Effect of adaptive cruise control systems on mixed

0Effectofadaptivecruisecontrolsystemsonmixedtrafficflownearanon-rampL.C.Davis*,PhysicsDept.,UniversityofMichigan,AnnArbor,MI48109AbstractMixedtrafficflowconsistingofvehiclesequippedwithadaptivecruisecontrol(ACC)andmanuallydrivenvehiclesisanalyzedusingcar-followingsimulations.Unlikesimulationsthatshowsuppressionofjamsduetoincreasedstringstability,simulationsofmergingfromanon-rampontoafreewayhavenotthusfardemonstratedasubstantialpositiveimpactofACC.Inthispapercooperativemergingisproposedtoincreasethroughputandincreasedistancetraveledinafixedtime(reducetraveltimes).InsuchasystemanACCvehiclesensesnotonlytheprecedingvehicleinthesamelanebutalsothevehicleimmediatelyinfrontintheoppositelane.Priortoreachingthemergeregion,theACCvehicleadjustsitsvelocitytoensurethatasafegapformergingisobtained.Ifon-rampdemandismoderate,partialimplementationofcooperativemergingwhereonlymainlineACCvehiclesreacttoanon-rampvehicleiseffective.Significantimprovementinthroughput(18%)andincreasesupto3kmindistancetraveledin500sarefoundfor50%ACCmixedflowrelativetotheflowofallmanualvehicles.Forlargedemand,fullimplementationisrequiredtoreducecongestion.Keywords:Trafficmodel;Trafficflow;Trafficdynamics;Congestedflow*Email:[e-mail]1Effectofadaptivecruisecontrolsystemsonmixedtrafficflownearanon-rampL.C.Davis,PhysicsDept.,UniversityofMichigan,AnnArbor,MI481091.IntroductionAdaptivecruisecontrol(ACC)systemsarenowavailableonsomeluxurycarsandmightbeusedonasignificantfractionofallvehiclesinthefuture.ACCadjustsvehiclespeedaccordingtotherangeandrateofchangeofrangetotheprecedingvehicletomaintainasafedistance.Throttlecontroland,insomedesigns,mildbrakingcanbeemployedaboveacutoffspeedtoachievethedesiredrangeandvelocity.FuturegenerationsofACCcouldtakecompletecontrolofthelongitudinalmotion.ForrecentdiscussionsofACC,seeBareketetal.(2003)aswellasVanderWerfetal.(2002).Severalpapers(basedonsimulations)assessingtheimpactoftheincreasingproportionofACCvehicleshaveappeared.Inadditiontoimprovingdrivercomfortandsafety,system-widebenefitsforfreewaytraffichavebeensuggested.Kukuchietal.(2003)aswellasKerner(2003)foundthatACCvehiclestendtopromotestabilityoftrafficflow.Davis(2004b),likeKerner(2003),showedthatACCcansuppresswidemovingjamsbyincreasingstringstability.TreiberandHelbing(2001)reportedthatif20%ofvehicleswereequippedwithACC,nearlyallcongestioncouldbeeliminatedonaGermanautobahn.BoseandIoannou(2003)showedthattheflow-densitycurveformixedtrafficshouldfallbetweenthecurvesformanualandACCvehicles.IoannouandStefanovic(2005)alsoanalyzedmixedtraffic,consideringtheeffectsofunwantedcut-ins(See,forexample,Sultanetal.,2002.)duetolargergapsinfrontofACCvehicles.TheydemonstratedthatthesmoothnessofACCvehicleresponseattenuatestheperturbationduetoacut-in.Overall,IoannouandStefanovic(2005)concludedthattherewereenvironmentalbenefitsduetoreducedexhaustemissions.NotalltheeffectsofACContrafficwerefoundtobefavorable.Inadditiontothecut-inproblem,Kerner(2003)foundthatACCvehiclesmightinducecongestionatbottlenecks.OnlymarginalimprovementsintraveltimeswerefoundbyBoseandIoannou(2003)and2byDavis(2004b)inon-rampsimulations.Sincecongestionoftenoccursatbottleneckscausedbymergingvehicles,theabilityofACCtoalleviatecongestioncanthereforebequestioned.ThepurposeofthepresentworkistoshowhowtheintroductionofsimplecooperativemergingbetweenACCvehiclesandothervehiclesreducestraveldelaysandincreasesflow.Noattemptismadetodescribehowtheextracapabilitycouldbeimplementedinhardwareorsoftware.Onlythebenefitsofsuchacapabilityareexamined.Thispaperisorganizedasfollows.ThedynamicsofbothACCandmanualvehiclesisdescribedinSec.2.Mergingaton-rampsandsimulationsformixedtrafficwithoutcooperativemergingarediscussedinSec.3.TheformalismforcooperativemergingisgiveninSec.4.SimulationswithcooperativemergingarereportedinSec.5.ConclusionsarestatedinSec.6.2.Vehicledynamics2.1.AdaptivecruisecontrolvehiclesThedynamicsofACCvehiclesforthesimulationmodelisdescribedinthissection.Forthenthvehicleinalane,theequationofmotionis())(),()()(tvtxVtvdttdvnnnn∆∆=+τ,(1)wherethedistancebetweenthenthvehicleandtheprecedingone(n-1)is).()()(1txtxtxnnn−=∆−(2)Thisquantityistheheadway(includingvehiclelength)anditsrateofchangeisthevelocitydifference).()()(1tvtvtvnnn−=∆−(3)Themechanicaltimeconstantisτandtheright-handsideofEq.(1)is())()(1))(),((tvDtxhtvtxVnndnn∆+−∆=∆∆τ.(4)Theheadwaytimeishd.UsingtheworkofLiangandPeng(1999,2000),Davis(2004b)establishedthatthisformofcontrollawisstringstable.3Theconstraintsimposedbyvehiclemechanicallimitationsonaccelerationanddecelerationaredecelnacceladtdva−≥≥.(5)Themaximumaccelerationisaaccel=3m/s2andthemaximumdecelerationisadecel=10m/s2.Toavoidcollisions,theGipps-likecondition(Gipps,1981)gnadtdv−≤(6)mustbesatisfiedwhenDtvtatvtvtxndgnnn−−+∆−)(2)()()(221.(7)HereD=7mandagis3m/s2.Theconditiongnadttdv−=/)(isimposedwhentheequationofmotionfailstogivesufficientdeceleration.2.2.ManualvehiclesInadditiontothemechanicaltimeconstantτ,humandriversdonotrespondimmediatelyandthereforeexhibitadelaytimetd(typicallyabout0.75s),whichisincludedinthem