Modelling decisions of control transitions and target speed regulations in full-range Adaptive Cruise Control based on Risk Allostasis Theory

Delft University of Technology

Modelling decisions of control transitions and target speed regulations in full-range

Adaptive Cruise Control based on Risk Allostasis Theory

Varotto, Silvia; Farah, Haneen; Toledo, Tomer; van Arem, Bart; Hoogendoorn, Serge

DOI

10.1016/j.trb.2018.09.007

Publication date

2018

Document Version

Final published version

Published in

Transportation Research. Part B: Methodological

Citation (APA)

Varotto, S., Farah, H., Toledo, T., van Arem, B., & Hoogendoorn, S. (2018). Modelling decisions of control

transitions and target speed regulations in full-range Adaptive Cruise Control based on Risk Allostasis

Theory. Transportation Research. Part B: Methodological, 117(Part A), 318–341.

https://doi.org/10.1016/j.trb.2018.09.007

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ContentslistsavailableatScienceDirect

Transportation

Research

Part

B

journalhomepage:www.elsevier.com/locate/trb

Modelling

decisions

of

control

transitions

and

target

speed

regulations

in

full-range

Adaptive

Cruise

Control

based

on

Risk

Allostasis

Theory

Silvia F. Varotto

a,∗

_{, Haneen Farah}

a

_{, Tomer Toledo}

b

_{, Bart van Arem}

a

_,

Serge P. Hoogendoorn

a

a Department of Transport and Planning, Faculty of Civil Engineering and Geosciences, Delft University of Technology, Stevinweg 1, P.O.

Box 5048, Delft 2600 GA, The Netherlands

b Transportation Research Institute, Faculty of Civil and Environmental Engineering, Technion - Israel Institute of Technology, 711 Rabin

Building, Haifa 320 0 0, Israel

a

r

t

i

c

l

e

i

n

f

o

Article history: Received 30 April 2018 Revised 5 August 2018 Accepted 7 September 2018 Available online 19 September 2018

Keywords:

Control transitions Adaptive Cruise Control On-road experiment Driver behaviour

Continuous-discrete choice model

a

b

s

t

r

a

c

t

AdaptiveCruiseControl(ACC)andautomatedvehiclescancontributetoreducetraffic con-gestionandaccidents.Recently,anon-roadstudyhasshownthatdriversmaypreferto de-activatefull-rangeACCwhenclosinginonaslowerleaderandtooverruleitbypressing thegaspedalafewsecondsaftertheactivationofthesystem.Notwithstandingthe influ-enceofthesecontroltransitionsondriverbehaviour,atheoreticalframeworkexplaining driverdecisionstotransfercontroland toregulatethetarget speedinfull-rangeACCis currentlymissing.

This research develops a modelling framework describing the underlying decision-makingprocessofdriverswithfull-rangeACCatanoperationallevel,groundedonRisk Al-lostasisTheory(RAT).Basedonthistheory,adriverwillchoosetoresumemanualcontrol ortoregulatetheACCtargetspeedifitsperceivedlevelofriskfeelingandtaskdifficulty falls outsidetherangeconsidered acceptableto maintainthe systemactive.Thefeeling ofriskandtaskdifficultyevaluationisformulatedasageneralizedorderedprobitmodel withrandomthresholds, whichvarybetweendrivers andwithindrivers overtime. The ACCsystemstatechoicesareformulatedaslogitmodelsandtheACCtargetspeed regula-tionsasregressionmodels,inwhichcorrelationsbetweensystemstatechoicesandtarget speed regulationsare capturedexplicitly. Thiscontinuous-discrete choicemodel frame-workisabletoaddressinterdependenciesacrossdrivers’decisionsintermsofcausality, unobserveddrivercharacteristics,andstatedependency,andtocaptureinconsistenciesin drivers’decisionmakingthatmightbecausedbyhumanfactors.

Themodelwasestimatedusingadatasetcollectedinanon-roadexperimentwith full-rangeACC.Theresultsrevealthatdriverdecisionstoresumemanualcontrolandto reg-ulatethetargetspeedinfull-rangeACCcanbeinterpretedbasedontheRAT.Themodel canbeusedtoforecastdriverresponsetoadrivingassistancesystemthatadaptsits set-tingstopreventcontroltransitionswhileguaranteeingsafetyandcomfort.Themodelcan alsobeimplementedintoamicroscopictrafficflowsimulationtoevaluatetheimpactof ACContrafficflowefficiencyandsafetyaccountingforcontroltransitionsandtargetspeed regulations.

© 2018ElsevierLtd.Allrightsreserved.

https://doi.org/10.1016/j.trb.2018.09.007

1. Introduction

Automatedvehiclesare expectedto mitigatetrafficcongestionandaccidents(EuropeanCommission,2017). Automated vehiclesmayhaveabeneficialimpactonroadcapacity,trafficflowstability,andqueuedischargerates(Hoogendoornetal., 2014).The firststeptowardspredictingtheseimpactsistoinvestigatecurrentlyavailablesystemssuchasAdaptiveCruise Control(ACC).ACCassists drivers inmaintaining atarget speed andtime headway andthereforehasa direct adaptation effectonthelongitudinalcontroltask(MartensandJenssen, 2012). TheinfluenceofACCsystemsondriverbehaviourhas beeninvestigated, mainly via driving simulatorstudies, since the 1990s. On-roadexperiments (Alkim etal., 2007; Malta etal.,2012;NHTSA,2005;Schakeletal.,2017)haveshownthatACCsystemsinfluencesubstantiallydriverbehaviour.When theACC isactive,drivers keep largertime headways(Alkimetal., 2007;Maltaetal., 2012; NHTSA, 2005;Schakelet al., 2017),andchangelaneinadvancetoanticipatepossibleinteractionswithslowervehicles(Alkimetal.,2007).Theseresults, however,mightbeinfluencedbytheconditionsinwhichtheACCsystemisactivated,suchaslight-mediumtraffic, medium-highspeeds,andnon-criticaltrafficsituations.

Incertain traffic conditions,drivers might prefer to disengage the systemand resumemanual control, orthe system disengagesbecauseofitsoperationallimitations.Thesecontroltransitions(Luetal.,2016)betweenautomatedandmanual drivingmayinfluencetrafficflowefficiency(Varottoetal.,2015)andsafety(Vlakveldetal.,2015).Luetal.(2016)classified controltransitions basedon who (automationor driver)initiatesthe transitionandwho isin control afterwards: ‘Driver Initiatestransition,andDriverControlsafter’(DIDC),‘DriverInitiatestransition,andAutomationControlsafter’(DIAC),and ‘AutomationInitiatestransition,andDriverControlsafter’(AIDC).Thesituationsinwhichthesetransitionshappenare influ-encedbythecharacteristicsofthedrivingassistancesystem,thedriversthemselves,theroad,andthetrafficflow(Varotto etal., 2014). FieldOperationalTests (FOTs)havesuggestedthat driversinitiateDIDC transitionswithACCsystemsthat do not operateat speedslower than 30km/h to avoidpotentially safety-critical situations (Xiong andBoyle, 2012), to keep a stablespeed in medium–densetraffic conditions (Vitiet al., 2008), to adaptthe speed before changing lane, tocreate orreduce agapwhen othervehicles mergeinto thelane,andto avoidpassing illegallya slowervehicleonthe left lane (PauwelussenandFeenstra,2010).Recently,ACCsystemsoperatingalsoatlowspeedsinstop-and-gotrafficconditions( full-rangeACC),thereforeovercomingthefunctionallimitationsofearlierversions,havebeenintroducedintothemarket.These ACCsystems might be activated anddeactivated in differentsituations, andare more likely to be active indense traffic conditions.Acontrolledon-roadexperimentshowedthatdriversusingfull-rangeACCinitiateDIDCtransitionswhenexiting thefreeway,when approachinga moving vehicle,whenchanging lane,andwhena vehiclecutsinor theleader changes lane(Pereiraetal.,2015).

ACC might have a positive impact on traffic flow efficiency when it is active in dense traffic (Van Driel and Van Arem,2010).Toevaluatethisimpact,mathematicalmodelsofautomatedandmanuallydrivenvehiclescanbeimplemented intomicroscopictrafficsimulationmodels.However,mostcar-followingandlane-changingmodelscurrentlyusedto evalu-atetheimpactofACCdonotdescribecontroltransitions.Afewmicroscopictrafficsimulationmodels(Klunderetal.,2009; Van Aremet al., 1997;Xiaoetal., 2017) haveproposed deterministic decisionrules fortransferring control, disregarding inconsistenciesinthedecision-makingprocess, heterogeneitybetweenandwithin drivers,anddependenciesbetween dif-ferentlevelsofdecisionmaking(forareview,werefer toVarottoetal.,2017). Thus,thetrafficflow predictionsbasedon thesemodelscouldbeunreliable.

Toimprove the realism of currenttraffic flow models, insights from driver psychologyand human factors should be incorporated(Hamdar etal., 2015;SaifuzzamanandZheng,2014).Todate,fewstudieshaveproposed aconceptualmodel framework explaining control transitions based on theories of driver behaviour and have estimated the probability that driverstransfercontrolbasedonempiricaldata.Usingamixedlogitmodel,XiongandBoyle(2012)predictedthelikelihood thatdriverswouldbrakeresumingmanualcontrolwhiletheywereclosinginonaleader.Recently,weidentifiedthemain factorsinfluencing drivers’ choiceto initiate a DIDCtransitions withfull-range ACCin a widerrange ofsituations which didnot involvelane changes(Varottoetal.,2017).Drivershavehigherprobabilitiestodeactivate theACCwhenclosingin onaslowerleader,whensupposingvehiclescuttingin,andbeforeexitingthefreeway.Drivershavehigherprobabilitiesto overruletheACCsystemby pressingthegaspedalwhenthevehicledeceleratesandafewsecondsaftertheactivationof thesystem.Interestingly,somedrivershavehigherprobabilitiestoresumemanualcontrolthanothers.However,thisstudy didnotcaptureexplicitlytheunobservableconstructsthatinformdriverdecisionsandignoredthe possibilityofadapting theACCsystemsettings(speedandtimeheadway)toregulatethelongitudinalcontroltask.

Thisstudydevelops such amathematical framework to modeldriver decisionsto resumemanual controland to reg-ulatethe target speed in full-range ACC.The model is basedon the Risk Allostasis Theory(RAT) (Fuller,2011), captures explicitlyinterdependencies betweenthe two decisions, andcan be fully estimatedbased on driver behaviour data.The paperis organisedasfollows.Section 2reviewsdriver control theoriesanddriver behaviour models that are suitable to explaindriverinteraction withACC.Thissection concludeswiththeidentified researchgaps.Section 3proposesthe

con-∗ _{Corresponding author.}

E-mail addresses: s.f.varotto@tudelft.nl (S.F. Varotto), h.farah@tudelft.nl (H. Farah), toledo@technion.ac.il (T. Toledo), b.vanarem@tudelft.nl (B. van Arem),

ceptualmodelframeworkfordriverdecisionstoresumemanualcontrolandtoregulatethetargetspeedinfull-rangeACC. Section 4describesthe mathematicalformulationofthemodellingframeworkandSection5themaximumlikelihood es-timation method.Section 6presentsthecasestudy, includingadescription oftheon-roadexperiment, thedata analysis, theestimationresults,andvalidationanalysesofthemodel.Section7summarizesthemaincontributionsoftheproposed modellingframeworkanddirectionsforfutureresearch.

2. Literaturereview

The literature review focuseson studies proposing conceptual and mathematical models of driverbehaviour that are suitabletoexplaincontroltransitionsandtargetspeedregulationinACC.Section2.1introducesdrivercontroltheoriesand Section2.2conceptualmodelsexplainingadaptationsindriverbehaviour.Section2.3discussesamodelframeworkthathas thepotential tocaptureinterdependenciesbetweendifferentdriverbehaviours.Section2.4summarizestheresearch gaps andformulatestheresearchobjectives.

2.1. Drivercontroltheories

Thedrivingtaskcanbedividedintothreelevels:strategical(planning),tactical(manoeuvring),andoperational(control) (Michon, 1985). The strategicallevel represents theplanning phase ofthe trip, forinstance interms of mode androute choice. Thetactical levelincludes decisions onmanoeuvressuch asovertakingand gapacceptance.The operationallevel definesthedirectlongitudinalandlateralcontrolofthevehicle.Thislevelhasbeenstudiedindrivercontroltheories(for areview,werefer toRanney,1994;Rothengatter,2002;Fuller,2011). Severaltheorieshavebeendevelopedtoexplainthe underlyingmotivationalandcognitiveaspectsofdrivercontrol,suchastheRiskHomeostasisTheory(Wilde,1982),the Zero-risk Theory(NäätänenandSummala,1974;Summala,1988), theTask-Capability-Interface(TCI)model(Fuller,2000,2005), theMonitorModel(Vaa, 2007), andtheSafetyMarginModel(Summala,2007).Thesemodels differintermsofthe refer-encecriteriainthecontrolsystem(e.g.,riskofcollision,taskdifficulty,emotions,drivingcomfort).However,thesedifferent referencecriteriamayreflecta hiddenconsensus(Fuller,2011):themostimportantmotives influencingdrivers’decisions maybeclassifiedundertaskdemandelements,whilemotivessuchasdrivingcomfortcanbeconsideredsecondarytothose relatingtosafety.

Fuller(2011)proposedtheRiskAllostasisTheory(RAT),whichassimilatedthemostrecentcompetingtheories(Summala, 2007;Vaa,2007)intotheTCImodel(Fuller,2000,2005).TheRATarguesthatdrivercontrolactionsareprimarilyinformed bythedesiretomaintainthefeelingofriskandtaskdifficultywithinanacceptablerange,whichvariesovertime.Drivers perceive riskfeelingsinthe samewayasthey experience taskdifficulty (Fulleretal., 2008).The maximumvalue oftask difficultyacceptableisassociatedwithfearoflosingcontrolandtheminimumvalue oftaskdifficulty acceptableis associ-atedwithfrustrationdeterminedbylow drivingperformances(Fuller,2011).Theperceived taskdifficulty isrelatedtothe differencebetweenperceivedtaskdemandandperceiveddrivercapability(Fuller,2000,2005).

Theperceivedtaskdemandisinfluencedbythepresenceandbehaviour(bothactualandanticipated)ofotherroadusers, bytheroadenvironment(e.g.,roadsurfaceandvisibility),andbythecharacteristicsofthevehicle(e.g.,interfaceandvehicle performance)(Fuller,2002;FullerandSantos,2002).Theperceiveddrivercapabilityisdeterminedbydrivercharacteristics such asdriving experience andageand by humanfactors such asdistraction, emotions,stress and fatigue(Fuller,2002; FullerandSantos,2002).Theperceiveddrivercapabilityisultimatelyexpressedindriverbehaviourcharacteristicssuch as thechosen speedanddistanceheadway (Fuller,2011).Whentheperceivedcapabilityisstable, variationsintheperceived taskdemanddirectlyinfluencethefeelingofriskandtaskdifficulty.Empiricalfindingshaveshownthatthefeelingofrisk andtaskdifficulty increasewhen thespeedincreases(Fuller etal., 2008; Lewis-EvansandRothengatter,2009)andwhen the timeheadway decreases (Lewis-Evansetal., 2010). At speedshigherthan themostcomfortablespeed forthedriver, theperceivedfeeling ofriskandtaskdifficultyare correlatedtoestimatesofstatisticalrisk(Fulleretal.,2008).The latter can be expressed by measurable variables such as time to collision or time to line crossing. At lower speeds, however, the perceived feeling of risk is not correlated to estimates of statistical risk (Fuller et al., 2008). This is one of the key differencesfrom previous driver control theoriesbased on estimatesof statisticalrisk (Wilde,1982). It is still subject of debate in thefield ofdriver psychologywhether drivers can perceivechanges in risk feelings inlow risk situations and are informed by thesechanges in their behaviours(Fuller,2011; Lewis-Evans etal., 2010; Lewis-Evansand Rothengatter, 2009).

The acceptable level ofrisk feeling andtask difficulty can be influenced by driver characteristics (gender,experience, age and personality) and factors that vary over time for each individual driver(e.g., journey goals and emotionalstate) (Fuller,2011). Thisvariation of therisk thresholds over time is one ofthe key features that distinguish theRisk Allosta-sis Theoryfromprevious theoriesbased onrisk homeostasis.Driversdecrease their speed whenthe risk feeling andtask difficulty arehigherthanthemaximumvalue acceptableandincreasethespeed whentheyare lowerthantheminimum valueacceptable.However,theymightbeconstrainedintheirdecisionsbyperformancelimitationsofthevehicle,congested traffic,andcompliancetospeedlimits. Thesefindings fromdriverpsychologyshouldbeincludedintoaconceptualmodel frameworktoexplaindriverbehaviourwithdrivingassistancesystemssuchastheACC.

2.2.Conceptualmodelsforadaptationsindriverbehaviour

Indriverpsychology,adaptationsaredefinedasthebehaviouralaspectsthatcanbeobservedafterachangeinroadtraffic (MartensandJenssen,2012).Fewstudieshaveproposedconceptualmodelsforadaptationsindriverbehaviourbasedonthe controltheoriesdescribedintheprevioussection.TheusageofACC,whichmaintainsatargetspeedandtimeheadway,has adirectimpactonthelongitudinalcontroltaskofdrivers.XiongandBoyle(2012)proposedaconceptualmodelofdrivers’ adaptation toACC which includes initiating factors (actual risk) andmediating factors (perceivedrisk). In thismodel, the actualriskisdeterminedbythedistanceheadway,environmentalconditions(weather,roadtype,lightingconditions,traffic density)andtheresponseofthesystem,whiletheperceivedriskisinfluencedbytheACCsystemsettings(speedandtime headway),the driver characteristics,experience with andattitudes towards the system. This model is applied topredict driverdecisionmaking(i.e.,manuallybrakeornot)whenapproachingaslowerleader.

Similarly, driver control theories have been used to explain adaptation effects in longitudinal driving behaviour. Hoogendoorn et al. (2013) and Saifuzzaman et al. (2015) incorporated the Task-Capability-Interface (TCI) model proposed by Fuller (2005) into car-following models to capture compensation effects due to driver distraction. Hoogendoornetal.(2013)assumedthatthemaximumacceleration,themaximumdeceleration,thefreespeedandthe de-siredtimeheadwayaredependentonthetaskdifficulty,expressedasdifferencebetweentaskdemandanddrivercapability. However,thetaskdifficultywasnotexplicitlylinkedtomeasurabledriverbehaviourcharacteristicsanddriver characteris-tics.Saifuzzamanetal.(2015)definedthetaskdifficultyastheratiooftaskdemandanddrivercapability.Thetaskdemand increaseswhenthespeedofthesubjectvehicleincreasesandwhenthedistanceheadwaydecreases.Thedrivercapability isinverselyproportionaltothedesiredtimeheadway(unobservable)andthesensitivitytowardsthetaskdifficultylevelis capturedbyaspecificparameter.Humanfactorsarecapturedbyacomponentofthereactiontimeandaparameter repre-sentingtheperceivedrisk.Thetaskdifficultyfunctionwasusedtomodifythedesiredaccelerationinexistingcar-following models.These advanced car-followingmodels were applied to predict driverbehaviour in regular driving conditionsand underdistractionduetophoneusage.

Thesestudiesshowthat drivercontroltheoriescanbeincorporatedintoexistingmodelsofdriverbehaviourtocapture adaptations.Thefeelingofriskandtaskdifficultycanbeexpressedasafunctionofdriverbehaviourcharacteristicssuchas speedanddistanceheadway.AconceptualmodelframeworksimilartothatoneproposedbyXiongandBoyle(2012)canbe developedtoexplaindifferentdriverbehaviourswithACC(controltransitionsandtargetspeedregulations)inawiderange oftrafficsituations.

2.3.Integrateddriverbehaviourmodels

Few driver behaviour models (e.g.,car-following and lane changing models)have captured the interdependencies be-tween differentdriving behavioursandexplained thesebehavioursbased onunderlying constructs thatmotivate drivers’ decisions.Forthesepurposes,previousstudieshaveproposedmodellingframeworksbasedondiscretechoicemodels,which areflexiblefromabehaviouralperspective,providestatisticaltechniquestocapturecomplexerrorstructuresandfacilitate arigorousestimationofthemodelparameters(Choudhury,2007;Danafetal.,2015;FarahandToledo,2010;Koutsopoulos andFarah,2012; Toledo, 2003). Inaddition, thesemodels are suitable forimplementationinto a microscopic traffic flow simulation because each individual is modelled independently. Toledo (2003) developed an integrated driving behaviour modelpredictingbothacceleration(regressionmodels)andlane changes(discretechoicemodels)basedondrivers’ unob-servableshort-termgoalsandplans.Thismodelstructureaccommodateschangesinbothdiscreteandcontinuousvariables, capturinginterdependenciesacrossdrivingdecisionsintermsofcausality,unobserveddriverandvehiclecharacteristics,and statedependency(Toledoetal.,2007;Toledoetal.,2009).Theparametersofallmodelcomponentswereestimated simul-taneouslyusingmaximumlikelihoodmethods(Toledoetal.,2009).Weconcludethatanintegrateddriverbehaviourmodel canbe developedtomodelmathematicallydriverdecisionsto transfercontrolandregulatethe targetspeed infull-range ACCcapturingunobservableconstructssuchasfeelingofriskandtaskdifficulty.

2.4.Researchgapsandobjectives

Fewstudies haveproposed conceptualmodelframeworksbased oninsightsfromdriverpsychology toexplain drivers’ choicestoresumemanualcontrolinACC.ThemodelframeworkproposedbyXiongandBoyle(2012)islimitedtosituations inwhich thesubject vehicleapproachesa slower leader.Acomprehensive conceptualframework for driverbehaviour at anoperationallevelwithACCandaflexible mathematicalformulationforthismodellingframeworkarecurrentlymissing. Previous studies ignored the possibility of adapting the ACC system settings (time headway andspeed) to regulate the longitudinalcontroltask.DriverscandecreasetheiractualspeedbybrakingorbydecreasingtheACCtargetspeedandcan increasetheiractualspeedbypressingthegaspedalorbyincreasingthetargetspeed.Tomodeldecisionsthatarenaturally linkedsuchascontroltransitionsandtarget speedregulationsandtoexplainthesedecisionsbasedoncurrenttheoriesof driverbehaviour,weneedaflexiblemodellingframeworkcapturingunobservableconstructsandinterdependenciesbetween discreteandcontinuousvariables.Themainobjectivesofthecurrentstudyareasfollows:

(1) todevelopa conceptualmodelframeworkthat explainsdriverdecisionstoresumemanual controlandtoregulatethe targetspeedgroundedontheRiskAllostasisTheory(Fuller,2011);

(2) todevelop amathematicalformulationforthismodellingframeworkbasedontheintegrateddriverbehaviour models (Toledo, 2003),whichdescribesunderlyingconstructs,capturesinterdependenciesbetweendifferentdecisions,andcan befullyestimatedusingdriverbehaviourdata.

3. Modellingframeworkfordriverdecisionstoresumemanualcontrolandtoregulatethetargetspeedinfull-range ACC

Theconceptual modellingframework assumesthatfeeling ofriskandtaskdifficulty (Fuller,2011) arethemainfactors thatinformdrivers’decisionswithfull-rangeACCatanoperationallevel.Thishypothesisissupportedbyempiricalfindings inVarottoetal.(2017).Driverswillchoosetodecrease(orincrease)theiractual speediftheperceivedlevelofriskfeeling andtaskdifficulty (RFTD)ishigher(orlower)than themaximum(or minimum) valuewhich isconsideredacceptable to maintaintheACCactive andthecurrentACCtarget speed.The actualspeed canbe regulatedby adaptingthe ACCtarget speedorbyresumingmanualcontrol.

Fig.1presentsthemodelframework.We proposetwolevels ofdecisionmaking describingbothtransitions tomanual control (discretechoice)andtarget speed regulations(continuouschoice)withACC:risk feelingandtaskdifficulty evalu-ation,andACCsystemstate andACCtarget speedregulationchoice.The decision-makingprocess islatent(unobservable). Driver actionstoresumemanual controlandtoregulatethetargetspeed areobserved,whiletheperceived levelofRFTD islatent.Atthehighestlevel,thedriverevaluateswhethertheperceivedlevelofRFTDfallswithintherangewhichis con-sideredacceptable tomaintainthe ACCactive andthecurrentACCtarget speed.The perceived RFTDisinfluenced bythe driver behaviourcharacteristics ofthe subjectvehicle andofthe leader.The acceptablerange withtheACC active varies betweendriversandwithin driversovertime,beinginfluencedbydrivercharacteristics,bythefunctioningofthesystem, andbytheenvironment.IftheperceivedRFTDlevelishigherthanthemaximumvalueacceptable,thedriverwillchoose todeactivatethesystemortodecreasetheACCtarget speedmaintainingthesystemactive.Iftheperceived RFTDlevelis lowerthantheminimumvalueacceptable,thedriverwillchoosetooverruletheACCbypressingthegaspedal,toincrease theACC targetspeed maintainingthesystemactive, ornotto intervene.The latterisintroduced tocapturedrivers’ diffi-cultiestoperceivechangesinfeelingofriskandtaskdifficultyinlowrisksituations,whichmightbeinfluencedbyhuman factors(unobservable)suchaserrors,shiftsinattentionanddistraction(FullerandSantos,2002).Thesedecisionsare influ-encedbythedriverbehaviourcharacteristics,bythefunctioningofthesystem,byenvironmentalconditions,andbydriver characteristics.

The modelframeworkallows capturingdirectlydrivers’propensity tomaintaintheACC systemactive and interdepen-denciesamongdecisions to transfercontrol andtoregulate the targetspeed through appropriate modelspecificationsat thedifferentlevelsofdecisionmaking.ThisisfurtherexplainedinSection4,whichpresentsthemathematicalformulation ofthemodelbasedonthisconceptualstructure.

4. Mathematicalformulationofthemodelfordriverdecisionstoresumemanualcontrolandtoregulatethetarget speedinfull-rangeACC

Toimplementtheconceptual modelpresentedinSection3,we needaflexible mathematicalframework whichisable tocaptureunobservableconstructsandinterdependenciesbetweendifferentdecisionsmadebythesamedriver.Modelling frameworksbased on choice models satisfy theserequirements. In thisstudy,choice models are preferred to alternative methods (e.g., artificial intelligence) because the model structure can be selected based on insights from driver control theoriesandtheestimationresultsaredirectlyinterpretable.

In this mathematical framework, the magnitude of the ACC target speed regulation is chosen simultaneously to the systemstateandcorrelationsbetweenthesetwochoicesarecapturedexplicitly.Inaddition,interdependenciesacross deci-sionsareaddressedintermsofcausality,unobserveddrivercharacteristics,andstatedependency(Toledo,2003).Causality isaddressedbymodellingthedecisionstakenatthelowerlevels asconditional onthedecisionstakenatthehigher lev-els.Thistwo-levelmodelstructureallowscapturingexplicitlydrivers’propensitytonotintervene whentheACCsystemis active.Unobserved drivercharacteristics are modelledby introducing driver-specific errorterms ineach level ofdecision making.Statedependency(i.e.,interdependenciesbetweenchoicesituationsovertime)isaddressedbyincludingthedriver behaviourcharacteristicsofthesubjectvehicleandofitsdirectleaderasexplanatoryvariablesinthedifferentlevels. The modelformulationispresentedinSections4.1–4.3.

4.1. Level1:riskfeelingandtaskdifficultyevaluation(discretechoice)

Theriskfeeling andtaskdifficultyevaluation(RFTDE)modelisformulated asa generalizedordered probitmodelwith randomthresholds(Castroetal.,2013;Eluruetal.,2008;GreeneandHensher,2009,2010).Thismodelformulation repre-sentstheordinalanddiscretenatureoftheriskfeelingandtaskdifficultyevaluation(risklowerthanacceptable,acceptable risk,andriskhigherthan acceptable),capturingbothobservedandunobserved heterogeneityintheminimumandinthe maximumrisk acceptable. This ordinal response structure is based on the assumption that an unobservable risk feeling andtaskdifficulty (RFTD)determines the observable decisions ofdrivers. The RFTDis modelledasa latent variablethat followsa normaldistribution.Driver nchooses attime twhethertheperceived RFTDislower thantheminimumrisk ac-ceptable(L),fallswithintheacceptableriskrange(Ac)orishigherthanthemaximumriskacceptable(H)aspresentedin Eq.(1): RFTDEn

(

t

)

=

⎧

⎪

⎨

⎪

⎩

L, RFTDn

(

t

)

<MinAcn

(

t

)

Ac, MinAcn

(

t

)

<RFTDn

(

t

)

<MaxAcn

(

t

)

H, RFTDn

(

t

)

>MaxAcn

(

t

)

(1)

where RFTDE is the choice indicator, and MinAcn(t) and MaxAcn(t) are the variables that represent the minimum and

the maximum acceptable risk for each driver at time t. The non-linear formulation of the minimum and of the maxi-mumrisk acceptableallows todistinguish mathematicallythethresholdsfromthelatent regression,guarantees thatboth thresholds are positive, andpreserves the ordering ofthe thresholds (− ∞ < MinAcn(t) < MaxAcn(t) < ∞) (Greene and

Hensher, 2009, 2010). The lowest and the highest acceptable risk are functions of explanatory variables as shown in Eqs.(2)–(3): MinAcn

(

t

)

=exp



μ

L₊

_τ

L_{· X}L n

(

t

)

+

γ

L·

ϑ

n



(2)

MaxAcn

(

t

)

=MinAcn

(

t

)

+exp



μ

H₊

_τ

H_{· X}H

n (t

)

+

γ

H·

ϑ

n



(3) where

μ

L _and

_μ

H _{are theconstants,}

_τ

L_and

τ

H_{are vectorsof parametersassociated withtheexplanatory variablesX}L

n

(

t

)

andXH

n

(

t

)

,

γ

Land

γ

Haretheparametersassociatedwiththeindividual-specificerrortermϑn∼ N(0,1).Thethresholdsvary

withinindividualsovertime duetoobservedvariablesandbetweenindividualsduetoobservedvariablesandunobserved heterogeneity.Relevant explanatoryvariables that canbe included intothe thresholdequationsare driver characteristics, variablesrelatedtothefunctioningoftheACCsystem,andcharacteristicsofthefreewaysegment.Thedriver-specificerror termϑncapturesunobservedpreferencesthatinfluenceallchoicestakenbytheindividualovertime.Thiserrortermvaries

betweendrivers butitisconstantbetweenchoicesituations forthesamedriver.Themeanrisk feelingandtaskdifficulty perceivedbydriversisafunctionofexplanatoryvariablesasdescribedinEq.(4):

RFTDn

(

t

)

=

ω

+

λ

· Xn

(

t

)

+

σ

·

δ

n

(

t

)

(4)

where

ω

istheconstant,

λ

isavectorofparametersassociatedwiththeexplanatoryvariablesXn

(

t

)

,and

σ

istheparameter associatedwiththeobservation-specificerrorterm

δ

n(t)∼ N(0, 1).Relevantexplanatoryvariables arethedriverbehaviour

characteristicsofthesubjectvehicleandoftheleader,such asspeed, relativespeed,anddistanceheadway(Fuller,2011). The observation-specific errorterm capturesunexplained variabilitybetween choice situations. The risk feeling andtask difficultyevaluationconditionalonthevalueofϑniscalculatedasfollowsinEqs.(5)–(7):

P

(

RFTDEn

(

t

)

=L

|

ϑ

n

)

=





MinAcn

(

t

)

−

ω

−

λ

· Xn

(

t

)

σ

(5) P

(

RFTDEn

(

t

)

=Ac

|

ϑ

n

)

=





MaxAcn

(

t

)

−

ω

−

λ

· Xn

(

t

)

σ

−





MinAcn

(

t

)

−

ω

−

λ

· Xn

(

t

)

σ

(6) P

(

RFTDEn

(

t

)

=H

|

ϑ

n

)

=1−





MaxAcn

(

t

)

−

ω

−

λ

· Xn

(

t

)

σ

(7) where



(· )isthecumulativedistributionfunctionofthestandardizednormaldistribution.Theparameters

μ

H_,

_τ

_,

_γ

_,

_ω

_,

λ

areestimatedwhile

σ

isfixedto oneand

μ

L _{isfixedtozeroforidentificationpurposes.Inthisframework,the}

driver-specificerrortermsareestimatedinboththresholdequationstocapturetheimpactofunobserved heterogeneityonboth theminimumandmaximumriskacceptable.

4.2. Level2:choiceofACCsystemstate(discretechoice)

Driverswho considertheRFTDlower thantheminimumvalue acceptable choosetooverrule theACCby pressingthe gaspedal(AAc),tomaintainthesystemactive andincreasethetargetspeed (AS₊),ornottointervene (AL).Thisdecision isformulatedasalogitmodel,inwhichtheutilityfunctionsUfordrivernattimetaregivenbyEqs.(8)–(10):

UAAc

n

(

t

)

=

α

AAc+

β

AAc· XnAAc

(

t

)

+

γ

AAc·

ϑ

n +

ε

AAcn

(

t

)

(8)

UAS+

n

(

t

)

=

β

AS+· XnAS+

(

t

)

+

ε

ASn+

(

t

)

(9)

UAL

n

(

t

)

=

α

AL+

γ

AL·

ϑ

n +

ε

ALn (t

)

(10)

where

α

AAc _and

_α

AL _{are alternative specific constants,}

_β

AAc_and

β

AS+ _{are vectors of parameters associated with the}

ex-planatoryvariablesXAAc

n

(

t

)

andXnAS+

(

t

)

,

γ

AAcand

γ

ALaretheparametersassociatedwiththeindividual-specificerrorterm ϑn∼ N(0,1), and

ε

AAcn

(

t

)

,

ε

ASn+

(

t

)

,and

ε

nAL

(

t

)

are i.i.d.Gumbel – distributederror terms.Inthe utility ofnot intervening

in low risk conditions, theconstant and the driver-specific errorterm are estimatedwhile the explanatoryvariables are assumedtohavean impactequalto zeroforidentificationpurposes (Choudhury,2007;Choudhury etal., 2007).Relevant explanatoryvariablescanincludethedriverbehaviour characteristicsofthesubjectvehicle andofitsleader, variables re-latedtothefunctioningofthesystem,characteristicsofthefreewaysegment,anddrivercharacteristics.Theprobabilityof choosingtheACCsystemstatek_∈C_lwithC_l={AAc, AS₊, AL}inlowrisksituationsispresentedinEq.(11):

P

(

Yn

(

t

)

=k

|

RFTDEn

(

t

)

=L,

ϑ

n

)

= exp



α

k₊

_β

k_{· X}k n

(

t

)

+

γ

k·

ϑ

n



lexp



α

l₊

β

l_{· X}l n

(

t

)

+

γ

l·

ϑ

n



(11)

DriverswhoconsidertheRFTDhigherthanthemaximumvalueacceptablechoosetodeactivatetheACC(I)orto main-tainthesystemactiveanddecreasethetargetspeed(AS− ).Thisdecisionisformulatedasalogitmodel,inwhichtheutility functionsUfordrivernattimetaregivenbyEqs.(12)–(13):

UnI

(

t

)

=

α

I+

β

I· XnI

(

t

)

+

γ

I·

ϑ

n +

ε

nI

(

t

)

(12)

UnAS−

(

t

)

= 0+

ε

ASn−

(

t

)

(13)

where

α

I_{isan alternativespecificconstant,}

_β

I_{isthevectorofparametersassociatedwiththeexplanatoryvariablesX}I n

(

t

)

,

γ

I_{istheparameters associatedwiththeindividual-specificerrortermϑ}

n∼ N(0,1),and

ε

nI

(

t

)

,and

ε

nAS−

(

t

)

arei.i.d.

Gum-bel– distributederrorterms.Relevant explanatoryvariablesare similartothose listedabove forlowrisk conditions.The probabilityofchoosingtheACCsystemstatei_∈C_hwithC_h={I, AS_{− }}inhighrisksituationsispresentedinEq.(14):

P

(

Yn

(

t

)

=i

|

RFTDEn

(

t

)

=H,

ϑ

n

)

= exp



α

i₊

_β

i_{· X}i n

(

t

)

+

γ

i·

ϑ

n



hexp



α

h₊

β

h_{· X}h n

(

t

)

+

γ

h·

ϑ

n



(14)

Theparameters

α

,

β

,

γ

areestimatedandcanbeassumedtohaveadifferentvalueineachleveloffeelingofriskand ineachutilityfunction.

4.3. Level2:choiceofACCtargetspeedregulation(continuouschoice)

ACCtarget speed regulationsare observedonly whendrivers choosetoregulate theACC targetspeed. The magnitude oftheregulationdependsonthechoice ofincreasingordecreasingtheACC targetspeed. Inthisframework,decisionsto increaseordecreasetheACCtargetspeedarecapturedexplicitly(i.e.,ifadriverchoosestoincreasetheACCtargetspeed, theincreasewillbealwayspositive).Torepresentthisprocess,theerrortermisassumedtobeapositiverandomvariable.

Inthiscasestudy,theabsolutevaluesoftheobservedACCtargetspeedincrease(ACCTarSpeed₊)anddecrease(ACCTarSpeed-) arelog-transformed.TheregressionequationsoftheACCtargetspeedincrease(YTS+

n )anddecrease(YnTS−

)

conditionalupon

choosingtoincreaseordecreasetheACCtargetspeedaregiveninEqs.(15)–(16):

YTS+ n

(

t

)

=

η

TS++

ξ

TS+· XnTS+

(

t

)

+  j=AS+

ϕ

TS+ j · C TS+ j +

γ

TS+_·

_ϑ

_{n +}

_ω

TS+_·

_υ

TS+ n

(

t

)

(15) YnTS−

(

t

)

=

η

TS−+

ξ

TS−· XnTS−

(

t

)

+

ϕ

ITS−· C TS− I +

γ

TS−_·

_ϑ

n+

ω

TS−·

υ

nTS−

(

t

)

(16)

where

η

TS+(− ) _{is theconstant,}

_ξ

TS+(−) _{is the vector ofparameters associated withthe explanatoryvariables X}TS+(−) n

(

t

)

,

ϕ

TS+

j withj ∈{AAc, AL} and

ϕ

ITS− are the parameters associated withthe selectivitycorrection termsCjTS+andCTIS−

re-spectively,

γ

TS+(− )_{istheparameterassociatedwiththeindividual-specificerrortermϑn∼ N(0,1),}

_ω

TS+(− )_isthe

parame-terassociatedwiththeobservation-specificerrorterm

υ

_nTS+(−)

(

t

)

∼ N(0,1

)

.Relevantexplanatoryvariablescanincludethe driverbehaviourcharacteristics ofthesubjectvehicleandofitsleader, variablesrelatedtothefunctioningofthesystem, characteristicsofthefreewaysegment,anddrivercharacteristics.TheselectivitycorrectiontermsC_jTS+andC_ITS−aregivenin Eqs.(17)–(18): CT_jS+=



Pj_{· ln}



_Pj



1− Pj + ln



PAS+



(17) CTS− I =



PI_{· ln}



_PI



1− PI + ln



PAS−



(18)

wherePAAc_{, P}AL _andPAS+ _{are the choice probabilities to overrule theACC system, not to intervene, and to increase the}

targetspeedinthelowrisk logitmodel(Eq.(11)), andPI_andPAS− _{arethechoiceprobabilitiestodeactivate anddecrease}

thetargetspeedinthehighrisklogitmodel(Eq.(14)).Theinclusionoftheselectivitycorrectiontermsintotheregression equationscorrectsforthesystemstate selectivitybiasundertheassumptionthatthechoiceprobabilitiesarelogitandthe errortermsarenormallydistributed(DubinandMcFadden, 1984;Train,1986).Thesecorrectiontermscaptureunobserved factorsthatinfluenceboththeprobabilityofthesystemstatechoiceandthemagnitudeofthetargetspeedregulation.The probabilitydensityfunctionsofthetarget speedincrease anddecreaseconditional onthechoicestodecreaseorincrease theACCtargetspeedaregivenbyEqs.(19)–(20):

P



YTS+ n

(

t

)

=log



ACCTarSpeed+n

(

t

)

|

Yn

(

t

)

=AS+,RFTDEn

(

t

)

=L,

ϑ

n



=

_ω

1_TS+





log

(

|

ACCTarSpeed+n

(

t

)

|

)

−

η

TS+−

ξ

TS+· X

(

t

)

− j=AS+

ϕ

TjS+· C TS+ j −

γ

TS+·

ϑ

n

ω

TS+



(19) P



YTS− n

(

t

)

=log



ACCTarSpeed−n

(

t

)

|

Yn

(

t

)

=AS−, RFTDEn

(

t

)

=H,

ϑ

n



= 1

ω

TS−





log

(

|

ACCTarSpeed−_n

(

t

)

|

)

−

η

TS−₋

_ξ

TS−_{· X}

₍

_t

₎

₋

_ϕ

TS− I · C TS− I −

γ

TS−·

ϑ

n

ω

TS−

₍₂₀₎

Theparameters

η

,

ξ

,

φ

,

γ

,

ω

areestimatedandcanassumeadifferentvalueineachregressionequation.

5. Maximumlikelihoodestimationoftheintegratedcontinuous-discretechoicemodel

The parameters of the choice models and of the regression models are estimated simultaneously withfull informa-tionmaximumlikelihoodmethods. GivenYn(t) theindicator associatedwiththesystemstate choice,YnTS

(

t

)

theindicator

associatedwith theobserved valuesof theACC target speed regulations,andRFTDEn(t)the indicator associated withthe

unobservableriskfeelingandtaskdifficultyevaluation,theunconditionalprobabilityofdeactivating(oroverruling)the sys-tem(Eq.(21)),of increasing(or decreasing) theACC target speed(Eq.(22)),andof notintervening(Eq.(23)) ina single observationaregivenasfollows:

P

(

Yn

(

t

)

|

ϑ

n

)

=P

(

Yn

(

t

)

|

RFTDEn

(

t

)

,

ϑ

n

)

· P

(

RFTDEn

(

t

)

|

ϑ

n

)

(21) P



Yn

(

t

)

,YnTS

(

t

)

|

ϑ

n



=P



YTS n

(

t

)

|

Yn

(

t

)

, RFTDEn

(

t

)

,

ϑ

n



· P

(

Yn

(

t

)

|

RFTDEn

(

t

)

,

ϑ

n

)

· P

(

RFTDEn

(

t

)

|

ϑ

n

)

(22) P

(

Yn

(

t

)

|

ϑ

n

)

=P

(

RFTDEn

(

t

)

=Ac

|

ϑ

n

)

+P

(

Yn

(

t

)

=AL

|

RFTDEn

(

t

)

=L,

ϑ

n

)

· P

(

RFTDEn

(

t

)

=L

|

ϑ

n

)

(23)

whereP

(

YTS

n

(

t

)

|

·)ispresentedinEqs.(19)–(20),P(Yn(t)|· )inEqs.(11)and(14),andP(RFTDEn(t)| · )inEqs.(5)–(7).Notably,

the unconditionalprobability of not interveningisthe sumof the probabilitiesof perceiving thefeeling of risk asto be acceptable andof not interveningwhen thefeeling ofrisk is lower than theminimum risk acceptable. Thisformulation allows decisionsofnot interveningtoarise fromtwo differentlevelsof perceivedrisk (acceptableandlow)andcaptures explicitlydrivers’propensitytonotintervenewhenthesystemisactive(Greeneetal.,2013).ThejointprobabilityoftheT observationsovertimeforthesamedriverisgivenbyEq.(24):

P



Yn

(

1

)

, YnTS

(

1

)

,..., Yn

(

T

)

,YnTS

(

T

)

|

ϑ

n



= T  t=1 P



Yn

(

t

)

, YnTS

(

t

)

|

ϑ

n



(24) Theunconditionaljointprobabilityoftheobservationsforeachdriverisobtainedbyintegratingoverthedistributionof ϑn,whichisassumedtobestandardnormal,aspresentedinEq.(25):

P



Yn

(

1

)

, YnTS

(

1

)

,..., Yn

(

T

)

,YnTS

(

T

)



=+∫∞ −∞P



Yn

(

1

)

, YnTS

(

1

)

,..., Yn

(

T

)

,YnTS

(

T

)

|

ϑ



(

ϑ

)

d

ϑ

(25)

TheintegraliscalculatedusingMonte-Carlointegration.Therandomdrawsaregeneratedusingthe‘ModifiedLatin Hy-percubeSampling’method(Hessetal.,2006).Thelog-likelihoodfunctionforalldrivers1,…,NisgivenbyEq.(26):

LL= N  n=1 ln



P



Yn

(

1

)

, YnTS

(

1

)

,..., Yn

(

T

)

,YnTS

(

T

)



(26) 6. Casestudy

The model can be estimated using driving behaviour data with ACC and information on individual drivers. Section 6.1briefly describestheon-roadexperiment, thecharacteristicsoftheACCsystem,andtheparticipants(fora de-taileddescription,seeVarottoetal., 2017).Section6.2presentstheanalysisofthedatatoexploretheconditionsinwhich drivers resumedmanual controlandregulatedthe targetspeed. Section6.3discusses theestimationresultsofthemodel andtheimpactoftheexplanatoryvariablesonthechoiceprobabilities.Section6.4proposesin-sample-out-of-timeand out-of-sample-in-timevalidationanalysesofthemodelestimated.

6.1. Datacollection

The on-road experimentconsisted of a singledrive (46-km long) on a pre-set test route on the A99 inMunich. The test route comprised fourfreewaysegments mostlycomposed ofthree lanesper direction. In thefirst freewaysegment, participantstestedthesystemandfoundtheirpreferredgapsetting.Duringtheexperimentontheremainingthreefreeway segments(35.5km),participantswereinstructedtodriveastheynormallywould,regulatingthetargetspeed settingsand resumingmanualcontrolatanytime.

The research vehicleused wasa BMW5Seriesequipped witharegular version offull-range ACC,which maintainsa target speed atspeedsbetween0and210km/handa target time headwayat speedshigherthan30km/h. Therange of the radar is120m.The target time headways that can be set are 1.0, 1.4, 1.8, and2.2s. The maximumacceleration and deceleration supported by the system are 3m/s2 _{and –3m/s}2_{. When the system is active, it is possible to set a target}

speedandtimeheadway byusingtheswitches.Driverscanresumemanualcontrol temporarilybypressingthegaspedal (transitiontoActiveandaccelerate)andcandeactivatethesystemby pressingtheon/off buttonorthebrake(transitionto Inactive).

Twenty-threeparticipants recruitedamongBMW employeesinMunichcompleted theexperiment. Fifteenparticipants weremale,andeightwerefemale.Participantshadbetween3and33yearsofdrivingexperience.Sixparticipantshadnever usedADAS(AdvancedDrivingAssistanceSystems)beforetheexperiment(no experience),ninehaddrivenwithADAS less oftenthanonceamonthduringthepreviousyear(mediumexperience),andeightonceamonthormoreoften(high expe-rience).NoneofthemhadbeendirectlyworkingonthedevelopmentoftheACCsystem.Beforetheexperiment,participants wereinstructed onthespecificationsofthesystem,signedan informedconsentform,andfilledaquestionnairereporting demographiccharacteristics(Kyriakidisetal.,2014),drivingexperience(Kyriakidisetal.,2014),experiencewithADAS,and drivingstyles (Taubman-Ben-Arietal., 2004).Theexperimentwascarriedout duringthepeak hoursofthemorning(7–9 am)and oftheevening (4–6 pm, 6–8pm)from June 29thtoJuly 9th2015. Participants drove between45and90 min, basedonthe trafficflow conditions.Speed, acceleration,distanceheadway (fromradar), speedoftheleader (fromradar), ACCsystemsettingsandstate,andGPSpositionweremeasuredandregisteredintheControllerAreaNetwork(CAN)ofthe instrumentedvehicle.Aftertheexperiment,participantsfilledaquestionnaireabouttheusageoftheACCsystem,workload experienced (Byersetal.,1989;Kyriakidisetal., 2014),andtheusefulnessandsatisfactionofthesystem(Kyriakidisetal., 2014;VanderLaanetal.,1997).Theempiricalcumulativedistributionfunctionsofthedrivercharacteristicsreportedinthe questionnairearepresentedinAppendixA,Fig.A1.Driversreportedhigherscoresonthepatientandcarefuldrivingstyle thanontheother drivingstyles,whichissimilartopreviousfindings (Taubman-Ben-Arietal.,2004).Driversreportedlow to mediumlevels ofworkloadwhile drivingwithACCandmedium to highlevels ofusefulnessandsatisfactionwiththe system.

Table 1

Mean and standard deviation of the driver behaviour characteristics when drivers transfer the ACC to Inactive (I), decrease the ACC target speed (AS-), maintain the ACC Active (A), increase the ACC target speed (AS + ), and transfer to Active and accelerate (AAc); a reduced version of this table focusing on transitions to manual control was presented in Varotto et al. (2017) .

Variables Description I AS- A AS + AAc

Time after last activation

Time after the ACC has been activated in s

76.0 (83.2) 102 (117) 153 (156) 115 (130) 50.3 (128)

Speed Speed of the subject vehicle in

km/h

94.8 (40.9) 93.1 (34.5) 72.6 (38.0) 82.1 (28.9) 86.5 (36.9)

Acceleration Acceleration of the subject vehicle in m/s 2 −0.0491 (0.549) −0.0935 (0.480) −0.00294 (0.390) 0.0956 (0.332) −0.272 (0.462) Target time headway—time headway

Difference between the ACC target time headway and the time headway (front bumper to rear bumper) in s

−0.574 (0.758) −0.546 (0.682) −0.361 (0.558) −0.585 (0.710) −0.160 (0.780)

Target speed—speed Difference between the ACC target speed and the subject vehicle speed in km/h

16.2 (22.2) 18.5 (21.0) 25.8 (25.0) 8.97 (12.1) 20.2 (24.9)

Distance headway Distance headway (front bumper to rear bumper) in m

49.8 (27.5) 49.8 (24.2) 36.5 (22.9) 44.7 (22.0) 39.1 (23.1)

Relative speed Speed difference between leader speed and subject vehicle in km/h

−7.84 (11.8) −3.16 (8.51) −0.829 (5.69) 2.62 (6.36) −1.04 (6.33) Relative acceleration Acceleration difference

between the leader and the subject vehicle in m/s 2

−0.287 (0.609) −0.0234 (0.517) 0.0140 (0.375) 0.0618 (0.377) 0.225 (0.479)

6.2.Dataanalysis

Thedatacollectedintheexperiment(23drivesof35.5km)wereanalysedtoinvestigatethesituationsinwhichdrivers resumedmanual control(presentedinVarottoetal.,2017)andregulatedtheACCtargetspeed.Wedidnotanalysecontrol transitionsinitiatedbythesystem, andtransitionsortarget speedregulationsthat occurredbetween10sbefore and10s aftera lane change.We reducedthe datato 1Hz resolution,obtaining 31,165 observations.Quality controlsshowedthat thequality ofthe reduceddata ishighfor ourmodellingpurposes andadditionaldata smoothingis not needed. Inthis paper,we analyse 23,568observations of 1s in which a leader is detected by the radar (120m) and the ACCsystem is active.106 observations(0.45%)were immediatelyfollowedby aDIDC transitionto Activeandaccelerate(overruling),210 (0.89%)byan increase intheACCtarget speed,55(0.23%)by aDIDCtransitionto Inactive(deactivations),125(0.53%) by adecreaseintheACCtargetspeed, and23,072(97.9%)byneithertransitionsnorspeed regulations.Driverstransferred to Activeandacceleratefrom0to26times(M=4.61,SD=5.88),increasedtheACCtargetspeedfrom1to24times(M=9.13, SD=5.34),transferred toInactivefrom0to7times(M=2.39,SD=1.83),anddecreasedtheACCtargetspeedfrom1to11 times(M₌5.43,SD₌2.86).

Togain insightinto theconditionsin whichcontrol transitionsandspeed regulationswere initiated, we analysed the empiricaldistributionfunctionsofthedriverbehaviour characteristicswhenneithertransitionsnorspeedregulations hap-pened,whentheACCwasdeactivatedoroverruled,andwhentheACCtargetspeedwasreducedorincreased(AppendixA, Fig.A2).ThemeanandthestandarddeviationofthesevariablesarepresentedinTable1.Thesimilarityofthedistributions betweenthedifferentgroupswastestedusingtwo-sampleKolmogorov-Smirnovtests(AppendixA,TableA1).Most transi-tionstoActiveandacceleratewereinitiatedafewsecondsaftertheactivation.Athighspeeds,deactivationsandtargetspeed reductionsoccurredmoreoftenthanoverrulingactionsandtargetspeedincrements.Whenthevehicledecelerated, transi-tionstoActiveandacceleratehappenedmoreoftenthantargetspeed increments.Deactivationshappenedmoreoftenthan target speedreductionswhen the targetspeed waslower than theactual speed. Overruling actionsoccurred moreoften thantargetspeedincrementswhenthetargetspeedwashigherthantheactualspeed.Onaverage,deactivationsandtarget speedreductionswereassociatedwithlargerdistanceheadways.Deactivationsandtargetspeedreductionshappenedmost oftenwhenthesubjectvehiclewasfasterthanthe leader,whiletarget speed incrementshappenedmostoftenwhen the subjectvehiclewasslower.Mostdeactivationsoccurredwhen thesubjectvehicleacceleratedmorethan theleader.Most targetspeedregulationsrangedbetween−20and+20km/h.Inaddition,cut-inmanoeuvresweredetectedasdescribedin Varottoetal.(2017).Thesefindingssuggestthatthedriverbehaviourcharacteristicsofthesubjectvehicleandoftheleader mayimpactsignificantlydrivers’decisionstoregulatethetargetspeedandtoresumemanualcontrol.

Controltransitionsandtarget speed regulations occurredmoreoftenin freewaysectionswhere vehicles changelanes morefrequently,potentiallydisturbingtraffic flow.Driversdeactivated thesystemmoreofteninproximitytoan on-ramp andbeforeexitingthefreeway(Varottoetal.,2017).DriversoverruledthesystemorincreasedtheACCtargetspeedmore oftenbetweenrampsthat arecloserthan600m(FGSV,2008) andinproximitytoan on-ramp.Driversshowedsignificant differencesinresumingmanualcontrolandregulatingtheACCtargetspeedbasedontheirindividualcharacteristics. Corre-lationanalysiswasconductedtoexploretherelationsbetweenthedrivercharacteristics,thenumberoftransitionsexecuted,

andthemagnitudeofthetargetspeedregulationselectedforeachdriver.DriverswhodeactivatedtheACCmoreoftenalso overruledthesystemmoreoften.DriversinexperiencedwithADASchosesmallertargetspeedincrements.Individual char-acteristicssuchasgenderandagewere correlatedsignificantlywithdrivingstyles,workloadexperiencedduringthedrive, andusefulnessandsatisfactionoftheACC.Furtheranalysisisneededtoinvestigatemoderatecorrelationresults.

6.3. Estimationresults

Inthiscasestudy,we assumedthat onlyonedecisionhappenswithin a1-sinterval.Thisinterval oftimeissimilarto themeanreactiontimebetweentherecognitionofastimulusandtheexecutionoftheresponseinliterature(Toledo,2003). Thedecisionsarerelatedtothedriverbehaviourcharacteristicsrecordedatthebeginningoftheinterval.Multiple1-s ob-servations,repeatedovertime,areavailableforeachdriver(paneldata).Notably,themodelspecificationpresentedinthis sectionistheresultofanintensivemodellingprocessinwhichseveralspecificationsandmodelstructureswerecompared basedon statisticaltests. Weestimatedthe modelusingthesoftwarePythonBiogeme(Bierlaire,2016).All model compo-nentswere estimatedsimultaneously usingfull information maximumlikelihoodmethods asdescribedin Section 5.The log likelihoodandthe goodness offitindicators are presentedin Table2 andtheestimation resultsin Tables 3–5. Most parametersarestatisticallysignificantatthe95%confidencelevel.Sections6.3.1–6.3.3discusstheestimationresultsofeach modelcomponentandSection6.3.4presentstheimpactoftheexplanatoryvariablesontheunconditionalACCsystemstate choiceprobabilitiesandonthemagnitudeofthetargetspeedregulation.

6.3.1. Riskfeelingandtaskdifficultyevaluation

Intheorderedprobitmodel,theriskfeelingandtaskdifficultyRFTDareinfluencedbythedriverbehaviour characteris-ticsofthesubjectvehicleandofitsleaderasshowninEq.(27):

RFTDn

(

t

)

=

ω

+

λ

Speed DHW ·

Speed

(

t

)

DHW

(

t

)

+

λ

RelSpeed · RelSpeed

(

t

)

+

λ

RelAcc · RelAcc

(

t

)

+

λ

AntCutIn3· AntCutIn3

(

t

)

+

δ

n

(

t

)

(27)

where

ω

is the constant,

λ

Speed DHW

,

λ

RelSpeed,

λ

RelAcc,

λ

AntCutIn3 are the parameters associated with the explanatory variables

listed inTable3,and

δ

n(t)∼ N(0,1) isthe observation-specificerrorterm. Speedisdivided by distanceheadwaybecause

drivers are assumed to be more sensitive to changes in risk feelings at shortdistance headwaysand athigh speeds. In addition,speedanddistanceheadwayarehighlycorrelated.Thelowestandthehighestacceptableriskarefunctionsofthe functioningoftheACCsystemanddrivercharacteristicsaspresentedinEqs.(28)–(29):

MinAcn

(

t

)

=exp



τ

L

TimeAct· log

(

TimeAct

(

t

)

)

+

τ

PatCarL · PatCarn +

γ

L·

ϑ

n



(28)

MaxAcn

(

t

)

=MinAcn

(

t

)

+exp



μ

H₊

τ

H

TimeAct· log

(

TimeAct

(

t

)

)

+

τ

PatCarH · PatCarn+

γ

H·

ϑ

n



(29) where

μ

H_{istheconstant,}

_τ

L

TimeAct,

τ

PatCarL ,

τ

THimeAct,and

τ

PatCarH aretheparametersassociatedwiththeexplanatoryvariables

listedinTable3,

γ

L _and

_γ

H _{aretheparametersassociatedwiththeindividual-specificerrortermϑ}

n∼ N(0,1).The

logarith-mictransformationofthetimeafterlastactivationisconsistentwiththeempiricalfindingsandshowedasignificantbetter fitthanalinearspecification.Theroadlocation,theother drivingstyles (recklessandcareless,angryandhostile,and anx-ious),gender,age,experiencewithADAS,workload,andusefulnessandsatisfactionwithACCdidnotinfluencesignificantly theacceptablerange.

TheestimationresultsinTable3showthatdrivers perceivehigherrisk athigherspeedsandatshorterdistance head-ways.Inaddition,they perceivehigherrisks whenthey arefaster(negativerelative speed)andacceleratemore(negative relativeacceleration) thantheleader, andwhentheysuppose thata vehiclewillcutinduringthenext threeseconds.To analysetheimpactofvariationsintheexplanatoryvariablesinthethresholdequations,wecalculatedthelowestand high-estriskacceptablewithACCactiveandthemeanfeelingofriskinobservationsinwhichonlyoneexplanatoryvariablewas alteredwhilemaintainingalltheothervariablesfixed.Weassumedthat,inthebaselineobservation,thedriverhad experi-encewithADASandascoreonthepatientandcarefuldrivingstyleequaltothemeaninthissample.Thespeedwasequal

Table 2

Statistics of the continuous-discrete choice model. Statistics

Number of drivers 23

Number of observations 23,568

Number of constants 8

Number of parameters associated with explanatory variables (K) 28

Constant log likelihood L (c) −3496

Final log likelihood L ( ˆ β) −3078

Adjusted likelihood ratio index (rho-bar-squared) ¯ρ2 = 1 − (L(βˆ)− K) L(c) 0.112

Table 3

Estimation results of the continuous-discrete choice model: risk feeling and task difficulty evaluation.

Variable Description Parameter Estimate Robust t -stat. Robust p -value

Risk feeling and task difficulty

– Constant risk feeling and task difficulty

with ACC active ω

1.76 8.55 < 0.005

Speed/DHW Speed of the subject vehicle in km/h

divided by distance headway (front bumper to rear bumper) in m

λSpeed/DHW 0.0426 1.52 0.13

RelSpeed Relative speed (leader speed – subject

vehicle speed) in km/h λRelSpeed −0.0381 −9.64 < 0.005

RelAcc Relative acceleration (leader

acceleration – subject vehicle acceleration) in m/s 2

λRelAcc −0.249 −3.87 < 0.005

AntCutIn3 Number of cut-ins in the following

three seconds λ

AntCutIn3 0.528 7.12 < 0.005

Lowest and highest acceptable risk

– Constant highest acceptable risk with

ACC active μ

H _{1.05 18.74 < 0.005}

TimeAct Logarithm of time after the activation

of ACC in s τ

L

T imeAct −0.125 −3.98 < 0.005

TimeAct Logarithm of time after the activation

of ACC in s τ

H

T imeAct 0.0646 13.54 < 0.005

PatCar Score on the driving-style factor

‘Patient and careful’ 1 (MDSI

Taubman-Ben-Ari et al., 2004 )

τL

PatCar 0.337 1.32 0.19

PatCar Score on the driving-style factor

‘Patient and careful’ 1 (MDSI

Taubman-Ben-Ari et al., 2004 )

τH

PatCar −0.119 −2.03 0.04

ϑn Individual-specific error term γL 0.383 3.31 < 0.005

ϑn Individual-specific error term γH −0.0705 −5.15 < 0.005

Note: 1 Variable centred on the mean value between drivers.

Fig. 2. Impact of the explanatory variables and of the driver-specific error term on the minimum (light blue dashed line) and on the maximum (purple dashed line) risk acceptable with ACC active, compared to the mean feeling of risk and task difficulty (black dotted line). The variables are listed as follows: (a) time after last activation, (b) patient and careful driving style (centred on the mean value between drivers), and (c) driver-specific error term. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

to87.2km/h,theACCtargetspeed102km/h,theacceleration_−0.0467m/s2_{,thedistanceheadway45.3m,therelativespeed}

−0.781km/h,andtherelativeacceleration0.0365m/s2_{.TheACCsystemhadbeenactivatedfor94sandcut-inmanoeuvres,}

ramps,andexitsdidnotinfluencethedriver.Weselectedthesevaluesbasedontheaverageconditionsofthecontrol tran-sitionsandtarget speedregulations observed.Theresults arepresentedinFig. 2.Fewsecondsafter thesystemhasbeen activated(Fig.2a), drivers showedahigher minimumrisk acceptable andalower maximum risk acceptable(i.e.,drivers’ acceptablerangewiththeACCactiveissmaller).Thismeansthat,immediatelyafteractivation,driverspressthegaspedal orincreasethetargetspeedwhentheriskfeelingishigherinlowrisksituationsanddeactivateordecreasethespeedwhen theriskislowerinhighrisk situations.Interestingly,driverswho reportedahighscoreonthepatient andcarefuldriving style(Fig.2b)showedahigherminimumriskacceptableandalowermaximumriskacceptable(theiracceptablerangewith theACCactive issmaller). Thisresultmeansthatpatientandcarefuldrivers resumemanual controlorregulatethetarget