the University of Florida in Partial Fulfillment of the Requi r ements for the Degree of Master of Engineering CAPACITY CHANGE ANALYSIS AND ESTIMATION ON FLORIDA FREEWAYS By Bryan St. George August 2014 Chair: Lily Elefteriadou Major: Civil Engineering breakdown, the capacity of the freeway segment decreases. The focus of this thesis was to develop models that would predict the capacity drop, as well as the actual capacity, from ten sites around Florida. These sites were comprised of a variety of geometric characteristics that covered many bottleneck types. The models developed can be used to predict how much the capacity of a segment will change or, t o determine the capacity of a segment, before and after breakdown. They also provide valuable insight into how the dependent variables react to changes in the geometric characteristics.
11 CHAPTER 1 INTRODUCTION Capacity drop (also referred to as two capaci ty phenomenon) is a widely researched topic in transportation engineering, because of its effects on roadway operations. It is defined as a change in the throughput before and after congestion. Capacity drop values are inconsistent across studies, some eve n showing an increase in discharge flow, resulting in a capacity rise. Due to the inconsistency in the direction of change presented in the literature , the term capaci ty drop will be referred to as capacity change in this research . The wide range of capaci ty change values among studies is in part due to the lack of a universal capacity definition. The Highway Capacity Manual (2010) defines the maximum sustainable hourly flow rate at which persons or vehicles reasonably can be expected to traver se a point or a uniform section of a lane or roadway during a given time period, under prevailing roadway, environmental, traffic, y analysis for years. H owever, this definition has been challenged by researchers. Several n ew definitions of capacity have been used in various studies (Lorenz and Elefteria d o u, 2001 , E lefteriadou and Lertworawanich 2002) . Understanding capacity change is important for transportation plann ing, as well as for design ing an d operating our facilities . If planners know how a roadway will perform during a breakdown, they can better plan and design future facilities to coun teract the effects. This improves the freeway system resulting in faster travel times and fewer delays. Ope rators can use information about the capacity change to
12 determine if ramp metering or other mitigation techniques can reduce the magnitude of the capacity change. The main objective of this thesis is to observe several bottleneck locations and investigate whether the capacity change phenomenon is consistently observed. The results will be used to develop a model to estimate the capacity changes based on factors such as geometric configuration , bottleneck type, operating conditions, etc. This thesis will be gin with a literature review of past research on the two ca pacity phenomenon, followed by the methodology . The fourth chapter provides the data collection and analysis . The fifth chapter summarizes the model development phase. The final chapter provides c o nclusions and recommendations.
13 CHAPTER 2 LITERATURE REVIEW This chapter provides a literature review of past studies. In order to discuss the capacity change and how they vary among studies , the breakdow n and capacity definitions used als o need to be exp lored. To this end, the literature review is divided into three sections. The first section focuses on how past studies have defined breakdown events . The second section discusses ca pacity definitions used in the literature . The final section describes the observed capacity d rop values from past studies. Breakdown Definition Lorenz and Elefteriadou (2001) explored the relationship between breakdown occurrence and freeway capacity. The study was conducted at two on ramp locations along Highway 401 in Toronto , Ontario , Canada. Vehicle speed data were collected at both sites and recorded in 20 s intervals. Speed vs. time plots were created for all study days for both sites. The authors defined breakdown to occur when the average speed across all lanes dropped b elow 90 km/h (55.9 mph) for at least 5 minutes. The system was assumed to have recovered if the speed of all lanes exceeded 90 km/h for at least 5 minutes. Elefteriadou and Lertworawanich (2002) revised the breakdown definition and defined breakdown to occ ur when speeds dropped below 90 km/h (55.9 mph) for a period of 15 minutes. It is noted by the authors that individual freeways will have different speed thresholds and different time periods. They also concluded that g eometry and free flow speed can g reat ly affect these thresholds. Brilon (2005) pe rformed a parametric analysis on capacity data obtained from German Autobahns in an effort to derive the distribution of capacity. Only capacities at
14 bottlenecks were used. For this paper, breakdown occurred when the average speed dropped below 70 km/h (43.5 mph) , during one time interval (5 minutes) . In addition, the speed drop was at least 10 km/h (6.2 mph) to avoid intervals of recovery that occur within larger congestion period s . J ia et al. (2010) developed a methodology for determining breakdowns, while also investigating the distribution of pre breakdown flow. Data were obtained from San PeMS (Performance Measurement System) . Data w ere gathered for a 21 month period. Criteria were imposed on the data, resulting in a fi nal data set of seven on ramp locations; two from the San Antonio area and five from t he Bay Area. The data for all sites were aggregated into 15 min intervals. The pro posal for breakdown determ ination consists of finding each individual According to the authors, a breakdown occurs when the speed of the segment drops below the critical speed and at the same time, it s density is greater than or equal to the boundary between C and D Level of Service (LOS). The critical speed is calculated as the summation of the 15 minute flow rate (for the top one percentile flows) divided by the summation of the densities (for each 15 minute observation). As a precaution, the same analysis was performed on the next downstream sensor to ensure non congested conditions and avoid spillback. Zhang and Levinson (2010) tested multiple hypotheses related to ramp metering in the Twin Cities of Minnesota. The study tested the effects of ramp metering vs. no metering and whether having metering affects the capacity of the mainline. Two seven week periods were examined, one with mete ring on, the other with it off. The proposed
15 breakdown definition uses different thresholds of occupancy , based on which t hree flow regimes are defined; congested, uncongested, and intermediate. The congested condition is defined as having a minimum occupancy of 25 % per lane. If the segment has an occupancy of less than 20 % per lane, it is considered uncongested. Anything other than these two regimes is labeled intermediate. The upstream and downstream detectors are then observed. If the downstream detector is under uncongested conditions while the upstream detector i s co ngested for at least five consecutive minutes , then the segment between these two detectors is c onsidered an active bottleneck. K Ã¼ hne and L Ã¼ dtke (2012) used statistical methods to test a revision to the speed dro p definition used to identify a breakdown ev ent . T he authors recognize characteristics associated with a breakdown, such as the defined speed drop, pre breakdown traffic flow, a nd speeds after breakdowns, but do not explain further what these relationships are. Instead, t hey defined a breakdown base d on the queue length, denoted as n crit . T he authors state that this value is arbitrary, similar to the amount of speed drop that cla ssifies a breakdown. This definition was performed on the autobahn A9 near Munich, with and without the use of variable spe ed limits . The results for n crit were 12.8 and 9.75 vehicles, respectively . A sigmoidal distribution was found to be the best fit for the cumulative breakdown probability distribution for both with and without the use of variable speed limits. Each thresho ld value is dependent on the site, and varies based on the flow and speed. Oh and Yeo (2012) estimated capacity drop values at several on ramp merge locations, each with varying number of lanes. The authors explain that four traffic states
16 can exist: (1) f ree flow conditions, (2) transition to bottleneck, (3) bottleneck, and (4) recovery period. In order to determine when these conditions occur, three definitions were used. The first relates to free flow conditions which exist when both the upstream (V u ) an d downstream (V d ) speeds are greater than or equal to 50 mph. The second definition relates to both the transition period and the recovery period . These periods exist when V u is between 40 and 50 mph and V d is greater than or equal to 50 m ph. Bottleneck co nditions occur when : (2 1 ) (2 2 ) (2 3 ) Where, SD = standard deviation Kondyli et al. (2013) observed five on ramp merge freeway segments in order to develop models that would predict the breakdown flow. Data were collected and aggregated into 1 minute intervals. Three breakdown identification algorithms we re used for this study, a speed based , an occupancy bas ed , and a volume occupancy correlation algorithm . The speed and occupancy based algorithms define a breakdown based on the speed drop or occupancy rise associated with a breakdown. The speed or occupancy difference between consecutive 1 minute intervals ar e calculated. If there is a speed drop (or an occupancy rise) and the average speed preceding the drop (or occupancy preceding the rise) is greater than the average of the speeds (or occupancies) after the drop plus the threshold (10 mph for speed, 5 % for occupancy) for at least 10 minutes, then a breakdown has occurred . The other method used is a
17 volume occupancy correlation algorithm, where the correlation between volume and occupancy is calculated over a 15 minute period. If the correlation drops below a user defined threshold (in this paper .5), then congestion has begun. All three algorithms were used for the study, and it was determined that the speed based method detects breakdowns earlier than the occupancy and the volume occupanc y correlation metho ds. The following table summarizes the literature review findings rega rding the breakdown definition. Table 2 1 . Breakdown s ummary Authors Breakdown definition Comments Lorenz and Elefteriadou (2001) Average sp eed of all lanes drops be low 90 km/h for at least 5 min. System recovered if spee least 5 min. Elefteriadou and Lertworawanich (2002) Average speed dropped below 90 km/h for at least 15 min. Based on previous research , thresholds will vary between freeways; geometry and free flow speed affect thresholds. Brilon (200 5) Average speed drops below 70 km/h; speed drop must be at least 10 km/h. Jia et al. (2010) Speed drops below the critical boundary between C and D level of service (LOS). Critical speed and density vary by site; must calcu late values for all sites. Zhang and Levinson (2010) Upstream occupancy 25% per lane, downstream detector is uncongested (occupancy <20% per lane). Flow regimes are based on occupancy. K Ã¼ hne and L Ã¼ dtke (2012) Proposed another measure for breakdown dete rmination, critical queue length. Arbitrary value, based on site, flow, and speed. Oh and Yeo (2012) V u d V u + SD V d ) for 15 min(t 1, t, t+1) < 5 mph. V u = Upstream speed V d = Downstream speed SD = standard deviation Kondyli et al. (2013) Speed based method, occupancy based method, and volume occupancy correlation method. Speed based method detects breakdowns earlier than other two methods.
18 All the authors agree that certain criteria must be met for a breakdown to exist, howe ver they do not all agree on what the criteria should be. Speed thresholds are the most common determinants of a breakdown. Initially, it appears that a static value (90 km/h) over some time p eriod was acceptable. I n more recent studies , these speed values vary from site to site . Kondyli et al. (2013) observed a speed drop over a defined time period, and concluded that this method detects breakdowns earlier than other methods tested. The analysis provided in that study was used to determine breakdown start and end times for this thesis. At the same time, other measures have been evaluated for breakdown determination, such as density and queue length. These are also threshold values that can vary from site to sit e. In conclusion, several measures can be used to determine a breakdown, with a drop in speed over a period of time being the most common. These measures and their values may vary between sites, and individual site assessment is recommended to select the most suitable one. Capacity Definition P ersaud e t al. (199 8) explored capacity drop and the use of m etering effects in mitigating bottlenecks. Three locations in Toronto, Ontario, Canada were studied in this report . All sites have on ramp m erge bottlenecks, however the third site has a slight curve, whi ch may account for some differences. For this study, only the median lane was observed. This was because trucks are prohibited from using this lane. 5 minute aggregate data were used for the analys i s . Four values we re observed to describe the entire breakd own and recovery ; a time (T b ) that corresponds to the flow at breakdown (Q b ), as well as a time (T d ) that corresponds to the mean queue discharge flow (Q d ). Q b is t he breakdown flow, which is the average flows over the 5 minute period preceding the start o f breakdown. Q d was determined as the mean flow after the transition period
19 (from uncongested to congested conditions) until speeds recove red back to uncongested levels. Both of these values were used to determine capacity change values. Lorenz and Elefter iadou (2001) defined capacity to be the breakdown flow rate (i.e., the flow rate prior to the breakdown event). D ata obtained in 20 s time intervals were aggregated to 1 , 2 , 5 , and 15 minute intervals. The breakdown flows were recorded for each of the f our time intervals for two sites. The conclusions showed that breakdowns occurred at different capacities at both sites all days. Some days, multiple breakdowns had occurred at one site, but with different capacity values. Other days, a breakdown would occ ur at one flow value, and on another day, no breakdown would occur with flows much higher than the previous day. The conclusions drawn from these events are that a capacity value can vary from site to site, day to day, and even within the same day. The aut hors propose a refined definition for capacity for inclusion to the Highway Capacity Manual to incorporate the probability of a breakdown, th e rate of flow (expressed in pc/ h r/ l n and specified for a particular tim e interval) along a uniform freew ay segmen t corresponding to the expected probability of br eakdown deemed acceptable under prevailing traffic and roadway conditions in a specified direction. Elefteriadou and Lertworawanich ( 2002) compared several capacity definitions. Three definitions were utili zed for this study; (1) breakdown flow defined as the 5 (or 15 ) min flow immediately before the breakdown, (2) observed maximum pre breakdown flow defined as the maximum 5 (or 15 ) min flow occurring before the breakdown, and (3) observed maximum discha rge flow defined as the maximum 5 (or 15 ) min flow during the breakdown. Frequency histograms were created for all three
20 definitions, for both the 5 and 15 min peri ods, for both study sites. The Chi square and Kolmogorov Smirnov (K S) tests were used to compare the distributions to the normal distribution. At the 5% level of significance, the normal distribution was found to be a good fit for all three definitions. T tests were performed to compare the mean values of each site. The authors recommend usin g the breakdown flow for future capacity analysis projects for four reasons: (1) it was the lowest value in almost every analysis, making it a conservative value, (2) a breakdown needs to occur for the other two definitions to be used, (3) it complies with the current capacity definition as the boundary between congested and uncongested conditions, and (4) it can be associated wit h the probability of breakdown. Brilon (2005) tested several capacity distributions . The author first applied the Product Limit M ethod (PLM). Using this method, an estimated distribution function for capacity, denoted as F c (q), was c reated. The result s were based on 3 years of continuously collected counts at two freeway sections along German Autobahns , in 5 minute increments. Brilo n also investigated various distributions to fit t o the traffic breakdown volumes, such as the Gamma, Weibull, and normal d istributions. T he Weibull distribution was the most appropriate fit. Brilon (2005) conclude d that capacity, defined as the volume as traffic transitions from free flowing to congested conditions , is Weibull distributed. Furthermore, Brilon (2005) suggested to use the 50 th percentile of the Weibull function as the Cassidy and Rudjanakanoknad (2005) explored the effects of an isolated merge on capacity drop, and how ramp metering may mitigate the effects. An on ramp merge bottleneck along Freeway 805 in San Diego, California was chosen as the study site.
21 For this study, capacity was defined as the sustained flow a freeway discharges from all exits, when the merge ramps are queued, and the off ramps are not blocked. The capacities used for this study (the breakdown and discharge flow) were determined by creating cumulative curves , using the equation : (2 4 ) Where, O(t) = oblique coordinates V(t) = virtual vehicle count q 0 = specified rate t = time t 0 = start time The breakdown flow is the average flow of the period preceding the breakdown . The interval is not mention ed, but the cumulative curves show that it can vary based on what the conditions are leading to a breakdown. The discharge flow was the average flow over the entire discharge period. The capacity at the merge was found to vary based on the queues that form and the traffic conditions near the merge, rather than be a fixed value. Elefteriadou et al. (2006) discussed the current capacity definition provided by the Highway Capacity Manual (HCM). T hree possible capacity definitions are presented : (1) the maximum flow before the breakdown; (2) the flow the instant before the breakdown; (3) and the flow after the queue has formed. A time interval also needs to be established for each of the three potential capacity definitions. The authors agreed that six possible definitions could be used. Four of t hese are the maximum pre -
22 b reakdown 5 or 15 minute value and the 5 or 15 minute value prior to the breakdown. Finally, the sustained pre queue or the average queue discharge flow are also expl ored. The authors were unab le to come to a consensus on which definition is the best, but several conclusions were made. All the authors agree that maximum pre breakdown flow is closest to the definition provided by the HCM, but is difficult to obtain because a breakdown must occur in order to gather it. If a breakdown does not occur, it is possible that the flow could always be greater. During congested conditions, the queue discharge flow (qdf) is preferable over the maximum pre queue flow. An average value should be obtained. As f or the distribution for this varia ble, the authors argue that e ither the mean, 50 th percentile, or the 15 th percentile could be used for measuring the qdf. Chung, Rudjanakanoknad, and Cassidy (2007) investigated the capacity drop mechanism at three differe nt breakdown type locations. The cap acity of the three locations was found using O curves that a re created using Equation 2 4 . Trend lines are used to better visualize data; when these trend lines change slope on the O curve, a flow change has occurred. Vi sual inspection of the O curves show s when a breakdown begins, and the capacities existing before and after this time are used to calculate the capacity drop. The breakdown flow is the average flow of the period preceding the breakdown. The interval is not mentioned, but the cumulative curves show that it can vary based on what the conditions are leading to a breakdown. The discharge flow was the average flow over the entire discharge period. Each site experienced varying capacities among all days. The star t of the breakdown also varied amongst the days studied.
23 J ia et al. (2010) developed a methodology for identifying breakdowns, while also determining the best distribution for the pre breakdown flow , which the authors define as capacity . The data were firs t converted into passenger car equivalent flows, for consistency. The default HCM value of five percent was used for heavy vehicles. The remaining data were converted into average pre breakdown headways. The Kolmogorov Smirnov test for goodness of fit was applied to the data. Distrib utions tested were the shifted Lognormal, Normal, Exponential, Weibull, and Gamma. For all seven sites, the shifted L ognormal distribution was found to be the best fit. From the average pre breakdown headways distribution, pre breakdown flows could be derived, in units of pc/hr/ln . It was determined that the HCM definition of capacity does not represent the capacity seen in the field. A freeway can breakdown over a range of flows, making breakdown a probabilistic event. Oh and Y eo (2012) observed 16 on ramp merge bottleneck sites to estimate capacity drop. Data were collected from the Performance Meas urement System (PeMS), given in 30 s intervals. Capacity, denoted as Q c , and the discharge flow, Q d , were used to estimate the capa city drop. The capacity used for this study was defined maximum number of vehicles that persist for 5 min in a free flow state. reviewing several studies, the authors determined that the capacity is sustained over a 5 min interval, rathe r th an a 15 min interval. The 5 minute period before an upstream queue formed was observed. The maximum number of vehicles that persist for 5 min in s used as the capacity. Discharge flow w as calculated using the standard deviations of th e upstream and downstream speeds in 15 minute intervals.
24 The discharge flow was defined as the flow at which Equation 2 3 , was a minimum during the bottleneck. K Ã¼ hne and L Ã¼ dtke (2012) stated the capacity is the traffic volume which corresponds to a g iven probabi lity (e.g. 15%) for a breakdown within a given observation time (e.g. 1 min). These values are not recommendations given by the authors, but instead are an example of the work performed in the paper. The definition applies to all work followin g th eir paper, but the numbers change based on the observation interval. The following table presents a summary of the capacity defi nitions used in the literature. Table 2 2 . Capacity d efinition s ummary Authors Capaci ty definit ion(s) used for s tudy Comments Persaud, Yagar, and Brownlee (1998) Breakdown flow and mean queue discharge flow. The data were aggregated into 5 min averages. Elefteriadou and Lertworawanich (2002) Breakdown flow, maximum pre breakdown flow, and maximum discharge flow. 5 and 15 minute intervals were used. The normal distribution fit to all three definitions. Brilon (2005) Capacity distribution function is Weibull distributed. Cassidy and Rudjanakanoknad (2005) Sustained flow a freeway discharges from all exits. O curves used to determine when a breakdown occurred and the capacity. Elefteriadou et al. (2006) Breakdown flow, maximum pre breakdown flow, sustained pre queue, and average queu e discharge flow. 5 and 15 minute intervals were used.
25 Table 2 2. Continued Authors Capacity definition(s) used for study Comments Chung, Rudjanakanoknad, and Cassidy (2007) Breakdown flow. O curves used to determine when a breakdown occurred and th e capacity. Jia et al. (2010) Pre breakdown flow derived from average pre breakdown headways distribution. Average pre breakdown headway has a shifted lognormal distribution. Oh and Yeo (2012) Maximum number of vehicles over a 5 min period at free flow speed. 5 min period was chosen over 15 min period because of sustained capacity. K Ã¼ hne and L Ã¼ dtke (2012) raffic volume which corresponds to a given probabi lity (e.g. 15%) for a breakdown within a given observation time (e.g. 1 min). There are sever al definitions for capacity used in these studies. Many of the definitions used are similar, such as the breakdown, the pre breakdown, and the queue discharge flow. The most often used time intervals are either 5 or 15 minutes. T he papers differ in whethe r to use the ave rage f low or the maximum flow. During the course of their studies, some authors developed new definition s for capacity. Some of t hese definitions relate capacity to the probability of breakdown . In conclusion, there is not one conclusive de finition for capacity. However, there are some commonly used definitions which will be explored during this research . Capacity Drop Persaud et al. (1998) explored the capacity drop and how the use of ramp metering might be able to mitigate bottlenecks. The authors recorded several capacity drop values. At Site 1 ( on ramp merge bottleneck ) the capacity drop during the AM
26 period for the median lane was 14.4 percent and 11.6 percent for all lanes . During t he PM peri od, the median lane capacity drop was 1 6.9 pe rcent, while the drop for all lanes was 15.3 percent. At Site 2 ( on ramp merge bottleneck ) t he capacity drop for th e median lane in the AM period wa s 12 percent; for all lanes during the AM period the drop was 10.6 percent. At the third site ( expressway on ramp with a slight curve ) the capacity during the PM period for the median lane wa s 26.2 percent. Lorenz and Elefteriadou (2001) also explored the two capacity phenomenon. A histogram was develop ed for the queue discharge rate for Site A with data aggrega ted into 5 min periods . The median value for Site A was determined to be 1,600 veh icles per hour per lane (veh/ h r/ l n ) with a range between 700 and 2,000 veh/hr/ l n . The breakdown flow ranged between 900 and 2,800 veh/ h r/ l n for both sites using the aggregati on periods of 1 ,5 , and 15 minute periods. During the capacity drop analysis it was observed that the magnitude of the drop is dependent on the flow at which a breakdown occurs. If a breakdown occurs at a very large flow rate, a drop will almost certainly exist. However, a breakdown event occurring at low flow rates may actually cause an increase in the outgoing flow. One example is provid ed, a breakdown flow of 1,500 veh/ h r/ l n increases to a queue discharge flow rate of 1,600 v eh/ h r/ l n . Elefteriadou and L ertworawanich (2002) examined two sites in Toronto, Ontario, Canada. Three definitions were used for the study, the breakdown flow, maximum pre breakdown flow, and the maximum discharge flow. Instead of calculating the capacity change, the difference betwe en the capacity definitions was calculated. The authors concluded that the breakdown flow was less than the maximum pre breakdown and maximum queue discharge flows. Another important conclusion was that for site A the
27 maximum pre breakdown flow was less th an the maximum discharge flow. For site B, the reverse was true. The authors attribute this to different geometric characteristics of the two sites. Cassidy and Rudjanakanoknad (2005) explored the effects of an isolated merge on capacity drop, and how ramp metering may mitigate the effects. Capacity drop . These ranged from 8.3 to 17.3 percent, with an average of 11.7 percent . Analysis showed that the capacity drop originated from the sho ulder lane and propagated laterally across the (i.e. queue length) of 16 vehicles. This was reproduced during every study day. When the shoulder lane reached 16 vehic les, the number of lane changes across all lanes increased dramatically (approximately from 500/h to 1100/h). This increase was accompanied by the capacity drop. The authors conclude that, in order to avoid the queue forming in the shoulder lane, drivers w ill change lanes. This lane changing caused drivers to slow down and be more cautious resulting in a capacity drop . Chung et al. (2007) investigated the capacity drop mechan ism at three different bottleneck s . Relating the density of the network to the capa city drop was the main focus of this paper. The density for all three locations was calculated by dividing the vehicle accumulation by the distance between the start and end of the bottleneck. The bottleneck distance is taken as the distance between the tw o detectors that encompass the bottleneck. The first location was a merge bottleneck on Interstate 805 in San Diego, California . Capacity drops of at least 10 percent were common for this location.
28 The density of this location during the breakdowns ranged from 188 to 254 veh /km (116.8 to 157.8 veh/mi) . The second location was along SR 24 in San Francisco Bay Area; it consisted of a lane drop bottleneck. Capacit y drops ranged between 5 and 18 percent , while the density values were between 89 and 96 veh /km (5 5.3 to 59.67 veh/mi) . The final location was on the Gardiner Expressway in Toronto, Ontario, Canada; it was conside red a horizontal curve bottleneck . The capacity dr op values were between 3 and 12 percent ; density values b etween 153 and 179 veh /km (95.1 to 111.2 veh/mi) . The average densities for each site were normalized by number of lanes, in order to compare. These densities are similar among the three sites. Location 1 had an average density of 55 veh/hr/ln, location 2 with 46 veh/hr/ln, and location 3 with 56 veh/hr/ln. The smaller average density for the second location is explained by the authors as a result of the way the data were collected, which was different than the method used for locations 1 and 3. Zhang and Levinson (2010) examined multiple b reakdown sites in Minnesota with and without ramp metering. They determined that by using ramp metering, breakdowns can be postponed or even eliminated. It was also determined that the flow drops without metering ranged from 2 percent to 11 percent with a standard deviation of 2.2 percent . With meterin g the flow drops ranged from .1 percent to 9 percent w ith a standard deviation of 2.6 percent . The authors stress that these percentages are based on flow drops, not capacity drops. This is because no capacity definition was provided for this study. Instead, the authors used flows derived from cumulative curves analysis. The i ntervals for these capacities are not stated, but the average flow preceding the breakdown is used for the breakdown flow , while the aver age over the entire discharge
29 period is used for the discharge flow. They conclude by saying that the percentage flow drops are normally distributed. Oh and Yeo (2012) observed 16 on ramp merge bottleneck locations in California. The California Performance Measurement System (PeMS) was used to gather data. The number of lanes on the selected sites varied from 2 to 5, and the objective was to evaluate the impact of number of lanes on capacity drop. It was observed that higher number of lanes resulted in lowe r capacity drop values; the average capacity drop values for 2 , 3 , 4 , and 5 lane were 16.33 percent, 13.68 percent, 11.61 percent, and 8.85 percent , respectively. Another aspect of capacity drop that was investigated w as the effect of an off ramp. Five three lane highways were observed during this study, two with no downstream off ramp, one with a one la ne off ramp, and two with a two l ane off ramp. The results of the capacity drop analysis showed that the no off ramp study sites had larger ca pacity drop values than the two lane off ramps, showing a potential mitigation technique by having a two lane off ramp. However, a similar assumption could not be made for the one lane off ramp, since its ca pacity drop value was similar to the values for the no ramp situation. It is unclear if the reason why the sites with a two lane off ramp experience lo wer capacity drops is due to a greater discharge capacity or a lower pre breakdown capacity. The final analysis performed was on individual lanes capacity drop. Thes e observations showed that both capacity and discharge flow increase the further you move away from the shoulder lane. It also showed that b oth the pre breakdown and discharge flows decreased as you move closer to the shoulder, but the difference between t hese values grew smaller, resulting in a decreased capacity drop closer to the shoulder lane.
30 Table 2 3 summarizes the literature review findings related to the capacity drop . Table 2 3 . Capacity drop s ummary Authors B reakdown type Capacity drop (%) Comments On ramp merge configuration Persaud et al. (1998) On ramp merge On ramp merge On ramp merge 1 1.6 16.9 10.6 12 26.2 Lorenz and Elefteriadou (2001) On ramp merge 6.25 (increase ) Elefteria dou and Lertworawanich (2002) On ramp merge Site A: Differences between 677 and 238 veh/hr/ln Site B: Differences between 740 and 274 veh/hr/ln. Cassidy and Rudjanakanoknad (2005) On ramp merge 8.3 17.3; average 11.7 Capacity drop began when the shou lder lane reached 16 vehicles. Chung et al. (2007) On ramp merge At least 10 Average density/lane (veh/km/lane) similar among all sites. Zhang and Levinson (2010) On ramp merge 2 11 (without metering) .1 9 (metering) These values correspond to flows, not capacities. Oh and Yeo (2012) On ramp merge, 2 lanes On ramp merge, 3 lanes On ramp merge, 4 lanes On ramp merge, 5 lanes 16.33 13.68 11.61 8.85 Capacity, discharge flow, and capacity drop increase moving away from the shoulder lane.
31 Table 2 3. Continued Authors Breakdown type Capacity drop (%) Comments Horizontal curve configuration Chung et al. (2007) Horizontal curve 3 12 Average density/lane similar among all sites. Lane drop configuration Chung et al. (2007) Lane drop 5 18 Aver age density/lane (veh/km/ln) similar among all sites. As shown, t he most common type of bottleneck analyzed is the on ramp merge bottleneck. Some authors did examine bottlenecks due to lane drops and horizontal curves. The capacity change values range be tween 6.25 and 26.2 percent. This variability arises from differences in data collection techniques, capacity defi nitions, and type of bottleneck . Based on the results from Oh and Yeo (2012), i t appears that capacity drop originates from the shoulder lane , as vehicles attempt to change lanes, either because of a lane drop or on ramp merge. The capacity drop then continues laterally across the segment as more vehicles attempt to change lanes to avoid the slowdowns in the shoulder. Some researchers have atte mpt ed to recreate capacity drop in simulation . According to Laval and Daganzo (2006), lane changing causes capacity drop in freeways. Because of this, the authors proposed a new model that tracks lane changes. They introduced a hybrid approach to the kinem atic wave (KW) theory. The model was tested on a 3 lane freeway, which reduces to 2 lanes. After approximately 10 minutes (from t = 0 to t = 10) the capacity of the segment experiences a drop of 9.3 percent. This simulation was performed many times, with o nly slight variation in the initial capacity
32 drop value. The capacity drop results of simulation are consistent with the values seen in the field. Bertini and Leal (2003) observed the capacity drop at bottlenecks caused by lane drops; the results are simil ar to those found in this paper. The values are also similar to those of Cassidy and Rudjanakanoknad ( 2005 ) , who studied on ramp merge bottlenecks. The authors believe that the underlying cause of these breakdowns is lane changing, either due to a lane dro p or a merging section, which is why the results are similar across different studies. V an Wageningen Kessels et al. (2011) explored the accuracy of these models in representing capacity drop, as well as stop and go waves. They studied t he optimal velocity model (OVM) and the Lighthill Whitham Richards model (LWR). The OVM provide a good representation for capacity drop, however, there have been advancements to this model to include the capacity drop phenomenon, referred to in this paper as LWR + CD. The authors concluded that the models that best represent capacity drop are the Intelligent Driver Model (IDM) (Treiber et al., 2000), the LWR + CD (Edie, 1961), and the Payne + Hysteresis (Zhang, 1999). Parzani and Buisson (2012) attempted to create a model for merge sections that would also incorporate potential capacity drop effects. The authors suggested using two separate models, in conjunction, to create a model that impro ves on the LWR model. The first model used was the Aw Rascle single road model (AR model). It consists of a , which describes speed adapts to the environment. Because the au thors wished to look at merge bottlenecks, the second model is the Haut and Bastin (HB model) for junctions.
33 Several experiments were performed on the two models for validation purposes. Afterwards, a capacity drop simulation was performed. The results sho w that the flow before congestion exceed the flow after congestion, consistent with the capacity drop definition. However, the model should be validated with additional data from on ramp merge bottlenecks. Capacity increases were not seen in this simulatio n example. Table 2 4 . Capacity drop model s ummary Authors Traffic flow model Improvements Comments Laval and Daganzo (2006) Hybrid kinematic wave (KW) theory. A 9.3% drop was recorded, consistent with Bertini and Leal (2003) and Cassidy and Rudjanakanoknad (2005). V an Wageningen Kessels et al. (2011) OVM LWR. Models with best capacity drop representation: the Intelligent Driver Model (IDM), the LWR with capacity drop (LWR + CD), and the Payne + Hysteresis. Parzani and Buiss on (2012) Aw Rascle single road model. Haut and Bastin model. Uses the two models together to provide better results than the LWR model. Capacity drop was observed, but validation with field data is needed. Summary and Conclusions It can be seen from th is literature review that there are several approaches to perform this type of study leading to the inability to compare results between different studies. There is no consensus on the definitions of breakdown and capacity, but some
34 key points are consiste nt among them. With regards to breakdowns, thresholds are used to determine their activation. The most common is a when the average speed drops below a predefined speed over a specified time period. Authors that use this method agree that the magnitude of the speed drop, as well as the length of time, will vary across sites. Free flow speed, roadway geometry, and other factors can greatly affec t the speed thresh olds that define a breakdown . Capacity definitions also vary across studies. Variations of breakd own, pre breakdow n, and discharge flows are used . This research will follow similar steps to the studies reviewed. The main objective of this study will be to investigate whether the capacity drop phenomenon is consistently observed across several study si tes and quantify the relationship between the capacity change and several other parameters . The method for determining bottleneck activation will be the speed drop method, which is explained in the methodology section. Several parameters will be explored w hich will be used to compare the magnitudes of the capacity change . These results will be used to develop a model to estimate the capacity change based on the above ge ometric and traffic conditions.
35 CHAPTER 3 METHODOLOGY This chapter provides a n overview of the methodology followed by an in depth description of each step. Overview of Methodology The process begins by selecting study sites and the appropriate days of study. Data are collected for these days and used to determine the time of each breakdown. Based on these times, several capacity definitions are used to extract c apac ity values. These values are used to calculate the capacity change, which is then used to create regression mode l s to estimate capacities, capacity difference, and percentile diff erence . Step 1 The first step is to compile a list of acceptable study sites. These sites must be urban freeways with detector data available for at least a year. The sites must also experience recurrent conge stion due to high demand. D ifferent types of bo ttleneck s are examined: merge, d iverge, lane drop, and weaving. A list of acceptable study days is also needed. A period of at least a year is necessary in order to ensure a large sampl e. Weekends and holidays are omitted from the final list. The weather c onditions can be determined from the National Weather Service website. A monthly archive of weather conditions dating back to 20 10 were retrieved to obtain rainfall amounts as well as foggy conditions. Days with incidents and poor weather conditions (preci pitation over .2 inches or foggy conditions) are als o removed. Incident data were feature provides information on past incidents for many sites in Florida.
36 Step 2 The next step is to determine the time a breakdown occurred. The method used is the speed drop method. The cumulative curves method for determining breakdowns was explored and presented in the pilot study introduced in the thesis proposal. It produced less precise results than the speed drop met hod. Therefore, this method was not used for the rest of the sites analyzed. T he breakdown identification algorithm presented in Kondyli et al. (2013) will be used t o determine abrupt speed drops. The procedure begins by calculating the speed difference be tween two consecutive time periods: (3 1) A threshold, X mi/h, must next be considered. For this study, 10 mi/h will be used. When i < 0 , the following formula should be used: (3 2 ) Next , a duration, Y , that the speed drop lasts should be established. For this study, 10 min will be used. The following formula is used to determine whether the maximum speed is less than S i during the duration: (3 3 ) Congestion begins at time, t = i , which occurs right before the speed drop. A recovery period should also be identified, to indicate when flow has returned to uncongested conditions. Two conditions must be met for a recovery to have occurred: (i) An increase in speed ove r two consecutive time period s, and
37 (ii) The minimum speed during the duration, previously denoted as Y , is more than the average speed before and after the breakdown period, as shown: (3 4 ) Step 3 When the start of the breakdown has been determined, the capacity ne eds to be examined. Past research suggested many differen t definitions for capacity. Seven capacity definitions will be used during this investigation. These definitions were selected based on the literatu re review. They are as follows: B REAKDOWN FLOW . The 1 minute flow immediately before the breakdown event (i.e., before the abrupt speed drop). M AXIMUM PRE BREAKDOWN FLOW . The highest 1 minute flow that occurs during the 5 or 15 minutes before the breakdown (i.e., during undersaturated conditions). A VERA GE PRE BREAKDOWN FLOW . the average of the 5 or 15 minutes flow before the breakdown (i.e., during undersaturated conditions) . M AXIMUM 5 MINUTE FLOW IN 15 MINUTES BEFORE BREAK DOWN . The highest 5 min ute average flow that occurs during the 15 minutes before the breakdown ( i.e., d uring undersaturated conditions). A VERAGE DISCHARGE FLO W . The average flow during oversaturated conditions (i.e., the time interval after breakdown and prior to recovery). The capacity values are obtained using th e STEWARD database . The data are available in 1 min ute intervals. Step 4 The capacities are then used to determine the capacity difference and the percentile difference for each site. Seven capacities (breakdown, the maximum 5 and 15 minute pre breakdown, the average 5 an d 15 minute pre breakdown, the maximum 5 minute average pre breakdown flow, and the discharge flow) and six capacity
38 changes will be calculated for eac h site. The actual difference in veh/hr/ln or p c/hr/ln as well as the percentile difference will be calcu lated as follows: (3 5 ) (3 6 ) Where, Q 0 = the initial flow (either breakdown or pre breakdown) Q f = the discharge flow Step 5 Once the actual difference and percentile difference values have been calculated for all sites, using all definitions, a model can be developed. Explanatory variables to be considered include number of lanes, type of bottleneck, speed limit, free flow speed, breakdown flow, as well as any interaction terms that may be statistically signif icant. The dep endent vari able s ( capacity measure, actual difference, percentile difference ) will be evaluated as a function of the in dependent variables to identify any relationships. Equations will be developed of the form:
39 CHAPTER 4 DATA COLLECTION AND ANALYSIS This chapter provides information on the data collected and analyzed. T he first section provides an overview of the d ata collection, the second describes each site in detail , wh ile the last one summarizes the data analysis. Data Collection The first step in the data collection process was the site selection. Several different sites needed to be explored to deter mine if the type of site affects the capacity change. The locations of major b ottleneck s we re identified based on various sources: (FDOT, 2011 ; Wash burn et al, 2010) , and previous studies at UF TRC related to bottlenecks in Florida. Sites we re selected based on the following criteria: Sites have to be urban freeways; Sit es have to experience recurrent congestion due to high demand and not due to incidents; Data should be available for at least 1 year; Construction work, incidents, weather information should be available so that the respective data need to be e liminated fr om further analysis; Detectors should have acceptable health, with little to no missing data. Table 4 1 presents the final list of sites. Table 4 1 . Selected urban freeway bottleneck locations City Fre eway Segment Type of b ottleneck Lanes Weave, 3 lanes on mainline with an auxiliary l ane Jacksonville I 95 NB North of Butler Blvd Weave 3 Merge, 3 lanes on m ainline Jacksonville I 95 NB At University Merge 3 Miami SR 826 EB At NW 47 th Avenue Mer ge 3 Combined (left and right hand) merge, 3 lanes on m ainline Orlando I 4 EB SR 408 Merge 3
40 Table 4 1. C ontinued City Freeway Segment Type of b ottleneck Lanes Merge, 4 lanes on m ainline Miami I 95 NB At NW 103rd Street Merge 4 Jacksonville I 95 NB At Philips Highway Merge 4 Lane addition at merge, 3 to 4 l anes Tampa I 4 EB At I 75 Merge 3 to 4 Major d i verge, 5 lanes on m ainline Miami I 95 NB At FL Turnpike Diverge 5 Diverge, 3 lanes on m ainline Jacksonville I 95 NB Bet. Baymeadows & Butler Blvd Diverge 3 Lane drop at diverge, 4 to 3 l anes Orlando I 4 SB At Kennedy Blvd Lane drop 4 to 3 The type of bottleneck was determined by visual inspection along with creating speed time plots using data from the STEWARD database. The INRI X website was also used to determine the origin of all bottlenecks a nd how far congestion spread upstream. Site Description The 10 sites selected for analysis are presented in this section , along with a de tailed description and a schematic. The schematic s are not drawn to scale, but do display nearby on and off ramps, along with the detectors located along the study segment. The detec tors labeled in red are used to gather speed and capacity information. Speed information was used to determine breakdown st art times. The ones labele d in blue are nearby detectors. I 95 NB at Butler Boulevard, Jacksonville, FL This site is located in Jacksonville, Florida, just downstream of the on ramp from Butler Blvd ( Figure 4 1 ). The bottle neck is activated due to weaving operations, and it consists of 3 lanes of traffic with an auxiliary lane. Data are not gathered for the auxiliary
41 lane, which was excluded from analysis. The speed limit at the site is 65 mph. Capacity data were collected fro m the downstream detector. Figure 4 1 . Schematic of I 95 NB at Butler Boulevard study section in Jacksonville, FL I 95 NB at University Boulevard, Jacksonville, FL This site is also located in Jacksonvi lle, Florida ( Figure 4 2 ). The bottleneck occurs due to an on ramp merge from University Boulevard. The site has 3 lanes per direction and the posted speed limit is 65 mph. Capacity values wer e measured from the downstream detecto r . Figure 4 2 . Schematic of I 95 NB at University Boulevard study section in Jacksonville, FL
42 SR 826 EB at NW 47 th Avenue, Miami, FL This site is located in Miami, Florida. The bottleneck is the re sult of a merge from NW 47 th Avenue. The mainline has 3 lanes per direction and a speed limit of 55 mph. Figure 4 3 display s a schematic of the study site. The capacity values correspond to the detector located do wnstream of the merge junction . Figure 4 3 . Schematic of SR 826 EB at NW 47th Avenue study section in Miami, FL I 4 EB at SR 408, Orlando, FL This site is located in Orlando, Florida along the eastb ound direction of I 4 . The bottleneck occurs due to an on ramp merge from the intersection with SR 408, as well as a left side on ramp merge with South Street ( Figure 4 4 ). The site has 3 lanes with an auxiliary lane on the right side; data were not available for this auxiliary lane. The speed limit is dictated by Variable Speed Limit signs, but its base line speed limit is 50 mph . No data were available for the detector located upstream of the Anderson Street ramp. The detector lo cated downstream of the merge from SR 408 WB was used for the capacity analysis .
43 Figure 4 4 . Schematic of the I 4 at SR 408 study section in Orlando I 95 NB at NW 103 rd Street, Miami, FL This is loc ated in Miami, Florida, and the bottleneck occurs due to the on ramp from NW 103rd Street ( Figure 4 5 ) . The segment has 4 lanes per direction as well as two HOT lanes; these were not analyzed in this project as they operate indepe ndently. The speed limit along the corridor is 55 mph. T he downstream detector wa s used to gather capacity information . Figure 4 5 . Schematic of I 95 NB at NW 103 rd Street study section in Miami, F L I 95 NB at Philips Highway, Jacksonville, FL This site is located in Jacksonville, Florida. The bot tleneck forms due to the merge from Philips Highway ( Figure 4 6 ). The site has 4 lanes along the mainline and the posted speed li mit is 65 m ph. T he detector downstream of the Philips Highway on ramp was used to gather capacity values.
44 Figure 4 6 . Schematic of the I 95 NB at Philips Highway study section in Miami, FL I 4 EB at I 75, Tampa, FL This site is located in Tampa, Florida along the eastbound section of I 4. A bottleneck occurs at the on ramp merge junction from I 75 NB onto I 4 EB ( Figure 4 7 ) . The speed limit is 70 mph and the bottleneck sect ion has 4 lanes per direction. Capacity information wa s collected from the downstream detector . Figure 4 7 . Schematic of I 4 EB at I 75 study section in Tampa, FL I 95 NB at the Turnpike, Miami, FL This site is located in Miami, Florida. The section is a major diverge bottleneck Figure 4 8 ) . The site has 5 la nes along the mainline, with 2 lanes exiting toward s the Turnpike. The speed limit a t the site is 55 mph. Detector data upstream of the major diverge were not available, therefore, the detector used for analysis is located immediately downstream of the diverge.
45 Figure 4 8 . Schemat ic of I I 95 NB Between Baymeadows Rd and Butler Blvd, Jacksonville, FL This study site is located in Jacksonville, Florida between Baymeadows Road and Butler Boulevard. The bottleneck occurs between t hese two junctions with the bottleneck caused by the diverge at Butler Boulevard. The freeway has 3 lanes per direction and a speed limit of 65 mph. T he detector located upstream of the Butler Blv d off ramp was used to determine capacity values ( F igure 4 9 ) . F igure 4 9 . Schematic of I 95 NB Between Baymeadows Road and Butler Boulevard study section in Jacksonville, FL I 4 WB at Lee Road, Orlando, FL This site is located alon g a section of I 4 in Orlando, Florida in the westbound direction. The bottleneck occurs due to a reduction in lanes from 4 to 3 downstream of
46 an off ramp onto Lee Road ( Figure 4 10 ) . The speed limit is dictated based on Variable Speed Limit signs, and the baseline speed limit is 50 mph. Capacity values were obtained based on t he detector located downstream from the lane drop . Figure 4 10 . Schematic of the I 4 WB at Lee Road study section in Orlando, FL Data Analysis After the site selection process was complete, data were collected from the STEWARD database. Data included occupancy, speed, and flow in 1 minute increments. Additional truck percentage information were obtained through FDOT for specific dates during the data collection period. The speed data provided were used to determine breakdown events ( Step 2 of the Methodology ) . Each event was carefully analyzed to determine if a true breakdown had occurred. Events were re moved if they did not meet the following criteria: Speeds during the breakdown event must be below 40 mph; The breakdown capacity mus t be greater than 1500 veh/hr/ln ; The flows preceding the start of breakdown must be consistently high. If all these crit eria are met, then the event moved onto the next stage of analysis, to calculate each of the seven selected capacity definitions. These values were divided by the number of lanes at the site, in order to compare statistics across all sites. The actual di ff erence and the percentile difference were calculated from these values. The
47 percentile differences were compared to a range of appropriate values based on the results of the literature review. Past research has shown an approximate range of percentile diff erences between 10 and 30 percent. Any data set that fell outside this range was subject to additional analysis. Oftentimes the flows before or after a percentile differences. T hese anomalies were most likely due to detector malfunction. These data could not be trusted, so they were removed from the final analysis. Tab le 4 2 presents the capacity measures of all 10 site s, with appropriate statistics. Tab le 4 2 . Capacity measure s tatistics for a ll s ites Events Statistic Capa city v alues (veh/hr/ln ) Breakdown Pre b reakdown Discharge Max in 5 m in Max in 15 m in 5 m in a vg 1 5 min a vg Max 5 m in a vg Weave, 3 lanes on mainline w ith an auxiliary l ane I 95 NB, At Butler 42 Average 2056 2303 2380 2079 1981 2143 1718 50th Percentile 2100 2320 2390 2110 1997 2166 1726 85th Percentile 2277 2500 2540 2260 2151 2287 1800 Merge, 3 lanes on m ainline I 95 NB, At University 51 Ave rage 2138 2304 2361 2092 2044 2168 1986 50th Percentile 2160 2300 2340 2124 2067 2208 1994 85th Percentile 2330 2470 2530 2246 2223 2346 2122 SR 826 EB, At NW 47th Avenue 88 Average 1737 1905 1970 1734 1684 1788 1617 50th Percentile 1730 1920 198 0 1746 1699 1796 1628 85th Percentile 1898 2079 2100 1860 1805 1920 1701 Combined (left and right hand) merge, 3 l ane s on m ainline I 4 EB, At SR 408 129 Average 2094 2293 2356 2063 1929 2120 1849 50th Percentile 2100 2320 2360 2088 1940 2144 1858
48 Table 4 2. Continued Events Statistic Capacity v alues (veh/hr/l n) Breakdown Pre b reakdown Discharge Max in 5 m in Max in 15 m in 5 min a vg 15 min a vg Max 5 m in a vg Combined (left and right hand) merge, 3 lanes on m ainline I 4 EB, At SR 408 12 9 85th Percentile 2316 2440 2500 2194 2072 2247 1903 Merge, 4 lanes on m ainline I 95 NB, At NW 103rd Street 68 Average 1828 1975 2048 1780 1754 1854 1646 50th Percentile 1853 1965 2055 1787 1764 1857 1640 85th Percentile 1995 2114 2145 1904 1849 1979 1731 I 95 NB, At Philips Highway 43 Average 1902 2064 2170 1856 1864 1962 1590 50th Percentile 1815 2040 2175 1875 1915 2019 1624 85th Percentile 2220 2366 2415 2118 2111 2173 1788 Lane addition at merge, 3 to 4 l anes I 4 EB, At I 75 50 Av erage 1591 1727 1781 1527 1494 1582 1431 50th Percentile 1575 1733 1770 1539 1496 1583 1459 85th Percentile 1735 1885 1905 1598 1570 1657 1522 Major diverge, 5 lanes on m ainline I 95 NB, At Florida's Turnpike 152 Average 1735 1798 1842 1650 1615 1701 1593 50th Percentile 1728 1800 1848 1663 1638 1714 1611 85th Percentile 1860 1896 1920 1738 1690 1782 1655 Diverge, 3 lanes on m ainline I 95 NB, Between Baymeadows and Butler 82 Average 2095 2325 2429 2103 2066 2142 1838 50th Percentile 211 0 2340 2420 2098 2080 2130 1848 85th Percentile 2320 2480 2580 2232 2174 2280 1903 Lane drop at diverge, 4 to 3 l anes I 4 WB, At Lee Road 71 Average 1847 2081 2178 1831 1796 1914 1700 50th Percentile 1840 2100 2180 1864 1800 1920 1698
49 Table 4 2. Continued Events Statistic Capacity v alues (veh/hr/ln ) Breakdown Pre b reakdown Discharge Max in 5 m in Max in 15 m in 5 m in a vg 1 5 min a vg Max 5 m in a vg Lane drop at diverge, 4 to 3 l anes I 4 WB, At Lee Road 71 85th Percentile 2060 2280 2360 1 996 1943 2056 1924 All s ites 776 Average 1895 2060 2130 1859 1816 1914 1700 50th Percentile 1860 2048 2118 1841 1796 1886 1680 85th Percentile 2200 2380 2440 2144 2067 2196 1889 The discharge flow is constantly lower than all other capacity defi nitions across every site, consistent with the capacity drop definition. The 5 and 15 minute maximum flows have the greatest values among the definitions. The brea kdown flow, along with the remaining pre breakdown definitions are similar, differing minute ly. For the most part , the higher the number of la nes, the lower the per lane capacity . For example, the average breakdown flow of the 3 lane merge at University is 2138 veh/hr/ln . The average of the breakdown flows for the 4 lane me rges are 1828 and 1902 veh/hr/ln . The SR 826 site is the obvious exc eption; the values observed are lower than most of the other on ramp merge sites, regardless of the number of lanes. The same ca n be said for the diverge sites: the higher the number of l anes, the lowe r the per lane capacity. The 3 lane diverge between Baymeadows and Butler has an average breakdown flow of 2095 veh/hr/ln , but the 5 lane major Turnpike has an average breakdown flow of 1735 veh/hr/ln . Table 4 3 provid es statistical informat i on on the actual differences.
50 Table 4 3 . Actual difference s tatistics for all s ites Events Statistic Actual difference v alues (veh/hr/ln ) Breakdown Pre b reakdown Max in 5 m in Max in 15 m in 5 min a vg 15 min a vg Max 5 m in a vg Weave, 3 lanes on mainline with an auxiliary l ane I 95 NB, At Butler 42 Average 337 584 661 361 263 424 50th Percentile 355 575 641 365 257 432 85th Percentile 583 764 814 501 439 580 Merge, 3 lanes on m ainline I 95 NB, At University 51 Average 152 318 375 106 58 182 50th Percentile 184 332 390 127 113 203 85th Percentile 322 499 536 288 238 354 SR 826 EB, At NW 47th Avenue 88 Average 119 288 353 117 66 170 50th Percentile 109 283 345 116 64 168 85th Per centile 279 433 470 227 148 267 Combined (left and right hand) merge, 3 lanes on m ainline I 4 EB, At SR 408 129 Average 245 444 506 213 80 271 50th Percentile 265 455 500 228 84 283 85th Percentile 443 596 668 342 207 388 Merge, 4 lanes on m ain line I 95 NB, At NW 103rd Street 68 Average 182 329 402 134 108 208 50th Percentile 197 323 397 142 114 218 85th Percentile 340 465 553 239 238 337 I 95, At Philips Highway 43 Average 311 474 580 265 274 372 50th Percentile 293 464 565 302 282 367 85th Percentile 484 626 737 400 386 509 Lane addition at merge, 3 to 4 l anes I 4 EB, At I 75 50 Average 160 296 349 96 63 151
51 Table 4 3. Continued Events Statistic Actual difference v alues (veh/hr/ln ) Breakdown Pre b reakdown Max in 5 m in Max in 15 m in 5 min a vg 15 min a vg Max 5 min a vg Lane addition at merge, 3 to 4 l anes I 4 EB, At I 75 50 50th Percentile 138 298 335 85 55 152 85th Percentile 305 419 459 201 149 227 Major diverge, 5 lanes on m ainline I 95 NB, At Florida's T urnpike 152 Average 143 206 250 57 23 108 50th Percentile 136 195 247 58 34 107 85th Percentile 262 297 326 137 98 179 Diverge, 3 lanes on m ainline I 95 NB, Between Baymeadows and Butler 82 Average 257 487 590 264 228 303 50th Percentile 254 4 72 557 258 242 290 85th Percentile 496 633 755 422 338 490 Lane drop at diverge, 4 to 3 l anes I 4 WB, At Lee Road 71 Average 147 381 478 131 96 214 50th Percentile 139 344 484 98 115 234 85th Percentile 378 574 634 322 250 347 All s ites 776 Average 195 360 430 159 115 214 50th Percentile 184 347 416 141 97 200 85th Percentile 390 556 630 317 277 371 Table 4 3 shows similar results to the capacity table ( Tab le 4 2 ) . The actual differ ence between the two maximum flows and the discharge flow are the greatest among all definitions. The maximum 5 minute flow in 15 minutes before the breakdown actual difference is most often the next greatest value, while the other defi nitions are roughly similar.
52 The result s from this table show that for merge sites, with the exception of the 3 lan e, combined merge site on I 4 at SR 408, with increasing number of lanes, the actual difference also increases. The average actual difference of the two 3 lane m erge sites are 152 and 119 veh/hr/ln , while the average of the two 4 lane merge s ites are 182 and 311 veh/hr/ln . The 3 lane, combined merge site has actual difference values around those of the 4 lane on ramp merge sites , an average of 245 veh/hr/ln . This trend is duplicated for all capacity definitions. As for the diverge sites, with increasing number of lanes , the capacity difference decreases. The 3 lane diverge has an average breakdown flow ac tual difference of 257 veh/hr/ln , but the 5 lane major diverg e has a value of 143 veh/hr/l n . Again, this trend is reproduced across all capacity definitions. Finally, Table 4 4 displays the s tatistical information for the percentile difference among all sites. Table 4 4 . Percentile d ifference statistics for all s ites Events Statistic Percentile d ifference v alues (%) Breakdown Pre b reakdown Max in 5 m in Max in 15 m in 5 min a vg 15 min a vg Max 5 m in a vg Weave, 3 lanes on mainline with an auxiliary l ane I 95 NB, At Butler 42 Average 15.25% 24.99% 27.49% 16.94% 12.93% 19.42% 50th Percentile 16.97% 24.52% 27.28% 17.52% 13.09% 19.87% 85th Percentile 25.68% 31.38% 32.63% 24.13% 21.06% 25.66% Merge, 3 lanes on m ainline I 95 NB, At University 51 Average 6.58% 13.54% 15.59% 4.52% 2.09% 7.89%
53 Table 4 4. Continued Events Statistic Percentile d ifference v alues (%) Breakdown Pre b reakdown Max in 5 m in Max in 15 m in 5 m i n a vg 15 min a vg Max 5 m in a vg Merge, 3 lanes on m ainline I 95 NB, At Unive rsity 51 50th Percentile 8.40% 14.18% 15.53% 5.82% 5.48% 9.47% 85th Percentile 13.41% 19.89% 21.93% 13.30% 11.05% 15.34% SR 826 EB, At NW 47th Avenue 88 Average 6.47% 14.84% 17.67% 6.43% 3.66% 9.31% 50th Percentile 6.23% 14.86% 17.85% 6.64% 3.71% 9 .33% 85th Percentile 15.62% 21.03% 23.01% 12.08% 8.48% 14.68% Combined (left and right hand) merge, 3 lanes on m ainline I 4 EB, At SR 408 129 Average 11.06% 19.00% 21.22% 9.95% 3.74% 12.47% 50th Percentile 12.38% 19.56% 21.34% 10.74% 4.24% 13.10% 85th Percentile 19.01% 24.65% 26.29% 15.52% 9.80% 17.38% Merge, 4 lanes on m ainline I 95 NB, At NW 103rd Street 68 Average 9.29% 16.37% 19.45% 7.28% 5.96% 11.01% 50th Percentile 10.63% 16.61% 19.31% 8.18% 6.69% 11.48% 85th Percentile 17.68% 22 .24% 27.04% 13.59% 13.44% 18.18% I 95, At Philips Highway 43 Average 15.76% 22.80% 26.67% 14.07% 14.64% 18.91% 50th Percentile 16.78% 22.72% 27.97% 15.06% 14.57% 19.76% 85th Percentile 25.41% 28.11% 30.69% 21.19% 20.27% 24.32% Lane addition at mer ge, 3 to 4 l anes I 4 EB, At I 75 50 Average 9.65% 16.82% 19.44% 6.11% 4.13% 9.42% 50th Percentile 8.93% 17.29% 18.58% 5.46% 3.69% 9.28% 85th Percentile 18.30% 22.54% 24.97% 12.39% 9.65% 14.18% Major diverge, 5 lanes on m ainline I 95 NB, At Flori da's Turnpike 152 Average 7.91% 11.26% 13.45% 3.26% 1.19% 6.24% 50th Percentile 7.84% 11.16% 13.34% 3.68% 2.07% 6.25%
54 Table 4 4. Continued Events Statistic Percentile d ifference v alues (%) Breakdown Pre b reakdown Max in 5 m in Max in 15 m in 5 m in a vg 15 min a vg Max 5 m in a vg Major diverge, 5 lanes on m ainline I 95 NB, At Florida's Turnpike 152 85th Percentile 14.44% 15.84% 17.35% 7.87% 6.01% 10.40% Diverge, 3 lanes on m ainline I 95 NB, Between Baymeadows and Butler 82 Average 11.29% 20. 65% 24.03% 12.31% 10.80% 13.86% 50th Percentile 12.10% 20.73% 23.88% 12.14% 11.65% 13.53% 85th Percentile 21.21% 26.83% 29.56% 18.58% 16.44% 21.32% Lane drop at diverge, 4 to 3 l anes I 4 WB, At Lee Road 71 Average 7.24% 17.99% 21.78% 6.86% 5.11% 10.93% 50th Percentile 7.54% 16.30% 21.45% 5.88% 5.66% 12.20% 85th Percentile 18.89% 27.17% 29.47% 17.39% 14.15% 19.14% All s ites 776 Average 9.57% 16.92% 19.67% 7.99% 5.33% 10.67% 50th Percentile 9.98% 16.84% 19.25% 7.98% 5.09% 10.73% 85th Pe rcentile 18.76% 24.42% 27.26% 15.55% 13.32% 17.80% The percentile dif ference is greatest for the 5 and 15 minute maximum flows, as would be expected. The maximum 5 minute flow 15 minutes before breakdown has the next greatest percentile difference. Thi s follows the same pattern as the actual difference results. Th e results of the percentile difference are similar to those of the actual difference , with respect to number of lanes . For merge sites, increasing number of lanes results in an increase in capa city change, wit h the exception of the combined merge. The average percentile difference for both 3 lane merge configurations are 6.58% and 6.47%, using the breakdown flow definition. The 4 lane averages are 9.29% and
55 15.76%. This result is contradictory t o the results found in Oh and Yeo (2012), which found that increasing number of lanes, decreases the capacity drop at on ramp merge locations. One explanation for this might be that Oh and Yeo observed several locations with 2 , 3 , 4 , and 5 lane configur ations, while this thesis observed two sites with 3 and 4 lanes each. A greater sample size may produce more consistent results. The combined merge experiences values similar to those found at 4 lane, on ramps (an average of 11.06%), same as the actual di fference. Finally, for diverge sites, increasing lanes results in decreasing percentile difference . Using the breakdown flow definition , the 3 lane diverge experiences an average percentile difference of 11.29%, while the 5 lane major diverge has an avera ge value of 7.91 % .
56 CHAPTER 5 MODEL DEVELOPMENT This chapter focuses on the model development proce ss, from determin ing the independent variables and testing them to model creation. Variable Testing During the testing process, it was decided to reduce the number of capacity definitions, since many of them seemed redundant and yielded similar results. The definitions for which models are developed are the breakdown flow, the 5 min flow before breakdown, the 15 min flow before breakdown, the max 5 min flow i n 15 min before breakdown, and the discharge flow. These five definitions were compared to the four variables chosen to be included in the final model; truck percentages, free flow spee d, number of lanes, and bottleneck type . Truck Percentages Truck percen tage data were gathered from FDOT Statistics Office. Out of the 776 breakdown events, truck percentage data for 566 events were available . The percentages were collected for the period preceding the breakdown, as well as during the brea kdown and congestion . Figure 5 1 through Figure 5 4 compare the pre breakdown capacity (in veh/hr/ln ) to the pre breakdown truck percentages. Figure 5 5 depicts the discharge flow against the disc ha rge period truck percentages.
57 Figure 5 1 . Breakdown flow vs truck percentage for all s ites Figure 5 2 . 5 min f low before breakdown vs truck percentage for all s ites 0 500 1000 1500 2000 2500 3000 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% Breakdown Flow (veh/hr/ln) Truck Percentage (%) Breakdown Flow vs Truck Percentage 0 500 1000 1500 2000 2500 3000 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 5 Min Flow Before Breakdown (veh/hr/ln) Truck Percentage (%) 5 Min Flow Before Breakdown vs Truck Percentage
58 Figure 5 3 . 15 min flow before breakdown vs truck p ercentage for all s ites Figure 5 4 . Max 5 min flow in 15 min before b reakdown vs truck percentage for all s ites 0 500 1000 1500 2000 2500 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% 15 Min Flow Before Breakdown (veh/hr/ln) Truck Percentage (%) 15 Min Flow Before Breakdown vs Truck Percentage 0 500 1000 1500 2000 2500 3000 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% Max 5 Min Flow in 15 Min Before Breakdown (veh/hr/ln) Truck Percentage (%) Max 5 Min Flow in 15 Min Before Breakdown vs Truck Percentage
59 Figure 5 5 . Discharge flow vs truck percentage for all s ites The truck percentages are widely distributed during the pre breakdown period, but are more densely packed during the discharge time frame. Across the breakdown and pre breakdown definitions, a slightly positive correl ation can be seen from these graphs, meaning that an increase in the truck percentage will have a corresponding increase on these capacities . This result is consistent with the HCM which has passenger car equivalency (PCE) values decreasing with increasing truck percentage, presumably because truck platooning decreases the overall effects of trucks on capacity. However, it may also be the result of having truck percentage data in 1 hour increments. A negative correlation can be seen in the d ischarge flow, w hich sees a decrease in discharge flow as the truck percentage increases . I t should be noted that the I 95 sites at NW 103 rd Street and at the Turnpike used truck percentages from further north on I 95, a few miles north of both of these sites. T he detector where the information was retrieved from was the closest one to either of these sites, and may not be as accurate as the other eight s ites. 0 500 1000 1500 2000 2500 3000 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% Discharge Flow (veh/hr/ln) Truck Percentage (%) Discharge Flow vs Truck Percentage
60 The truck percentages were used to determine the corresponding PCEs . M odels were developed for each defi nit ion that used flows in veh/hr/ln and in pc /hr/ln . Truck percentages were not used as a variable in th e models predicting units of pc /hr/ln . Free Flow Speed Free flow speeds (FFS) were calculated using the 1 minute data provided by STEWARD. Data were fil tered to include only value s following the criteria below: Flow less than 1000 veh/hr/l n; Speeds greater than the speed limit minus 10 mph (uncongested conditions). The remaining speeds were then averaged to calculate the FFS. This calculation was performe d for all sites. The resulting graphs are presented in Figure 5 6 through Figure 5 10 . Figure 5 6 . Breakdown flow vs free low speed for a ll s ites 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 50 55 60 65 70 75 Breakdown Flow (veh/hr/ln) Free Flow Speed (mph) Breakdown Flow vs Free Flow Speed
61 Figure 5 7 . 5 min flow b efo re breakdown vs free flow speed for a ll s ites Figure 5 8 . 15 min flow before breakdown vs free flow s peed for all s ites 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 50 55 60 65 70 75 5 Min Flow Before Breakdown (veh/hr/ln) Free Flow Speed (mph) 5 Min Flow Before Breakdown vs Free Flow Speed 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 50 55 60 65 70 75 15 Min Flow Before Breakdown (veh/hr/ln) Free Flow Speed (mph) 15 Min Flow Before Breakdown vs Free Flow Speed
62 Figure 5 9 . Max 5 min f low in 15 m in b efore breakdown vs free flow speed for a ll s ites Figure 5 10 . Discharge flow vs free flow speed for a ll s ites For all five definitions, the graphs show a positive correlation; higher speeds result in higher capacities. N ine of the sites experienced higher FFS compared to the posted speed limit. The one site that did not follow this trend was the lane addit ion at merge on I 4 EB at I 75. FDOT sources speculated that this may be due to a major 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 50 55 60 65 70 75 Max 5 Min Flow in 15 Min Before Breakdown (veh/hr/ln) Free Flow Speed (mph) Max 5 Min Flow in 15 Min Before Breakdown vs Free Flow Speed 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 50 55 60 65 70 75 Discharge Flow (veh/hr/ln) Free Flow Speed (mph) Discharge Flow vs Free Flow Speed
63 construction project in the vicin ity of the site. H owever , this project was located further west than the location of this site and it does not seem likely that this is the cause of the lower free flow speed. Number of Lanes The number of lanes varied across all sites from three to five. Figure 5 11 through Figure 5 15 contain the graphs of the capacity definition vs th e number of lanes. Figure 5 11 . Breakdown flow vs number of lanes for a ll s ites 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 2 3 4 5 6 Breakdown Flow (veh/hr/ln) Number of Lanes Breakdown Flow vs Number of Lanes
64 Figu re 5 12 . 5 min flow before breakdown vs number of l anes for all s ites Figure 5 13 . 15 min flow before b reakdown vs number of l anes for all s ites 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 2 3 4 5 6 5 Min Flow Before Breakdown (veh/hr/ln) Number of Lanes 5 Min Flow Before Breakdown vs Number of Lanes 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 2 3 4 5 6 15 Min Flow Before Breakdown (veh/hr/ln) Number of Lanes 15 Min Flow Before Breakdown vs Number of Lanes
65 Figure 5 14 . Max 5 min f low in 15 m in before breakdown vs number of lanes for a ll s ites Figure 5 15 . Discharge flow vs number of lanes for a ll s ites The graphs show a negat ive correlation for all five capacity definitions. Increasing number of lanes results in lower capacity , regardless of the bottleneck type . Oh and Yeo (2012) observed a similar trend among on ramp merge bottlenecks with regards to the capacity drop. 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 2 3 4 5 6 Max 5 Min Flow in 15 Min Before Breakdown (veh/hr/ln) Number of Lanes Max 5 Min Flow in 15 Min Before Breakdown vs Number of Lanes 1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 2 3 4 5 6 Discharge Flow (veh/hr/ln) Number of Lanes Discharge Flow vs Number of Lanes
66 Bottleneck Type The final variable used is the bottleneck type. In order to use this variable in a model, seven dummy variables needed to be created, each one corresponding to a bottleneck type. For instance, t he variable Type1 was created i f the bottleneck type is weaving, then this variable is 1, otherwise it is 0. This process was repeated for all seven bottleneck types. The graphs can be seen in Figure 5 16 through Figure 5 20 . Figure 5 16 . Breakdown flow vs b ottleneck type for a ll s ites 500 1000 1500 2000 2500 3000 Breakdown Flow (veh/hr/ln) Bottleneck Type Breakdown Flow vs Bottleneck Type Weaving Merge Combined Merge Merge with Lane Add Major Diverge Diverge Lane Drop
67 Figure 5 17 . 5 min f l ow before breakdown vs b ottleneck type for a ll s ites Figure 5 18 . 15 min flow before b reakdown v s bottleneck t ype for all s ites 500 1000 1500 2000 2500 3000 5 Min Flow Before Breakdown (veh/hr/ln) Bottleneck Type 5 Min Flow Before Breakdown vs Bottleneck Type Weaving Merge Combined Merge Merge with Lane Add Major Diverge Diverge Lane Drop 500 1000 1500 2000 2500 3000 15 Min Flow Before Breakdown (veh/hr/ln) Bottleneck Type 15 Min Flow Before Breakdown vs Bottleneck Type Weaving Merge Combined Merge Merge with lane Add Major Diverge Diverge Lane Drop
68 Figure 5 19 . Max 5 min f l ow before breakdown vs b ottleneck type for all s ites Figure 5 20 . Discharge flow vs b ottleneck type for a ll s ites 500 1000 1500 2000 2500 3000 Max 5 Min Flow in 15 Min Before Breakdown (veh/hr/ln) Bottleneck Type Max 5 Min Flow in 15 Min Before Breakdown vs Bottleneck Type Weaving Merge Combined Merge Merge with Lane Add Major Diverge Diverge Lane Drop 500 1000 1500 2000 2500 3000 Capacity (veh/hr/ln) Breakdown Type Discharge Flow vs Breakdown Type Weaving Merge Combined Merge Merge with Lane Add Major Diverge Diverge Lane Drop
69 The on ramp merge sites show a greater variability than the other bottleneck types, because o f the range of values provided by the number of lanes. The graphs look similar across all capacity definitions used. The merge with lane addition and the major diverge bottleneck types have the lowest observed capacities, with the smallest ranges. The weav ing, combined merge, and diverge types have similar ranges in each capacity definition. Percentile Difference Lorenz and Elefteriadou (2001) showed that a freeway segment can experience an increase in capacity, if the initial flow was lower. This trend was also seen during this analysis. Figure 5 21 show s the breakdown flow percentile difference vs the breakdown flow . Figure 5 21 . P ercentile d ifference vs breakdown f low for all s ites There is a posit ive correlation between the two variables; an increase in the breakdown flow results in an increase in the breakdown flow percentile difference. Negative capacity drops (or a rise in capacity) occur at lower capacity values. Higher -30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00% 40.00% 1000 1500 2000 2500 3000 Percentile Difference (%) Breakdown Flow (veh/hr/lane) Breakdown Flow Percentile Difference vs Breakdown Flow
70 drops in capacity are ob served at higher capacity values. The same trend exists for all of the capacity definitions studied. This provides some evidence that a rise in ca pacity may occur when the breakdown flow is low. Figure 5 22 displays the plot for t he breakdown flow percentile difference vs the discharge flow. Figure 5 22 . Breakdown flow percentile difference vs discharge flow for all s ites This plot shows a negative trend between the two variables, an increase in the discharge flow results in a decrease in the breakdown flow percentile difference. Many of the negative percentile differences occur at higher disc harge flows, supporting the theory that the capacity rises can occur when the initial flow is low, and then in creases during the breakdown. The pre breakd own flows occur over a period of 1 , 5 , or 15 minutes, while the discharge flow occurs over the entire discharge period. The discharge period can last ten minutes, at minimum, and up to several hours. -30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00% 40.00% 1000 1500 2000 2500 3000 Percentile Difference (%) Discharge Flow (veh/hr/lane) Breakdown Flow Percentile Difference vs Discharge Flow
71 In additi on to the effects of the independent variables on capacity, analysis was also performed on how these variables affected the percentile change. Figure 5 23 through Figure 5 26 show these relationships for the breakdown flow percentile change. The other definitions exhibit the same trends, therefore their graphs are omitted from this thesis. Figure 5 23 . Breakd own flow percentile change vs truck percentage for all s ites Fi gure 5 24 . Breakdown flow percentile change vs free flow speed for all s ites -30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00% 40.00% 0.00% 2.00% 4.00% 6.00% 8.00% 10.00% 12.00% 14.00% 16.00% Percentile Change (%) Truck Percentage (%) Breakdown Flow Percentile Change vs Truck Percentage -30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00% 40.00% 50 55 60 65 70 75 Percentile Change (%) Free Flow Speed (mph) Breakdown Flow Percentile Change vs Free Flow Speed
72 Figure 5 25 . Breakdown flow percentile change vs n umbe r of l anes Figure 5 26 . Breakdo wn flow percentile change vs bottleneck t ype -30.00% -20.00% -10.00% 0.00% 10.00% 20.00% 30.00% 40.00% 2 3 4 5 6 Percentile Change (%) Number of Lanes Breakdown Flow Percentile Change vs Number of Lanes -45.00% -35.00% -25.00% -15.00% -5.00% 5.00% 15.00% 25.00% 35.00% 45.00% Percentile Change (%) Bottleneck Type Breakdown Flow Percentile Change vs Bottleneck Type Weaving Merge Combined Merge Merge with Lane Add Major Diverge Diverge Lane Drop
73 It is difficult to see any trends associated with these plots. Determining relationships between the independent variables and the capacity change may not be as valuable as the relationships between the variable s and the different capacities. The bottleneck types with the greatest ranges are the diverge and lane reduction at a diverge sites. The left hand merge, lane addition at merge, and major di verge have the smallest ranges. Model Development Models were deve lope d to predict the flows of the selected definitions: the breakdown flow, the 5 min flow before breakdown, the 15 min flow before breakdown, max 5 min flow in 15 min before breakdown, and the discharge flow. Two models were developed for each defini tion, one for units of veh/hr/ln and another for pc /hr/ln , making a total of ten models. Table 5 1 summarizes the types of models developed. Table 5 1 . Model d evelopment to p redict c apacity Definition Flow veh/hr/l n pc/hr/ln Breakdown Yes Yes 5 Min a vg Yes Yes 15 Min a vg Yes Yes Max 5 min flow in 15 m in Yes Yes Discharge Yes Yes The same definitions were used for developing models for both the actual difference and the percentile dif ference using uni ts of veh/hr/ln and pc/hr/ln , resulting in four models for each definition. Table 5 2 explains this.
74 Table 5 2 . Model development to p redict actual difference and percentile d ifference Definition Per centile d ifference Actual d i fference veh/hr/ln pc /hr/ln veh/hr/l n pc /hr/ln Breakdown Yes Yes Yes Yes 5 min f low Yes Yes Yes Yes 15 min f low Yes Yes Yes Yes Max 5 min flow in 15 m in Yes Yes Yes Yes All of the variables discussed were used as indepen dent variables to predict the dependent variables. The output displays the coefficients for each variable, as well as their t value. The t values are compared t o the critical t value of 1.96; this corresponds to a confidence interval of 95 percent. I f the t value is greater than the critical, the variable is statistically significant and should remain in the model. If the value is less than the critical t, the variable i s removed. For all definitions, except for the discharge flow, the truck percentage used in the models is the pre congestion percentage. This is the percentage of trucks that was seen prior to the breakdown. The discharge flow models use the percentage of trucks seen during congested conditions . The developed models also include an interactio n variable between the bottleneck type and the number of lanes for the merge sites only, in order to determine how changes in the number of lanes affects merge bottleneck types. The interaction variable is the product of these two variables, and is labeled as Type2*Lanes . Breakdown Flow Definition The models developed in this section are based on the breakdown flow of every site. Table 5 3 displays the models developed for the capacity, actual difference, and the percentile differe nce .
75 Table 5 3 . Models r elated to the breakdown f low Units Breakdown f low Constant Breakdown f low # oflanes FFS Truck% Type3 1 Type4 2 Type5 3 Type7 4 R 2 value veh/hr/ln 644.41 N/A 19.70 327.01 334.13 0.35 pc/hr/ln 1002.04 N/A 14.42 N/A 398.52 283.15 0.39 Units Actual d ifference Constant Breakdown flow #oflanes FFS Truck% Type3 1 Type4 2 Type5 3 Type7 4 R 2 value veh/hr/ln 1538.83 0.65 150.25 193.34 39.40 0.58 pc/hr/ln 1743.18 0.65 203.28 N/ A 287.38 53.53 0.61 Units Percentile d ifference Constant Breakdown flow #oflanes FFS Truck% Type3 1 Type4 2 Type5 3 Type7 4 R 2 value veh/hr/ln 103.36 0.03 11.08 0.30 0.50 12.87 6.34 0.47 pc/hr/ln 51.55 0.03 2.93 N/A 6.67 0.45 N/A the variable was not used in the model. the variable was not significant enough to appear in the model based on a t value that was not greater than the critical t value. 1 Type3 refers to a combined (left and right hand ) merge bottleneck type. 2 Type 4 refers to a merge with a lane addition bottleneck type. 3 Type5 refers to a major diverge bottleneck type. 4 Type7 refers to a lane drop at diverge bottleneck type.
76 The R square values for the models predicting the capacity are low, indicating that the se models are not good at predicting the dependent variables. However, the R square values that predict the actual and p ercentile difference are higher, meaning th ese models are good predictors. The capacity coefficient is positive in all cases it appears , which is consistent with the plots. The higher the flow value the higher the actual or percentile difference. The free flow speed, truck percentage and number of lanes coefficients are also positive in all cases . This means that as these variables increas e (higher speeds, more trucks, greater number of lanes), the greater the output (breakdown flow, actual difference, percentile difference). The truck coefficients only appear in the percentile difference model using veh/hr/ln. The combined (left and right side) merge and merge with lane addition bottleneck types appear in the models t hat predict the breakdown flow, with the merge with a lane addition being negative. The major diverge and lane drop bottleneck types appear in the models for the actual and per centile difference, with the major diverge type being negative. This suggests that the merge with lane addition and the major diverge bottleneck types decrease the breakdown flow, actual difference, and percentile difference. Based on the analysis performe d, these two types have very low capacity values, as well as having the smallest range of capacities, actual and percentile differences among all bottleneck types. 5 Minute Flow Before Breakdown This section displays the models developed fo r predicting the actual difference, percentile difference, and flows for the 5 minute flow before breakdown definition. Table 5 4 summarizes the developed regression models.
77 Table 5 4 . Models r elated to the 5 minute fl ow before b reakdown Units 5 min flow before b reakdown Constant 5 minute f low #ofl anes FFS Truck% Type3 1 Type4 2 Type5 3 Type7 4 Type 2 *l anes 5 R 2 v alue veh/hr/ln 718.91 18.46 291.54 391.79 121.39 0.50 pc/hr/ln 360.91 24.95 N/A 405.37 41 1.19 39.20 0.52 Units Actual d ifference Constant 5 minute flow #ofl anes FFS Truck% Type3 1 Type4 2 Type5 3 Type7 4 Type 2 *lanes 5 R 2 v alue veh/hr/ln 1787.27 0.45 74.17 11.09 18.20 163.52 0.46 pc/hr/ln 1822.26 0.45 79.05 13.10 N/A 136.72 170.51 0.51 Units Percentile d ifference Constant 5 minute flow #ofl anes FFS Truck% Type3 1 Type4 2 Type5 3 Type7 4 Type 2 *lanes 5 R 2 v alue veh/hr/ln 89.39 0.02 3.91 0.61 0.94 8.95 0.35 pc/hr/ln 90.62 0.02 4.22 0.75 N/A 7.23 9.64 0. 40 N/A the variable was not used in the model. the variable was not significant enough to appear in the model based on a t value that was not greater than the critical t value. 1 Type3 refers to a combined (left and right hand ) merge bottleneck type . 2 Type4 refers to a merge with a lane addition bottleneck type. 3 Type5 re fers to a major diverge bottleneck type. 4 Type7 refers to a lane drop at diverge bottleneck type . 5 Type 2 *Lanes refers to the interaction term between merge bottleneck types and lanes.
78 The R square values for the models predicting the 5 minute flow before breakdown are greater than the corresponding models for the breakdown flow. However, the R square values for the actual and percentile difference models decreased between the tw o capacity definitions. The models for predicting the flow and the actual difference are reasonable, while the percentile difference models are not good at predicting. The capacity coefficient, number of lanes, free flow speed, and truck percentage variabl es are all positive. This means that when these three variables increase, the value they are predicting also increases. Only the free flow speed variable appears in the models predicting the 5 minute flow before breakdown. Again, the combined merge, merge with a lane addition, major diverge, and lane drop at diverge appear as bottleneck type variables. The merge with a lane addition and major diverge types have negative coefficients when they appear, while the other bottleneck types are positive. The intera ction variable also appears in the models predicting the 5 minute flow before breakdown. The coefficient is negative, meaning that for merge sites, increasing number of lanes results in a lower flow, which is consistent with the plots presented earlier. 15 Minute Flow Before Breakdown Table 5 5 displays the models developed for the 15 minute flow before breakdown defi nition. The 15 minute flow before breakdown, actual difference and percentile difference were modeled .
79 Table 5 5 . Models r elated to the 15 minute flow before b reakdown Units 15 minute flow before b reakdown Constant 15 minute f low #ofl anes FFS Truck% Type2 1 Type3 2 Type4 3 Type5 4 Type7 5 Type 2 *l anes 6 R 2 v alue veh/hr/ln 180.72 N/A 31.58 47.90 309.73 377.92 358.33 0.54 pc/hr/ln 219.51 N/A 33.11 N/A 117.68 379.27 365.56 368.65 0.54 Units Actual d ifference Constant 15 minute flow #ofl anes FFS Truck% Type2 1 Type3 2 Type4 3 Type5 4 Type7 5 Type 2 *lanes 6 R 2 value veh/hr/ln 1474. 12 0.53 172.61 9.33 101.06 282.16 101.20 0.48 pc/hr/ln 1467.58 0.54 178.74 N/A 46.40 297.54 94.86 0.50 Units Percentile d ifference Constant 15 minute flow #ofl anes FFS Truck% Type2 1 Type3 2 Type4 3 Type5 4 Type7 5 Type 2 *lanes 6 R 2 value veh/hr/ln 106.17 0.02 4.89 0.82 0.91 9.37 0.28 pc/hr/ln 64.83 0.03 2.65 0.22 N/A 21.97 7.68 7.57 0.44 N/A the variable was not used in the model. the variable was not significant enough to appear in the model based on a t value that was not greater than the critical t value. 1 Type2 refers to a merge bottleneck type. 2 Type3 refers to a combined (left and right hand ) merge bottleneck type. 3 Typ e4 refers to a merge with a lane addition bottleneck type. 4 Type5 refers to a major diverge. 5 Type7 refers to a lane drop at diverge bottleneck type. 6 Type 2 *lanes refers to the interaction term between merge bottleneck types and lanes.
80 The R square values for the models that predict the 15 minute flow before breakdown and the actual d ifference are similar to the corresponding models seen in the previous table. These models are good at predicting the dependent variables. The R square values for the percentile difference, however, are low (especially when using units of veh/hr/ln ) and ar e not good predictors. The capacity, number of lanes, free flow speed, and truck percentage coefficients are all positive. Again, the free flow speed only appears in the models that predict the 15 minute flow before breakdown. The merge bottleneck type app ears in this set of models, as well as the combined merge, merge with a lane addition, major diverge, and the lane drop at diverge types. All these types appear in the flow prediction model ex cept for the major diverge; t he merge and merge with lane additi on types are negative. The merge, combined merge, and major diverge types are negative in the models that predict the actual and percentile difference. The negative sign associated with these variables means that these bottleneck types have a negative impa ct on the 15 minute flow before breakdown and the actual and percentile differences. The positive coefficient means that those bottleneck types will increase the predicted values, meaning large capacities, as well as larger differences (both actual and per centile). The interaction variable appears in the model that predicts the percentile differe nce using units of pc/hr/ln , and has a positive coefficient. This is con sistent with the data analysis seen in Table 4 4 . Maximum 5 Minute Flow Before Breakdown This section presents the models developed for the flow, the actual difference , and the percentile difference for the maximum 5 minute flow before breakdown definition. Table 5 6 displays these models.
81 Table 5 6 . Models r elated to the maximum 5 minute flow before b reakdown Units Maximum 5 minute flow before b reakdown Constant Max 5 min flow # oflanes FFS Truck% Type2 1 Type3 2 Type4 3 Type7 4 R 2 value veh/hr/ln 179.07 N/A 27.87 62.89 352.27 408.77 0.54 pc/hr/ln 632.98 N/A 20.56 N/A 444.89 328.72 0.53 Units Actual d ifference Constant Max 5 min flow #oflanes FFS Truck% Type2 1 Type3 2 Type4 3 Type7 4 R 2 value veh/hr/ln 1759.93 0.44 74.41 11.32 19.26 138.31 0.46 pc/hr/ln 1766.25 0.44 77.76 13.09 N/A 141.05 139.97 0.51 Units Percentile d ifference Constant Max 5 min flow #oflanes FFS Truck% Type2 1 Type3 2 Type4 3 Type7 4 R 2 value veh/hr/ln 83.29 0.02 3.86 0.61 0.98 7.29 0.32 pc/hr/ln 81.74 0.02 4.01 0.72 N/A 7.1 5 7.48 0.36 N/A the variable was not used in the model. value that was not greater than the critical t value. 1 Type2 refers to a merge bottleneck type. 2 Type3 refers to a combined (left and right hand ) merge bottleneck type. 3 Type4 refers to a merge with a lane addition bottleneck type. 4 Type7 refers to a lane drop at diverge bottleneck type.
82 All of the models have R square values similar to the values seen in the last set of models. The models that determine the maximum 5 minute flow before breakdown and the actual difference are good predictors, while the percentile difference is not good a predictor. Again, the capacity, number of lanes, free flow speed, and truck pe rcentage coefficients are positive. The free flow speed is only present in the maximum 5 minute flow before breakdown models. The merge, combined merge, merge with a lane addition, and a lane drop at diverge bottleneck types appear in these models. All fou r types, except for the lane drop at diverge, appear in the models that predict the flow. The merge and merge with lane addition have negative coefficients. All other types are positive, when they appear. Again, the negative sign of these variables means t hat these bottleneck types lower the values that they are predicting. A positive coefficient will do the opposite. The interaction variable is not present in any of the models developed for this definition. Discharge Flow The final models presented are th ose that predict the discharge flow. Table 5 7 displays these model s.
83 Table 5 7 . Models r elated to the discharge f low Units Discharge flow Constant #ofLanes Speed limit Truck% Type1 1 Type4 2 Type6 3 Type7 4 Type 2 *lanes 5 R 2 value veh/hr/ln 1659.40 195.48 18.99 25.05 403.70 580.90 324.43 208.12 97.82 0.56 pc/hr/ln 1348.21 195.19 22.98 N/A 426.56 677.08 342.75 173.12 104.18 0.55 N/A the variable was not used in the model. the varia ble was not significant enough to appear in the model based on a t value that was not greater than the critical t value. 1 Type1 refers to a weaving bottleneck type. 2 Type4 refers to a merge with a lane addition bottleneck type. 3 Type6 refers to a diver ge bottleneck type . 4 Type7 refers to a lane drop at diverge bottleneck type. 5 Type2*lanes refers to the interaction term between merge bottleneck types and lanes.
84 The R square values for the discharge flow models are reasonable and similar to the p revio us flow predicting models. The coefficient for the number of lanes is negative for both models, and is consistent with the plots presented earlier. The truck percentage seen during the congested period is also negative, which was also observed using the pl ots. Finally, the speed limit was used as a variable instead of the free flow speed. This was done because the free flow speed may not be a relevant measure during congested The speed limit is positive in these models, indicating that higher speed limits result in higher flows, which is a correlation that was observed for all capacity definitions plotted against the free flow speed. The weaving and diverge bottleneck types appear in these mod els; this is the first time these types appear in any model. The merge with a lane addition and the lane drop at diverge types also appear. All four bottleneck types are negative. The interaction variable also appears in these models, and is ne gative, which is expected. This trend was seen in the analysis section in Tab le 4 2 .
85 CHAPTER 6 CONCLUSIONS AND RECOMMENDATIONS This chapter summarizes the results of this work and provide s recommendations for future work. Conclu sions Several conclusions can be drawn from the results of this study. Firstly, the models that predict the percentile difference, regardless of the definition used, have low R square values. Based on this statistic, these models should not be used to dete rmine the percentile difference directly. The models developed to predict the flow and the actual difference have higher R square values, making them better predictors. The only exception to this statement is for the models that predict the breakdown flow. These two models have low R squares and should not be used. It can be speculated that breakdown flow is highly dependent on driver behavior at the time of breakdown, and thus more difficult to correlate to the highway environment. Secondly, several resul ts can be drawn from the analysis of this paper. The variables used in the models were tested for trends. The most apparent trend was seen when comparing the capacity to the number of lanes; a strong negative correlation exists between these variables. The free flow speed was also tested against the different capacity definitions, with a slightly positive correlation seen in all cases. Truck percentages were tested as well, and for all pre breakdown flows, a slightly positive trend exists, while for the dis charge flow, a negative trend was observed. These trends were observed in th e models predicting the discharge flow. There were no apparent trends seen for these same variables when plotted against the selected capacity definitions.
86 There were also some com parisons made to the results of the literature review. The first one was observed in Oh and Yeo (2012). The authors found that increasing number of lan es reduces the percentile difference at on ramp merge sites. This thesis observed several bottleneck site s, and when analyzing all seven bottleneck types together, the percentile difference increases. These seven types were grouped into three types, weaving, merge, and diverge, to determine how the grouped types responded to the number of lanes variable. The merge site saw an increase in the percentile difference with increasing lanes, which is contradictory to the results of the Oh and Yeo (2012) study. An interaction variable was also created specifically to see the effects of the number of lanes on the on r amp merge sites. When this variable appeared in the models for the percentile difference, it had a positive coefficient, which is not consistent with the results of Oh and Yeo (2012). Another result from the literature was seen in Lorenz and Elefteriadou ( 2001). They concluded that a capacity rise may occur during a breakdown if the pre breakdown flows are low. This phenomenon was experienced during this study. Several times when a capacity rise occurred, the breakdown flows were less than 1900 veh/hr/lane. Very few capacity rise events occurred at flows higher than this. It should be noted that not every time a low flow occurred, was there a coinciding capacity rise. Also, not all capacity rises occurred at low flows. Recommendations Based on the research performed, a major recommendation for the future is to determine an acceptable definition for capacity. The definition provided by the Highway Capacity Manual provides a good summary for what the capacity should be, but fails to provide details on how to o btain a capacity value. The capacity values provided in the
87 HCM that are based on free flow speed, are only provided for basic freeway segments. The HCM does not provide capacity values for the types of segments examined here. The HCM values for basic free way segments are clearly not suitable for merge, diverge, and weaving segments. For instance, a FFS of 70 mph corres ponds to a capacity of 2400 pc /hr/ln , according to the HCM. But the results show breakdowns occurring a s low as 1400 pc /h r/ln , a thousand ve hicles short of the predicted value. Clearly, more investigation should be performed to determine acc eptable capacities of various types of freeway s egments . The breakdown definition should also be reexamined for future use. Previous research has shown man y methods in determining the start and end of a break down. Several use the threshold me thod, but use arbitrary speed threshold values to determine a breakdown. Strides were made in observing the queue length as well as the density of the roadway. These mea sures should be explored and tested for validity, in order to establish a better breakdown definition. Future research should also examine how the number of lanes impacts the capacity change, with regards to the bottleneck type. Each major bottleneck type (weaving, merge, and diverge) should be examined by collecting data at sites with a range of lanes on the mainline. Each bottleneck type could be examined separately to establish trends within each type. Finally, with regards to the developed models, the e quations that predict the percentile difference are less accurate than the remaining equations . Instead, the remaining models should be used, with the exception of the breakdown flow models. Because of the high R square values, these are good predictors fo r the dependent
88 variables. The actual difference can be determined directly, or one of the pre breakdown flows, as well as the discharge flow can be calculated. These two flows can be used to calculate either the actual or percentile flow, depending on wha t is needed. All three remaining pre breakdown capacity definitions experience similar trends and have similar R squares, so which definition to use is up to the user and what the purpose of the analysis is. The maximum 5 minute flow before breakdown saw h igher values for the capacity , so this definition could be used as an optimistic view for capacity. The 5 and 15 minute flow before breakdown saw smaller values for the capacity, and therefore could be used to predict a conservative value.
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91 BIOGRAPHICAL SKETCH Bryan majored in c ivil engineering at the University of Florida . He received his Bachelor of Scienc e in the fall of 20 08. program, he focused in transportation engineering and was a graduate research assistant at the Transportation Research Center of the University of Florida, Department of Civil and Coastal Engineering. He received his Master of Engin eerin g degree in the summer of 2014.