a car-following model based on safety margin considering

Research ArticleA Car-Following Model Based on Safety Margin consideringADAS and Driving Experience

Yugang Wang 12 and Nengchao Lyu 12

1Intelligent Transportation Systems Research Center Wuhan University of Technology Wuhan 430063 China2National Engineering Research Center for Water Transport Safety Wuhan 430063 China

Correspondence should be addressed to Nengchao Lyu lncwhuteducn

Received 16 October 2020 Revised 29 January 2021 Accepted 8 February 2021 Published 19 February 2021

Academic Editor Hui Yao

Copyright copy 2021 Yugang Wang and Nengchao Lyu is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

Existing studies had shown that advanced driver assistance systems (ADAS) and driver individual characteristics can significantlyaffect driving behaviorerefore it is necessary to consider these factors when building the car-followingmodel In this study weestablished a car-following model based on risk homeostasis theory which uses safety margin (SM) as the risk level quantizationparameter Firstly three-way Analysis of Variance (ANOVA) was used to analyze the influencing factors of car-followingbehavior e results showed that ADAS and driving experience have a significant effect on the driversrsquo car-following behavioren according to these two significant factors the car-following model was established e statistical method was used tocalibrate the parameter reaction response τ Other four parameters (SMDL SMDH α1 and α2) were calibrated using a classicalgenetic algorithm and the effects of ADAS and driving experience in these four parameters were analyzed using T-test Finally theproposed model was compared with the GHR model and the result showed that the proposed model has a smaller Root MeanSquare Error (RMSE) than the GHR model e proposed model is a method of simulating different driving behaviors that areaffected by ADAS and individual characteristics Considering more driver individual characteristics such as driving style is thefuture research goal

1 Introduction

With the increasing number of vehicles societies have beenfaced with significant challenges to congestion and trafficcrashes A recent report from World Health Organization[1] indicated that annually 124 million people die due totraffic crashes Human factors are the most important causeof traffic accidents and driver behavior plays a leading rolein safe driving Car-following behavior is one of the mostcommon and important behaviors in the driving processand it is closely related to traffic safety Researchers havebeen studying the car-following process for more than half acentury and have established a number of car-followingmodels that focus on traffic flow theory control algorithmsor driver psychology and physiology ese car-followingmodels are important to ADAS especially the ACC system[2 3] and are considered to be key assessment tools for

transportation systems [4 5] e existing car-followingmodel mainly includes the CA model (collision avoidancemodel) which is based on maintaining a safe braking dis-tance and the GMmodel (stimulus-response model) whichis based on a stimulus-response mechanism e CA modelcalculates the specific theoretical safety following distancecombined with vehicle braking performance and driverresponse time by using Newtonrsquos law of motion [6] e GMmodel uses the relative speed between the leading and hostvehicle as the stimulus standard uses the host vehiclersquosacceleration and deceleration as the reaction situation andintroduces the sensitivity as the adjustment coefficient tostudy the relationship between the parameters in the car-following process [7] ese evaluation models effectivelysimulate the car-following behavior and determine how thecar-following occurs in the actual scenario but the reasonsfor the vehicles to follow each other in some way are not

HindawiAdvances in Civil EngineeringVolume 2021 Article ID 6619137 10 pageshttpsdoiorg10115520216619137

discussed in depth Hamdar et al explained car-followingbehaviors based on the prospect theory and proposed a car-following model by evaluating the gains and losses whiledriving [8] Wildersquos risk homeostasis theory (RHT) anotherrisk-taking theory is also helpful in explaining car-followingbehaviors [9] A car-following model based on risk per-ception which is RHT and stimulus-response mechanismhelps understand car-following mechanisms and facilitatethe simulation of car-following behaviors that differdepending on varied individual characteristics which havedifferent levels of acceptable risk [10]

To improve driversrsquo attention and perceptual abilityvarious Advanced Driver Assistance Systems (ADAS) weredeveloped to provide drivers with correct preaccident hu-man errors ADAS are designed to complement driver ca-pabilities for perception cognition action selection andaction implementation in a dynamic environment [11 12]For the influence of ADAS on driving behavior manyscholars have carried out research from different aspectsBlaschke et al [13] tested the effectiveness of ADAS throughField Operational Tests (FOT) and found that the driver canmore accurately estimate the distance to the leading vehicleafter using ADAS and can maintain a safer time headway(THW) while driving Saito et al [11] conducted a simulateddriving experiment to test the performance of ADASthrough drivers awakening status and lane keeping per-formance e results show that ADAS helps reduce trafficaccidents which is related to fatigue driving Birrell et al [14]tested ADAS through FOT In their tests after using ADASthe driverrsquos fuel efficiency increased by 41 and the averageTHW increased to 23 seconds Adell et al [15] studied theeffects of ADAS on the safety distance and safe speed ofdrivers through FOT e results showed that both positiveand negative effects existed Lyu et al [16] studied the effectof driving experience on the effectiveness of ADAS throughFOT e results showed that ADAS had a positive impacton skilled drivers and unskilled drivers especially for un-skilled drivers in the following vehicle scenario But in thebraking scenario ADAS had a positive impact on unskilleddrivers but a negative impact on skilled drivers Lyu et al[17] evaluated the effectiveness of ADAS in improvingdriverrsquos risk perception in near-crash events using a novelmetric from risk homeostasis theory e results show thatADAS has a positive impact on the low-risk group andmoderate-risk group for all drivers but a negative impact onthe high-risk group for skilled drivers ese studies showthat ADAS can significantly affect the driverrsquos acceptable risklevel so it is necessary to consider the impact of ADAS whenestablishing a car-following model

In addition driver characteristics can significantly affectthe effectiveness of ADAS such as gender [18] and drivingexperience [19] Existing studies had shown that drivingexperience has an impact on driving performance Richdriving experience can make the excellent driving perfor-mance which is related to the driverrsquos learning process andexperience [20] Compared with skilled drivers unskilleddrivers take up more attention resources and cause higherworkload [21] and the accident risk is 2ndash4 times higher [22]In addition gender is one of the most commonly measured

variables in driving behavior researches and it has beenidentified as a key demographic variable that affects drivingperformance [23] erefore the driver characteristicsshould also be considered when establishing a car-followingmodel

is article analyzes which driver characteristics cansignificantly affect the driverrsquos car-following behavior firstlyen we establish the car-following model based on sig-nificant influencing factors

2 Database and Preparation

21 Field Operational Tests Design Driving simulator [11]and Field Operational Tests [14] approaches were employedto study the influences of ADAS to driver behavior With thedevelopment of intelligent vehicles and the application ofvehicle sensors it is becoming a trend to evaluate the effect ofADAS with Field Operational Tests Hence an instrumentedvehicle which is equipped with ADAS was developed tocarry out Field Operational Tests on a variety of roads inWuhan China

44 participants (24 males 20 females) were recruited inthese Field Operational Testseir age ranged from 22 to 55years old (mean 322 SD 82) On average they had 69years of driving experience ranging from 2 to 18 years Itshould be noted that in China many people obtain theirdriverrsquos license but do not obtain actual driving experienceIn order to avoid interfering with the credibility of theexperiment this research used a driverrsquos total drivingmileage rather than hisher driving license age as an indi-cator of proficiency In terms of drivingmileage participantsdrove an average of 110000 kilometers ranging from 400 to400000 kilometers In this study drivers with a total drivingrange of more than 40000 kilometers were defined as skilleddrivers while those with less than 40000 kilometers weredefined as unskilled drivers ere were 22 skilled driversand 22 unskilled drivers in the recruited participants

An instrumented vehicle has been developed to collectcomplete coverage of data on driversrsquo behavior vehiclekinematics and vehicle surroundings e main equipmentof the instrumented vehicle is shown in Figure 1 Mobileyewas used to obtain headway and lane position as well as toalert forward collision and lane departure One video camerawas used to collect vehicle surroundings video informatione INS system was used to obtain the vehiclersquos three-axisacceleration latitude and longitude Lidar was used toobtain the forward target information (distance velocityrelative velocity etc) e CAN bus was used to obtainvehicle data such as vehicle speed accelerator pedal infor-mation brake pedal information and steering wheel angleAll data was synchronized with the master time that wastransmitted by the monitoring software every 01 s

22 Extraction of the Car-following Data Based on LiDARand CAN bus data the car-following segments wereextracted Table 1 summarized the rules used to extract thecar-following segments from existing studies

2 Advances in Civil Engineering

e key to the extraction of car-following segments is thesetting of the threshold values Due to the differences intraffic environment and driving behaviors between domesticand foreign the threshold value in the literature could onlybe used as a reference and it needs to be revised according tothe data of these FOTs According to the distribution rangeof each parameter in the FOTs data and the threshold valuesin the existing literature the threshold values of the variouscar-following extraction rules in this study are determined asfollows

(1) Absolute lateral distance is lt25m which ensuresthat the target vehicle is in the same lane as theexperimental vehicle

(2) e longitudinal distance is lt120m and the hostvehicle speed is gt20 kmh ese two rules caneliminate traffic flow conditions of congestion andfree flow and the congestion is excluded when thehost vehicle speed gt20 kmh e distance betweentwo vehicles in free flow is too large in which case theleading vehicle cannot restrict the driving behaviorof the host vehicle so a longitudinal distance lt120mis required

(3) e absolute value of longitudinal relative velocity islt25ms2 and the absolute value of relative velocityis small enough to ensure that the vehicle is in astable car-following state

(4) e segment duration should be more than 30seconds to ensure the stability of the car-followingstatus

According to the above four extracting thresholds 354car-following segments were extracted from FOTs

23 Risk Perception Quantification Index We need a risklevel quantitative parameter to describe the driverrsquos riskperception changes in the car-following process Commonlyused risk level quantization parameters are Time Headway(THW) and Time to Collision (TTC) But THW and TTChave limitations as traditional indicators of risk quantifica-tion THW retains only the vehicle speed information anddoes not consider the impact on relative speed while TTCretains only the relative speed information and does not takeinto account the impact of the vehicle speed Additionally theexpected means of THW and TTC are quite different betweendrivers with different characteristics [28] erefore there is aneed for an indicator that is consistent between drivers withdifferent characteristics to evaluate the effectiveness of ADASis indicator should take into account the impact of speedand relative speed e safety margin proposed by the riskhomeostasis theory (RHT) [29] is a suitable indicator Nilsson[30] suggested that ldquoeverything in the driverrsquos visual field thatcould be an obstacle or a threat is surrounded by zones that is

GAC trumpchi GA3

OXTS RT2500OBD-II

Mobileye M630

MOVON

IBEO LUX4

Microwave

Figure 1 Equipment of instrumented vehicle

Table 1 Summary of car-following event extraction criteria in the existing literature

Absolute lateraldistance (m)

Host vehiclespeed (kmh) Longitudinal distance (m) Relative velocity (ms2) Segment duration (s)

Leblanc et al [24] gt40 lt20 gt15Chong et al [25] lt19 gt20 lt120 gt30Ervin et al [26] gt40 lt20Wang et al [27] lt25 gt18 gt7 and lt120 lt25 gt15

Advances in Civil Engineering 3

safety marginsrdquo In the driverrsquos control system the safetymargin (SM) is defined as the threshold that protects thedriver from danger [17] e SM is independent of the actualdriving situation In accordance with that definition the SMshould have the following features (a) it should be amonotonic function of the objective risk level (b) driversshould have a fixed acceptable SM to guide their behaviorsand (c) an acceptable SM varies depending on the driverrsquoscharacteristics however a certain type of driver (such as ahighly skilled driver) should have a similar acceptable SM

According to the barking process of the car-followingtask the risk level can be defined as [31]

ξ(τ t) V1(t) middot τ + V1(t)1113858 1113859

22a1(t)1113872 1113873 minus V2(t)1113858 111385922a2(t)1113872 1113873

D1(t)

(1)

In the above formula V1(t) is the host vehiclersquos speedV2(t) is the lead vehiclersquos speed a1(t) is the car-followingrsquosacceleration a2(t) is the lead vehiclersquos acceleration D1(t) isthe relative spacing between the two vehicles τ is the re-action time which consisted of the driverrsquos reaction time τ1and the braking systemrsquos reaction time τ2 is formulashows that when one vehicle was following another the leadvehicle emergency brake could be applied until its speeddropped to zero e driver of the car-following couldobserve the brake light signal of the lead vehicle and respondquicklye distance the car-following passes is expressed asV1(t) middot τ + ([V1(t)]22a1(t)) and the distance the lead ve-hicle passes is expressed as [V2(t)]22a2(t) In this case thequantitative objective driving risk level can be expressed asthe difference between the distance and the relative spacingat time t In this study the formula was changed based onelements of driver and vehicle system factors

ξ(τ t) ξ τ2 t( 1113857 +V1(t) middot τ1

D1(t) (2)

Basing driving simulator on that definition trafficsafety can be ensured when ξ(τ t)le 1 It is important tonote that in a real-world scenario it is possible thatξ(τ t)gt 1 however no accident will occur in some cir-cumstances is is because the absolute value of the ac-celeration of the car-following is greater than that of thelead vehicle However if the lead vehicle brakes by themaximum deceleration at this time a rear-end crash willstill occur even if the car-following brakes at the maximumdeceleration

erefore under ideal conditions

V1(t) middot τ1D1(t)

le 1 minus ξ τ2 t( 1113857 (3)

From here the SM can be defined as

SM(t) 1 minus ξ τ2 t( 1113857 (4)

According to previous research the limit value of theacceleration of the vehicle is 03 Gndash075G [32] Combiningthe FOTs on the actual road deceleration in the calculationof risk was set as

a1(t) a2(t) 70ms2 (5)

Braking system response time is usually between 010and 030 s During emergency situations a driver mayquickly and strongly apply the brakes us τ2 was set as015 s

erefore the SM can be calculated by the followingformula

SM(t) 1 minus ξ(015 t) 1 minus015lowastV1(t) + V1(t)1113858 1113859

2141113872 1113873 minus V2(t)1113858 11138592141113872 1113873

D1(t) (6)

According to the definition the smaller the SM is thehigher the objective risk level is which means that the risk ofrear-end is higher In the next section each car-followingsegment will calculate the mean value of SM Based on theANOVA of the mean value of SM the significant influencingfactors to driverrsquos car-following behavior can be obtained

24 Factors Affecting Car-Following Behavior Before theanalysis of variance judging by box figure there is no ab-normal data value and after Shapiro-Wilk test all groups ofSMmean are of normal distribution (Pgt 005) FurthermoreP value of Levene homogeneity test of variance is 0130which is greater than 005 and it is believed that the de-pendent variables in each classification have equal varianceAccording to the above test the data obey normal

distribution have no abnormal value and have equal var-iance so the three-way ANOVA can be analyzed

e results of three-way ANOVA are shown in Table 2e results of three-way ANOVA showed that ADAS

gender and driving experience did not have the interactionbetween three factors on the SMmean F (2 129) 0454P 0636 In the interaction between two factors the in-fluence of ADASlowast gender on the dependent variable wasnot statistically significant F (1 129) 0824 P 0193 theinfluence of ADASlowastdriving experience on the dependentvariable was statistically significant F (1 129) 0001P 11841 the influence of genderlowastdriving experience onthe dependent variable was not statistically significant F (1129) 0505 P 0688 In the main effect ADAS has nomain effect on the dependent variable F (1 129) 0017P 0896 the gender has no main effect on the dependent


variable F (1 129) 2538 P 0085 the driving experi-ence has a main effect on the dependent variable F (1129) 4159 P 0043

e results of ANOVA showed that only driving ex-perience can significantly affect the driverrsquos car-followingbehavior but in the interaction between two factors theinfluence of ADASlowastdriving experience on the dependentvariable was statistically significant erefore the effect ofADAS on the car-following behavior cannot be ignored esubsequent model will take into account the factors of ADASand driving experience

3 Car-Following Model Based onRisk Perception

31 Model Assumptions When the driver follows anothervehicle he will adjust the relative spacing to ensure an

acceptable level of risk at is the driver of the followingvehicle responds to the difference between the perceivedsafety margin (perceived risk level) and the desirable safetymargin (DSM) as the driver of the following vehicle decidesto accelerate (perceived safety margin is greater than DSM)decelerate (perceived safety margin is less than DSM) ormaintain a constant speed (perceived safety margin is withinDSM) [10] Since the proposed model is based on the dif-ference between the driverrsquos DSM and the perceived safetymargin it is called the DSM model

eDSMmodel for car-following is described as follows

an(t + τ) f SM(t) minus SMD( 1113857

α1 SM(t) minus SMDH( 1113857 SM(t)gt SMDH

α2 SM(t) minus SMDL( 1113857 SM(t)lt SMDL

0 else

⎧⎪⎪⎨

⎪⎪⎩(7)

where an(t) is the acceleration of a following car at time tSMDH is the upper limit of the DSM and SMDLdenotes thelower limit of the DSM e goal of our modeling is todescribe natural driving and DSM may change due topsychological factors However in the simulation used toanalyze the main factors affecting the automatic trackingprocess the random factors can be ignored so in the specifictraffic environment for the same type of driver SMDH andSMDL can be constant values α1 and α2 are the sensitivityfactors for acceleration and deceleration where α1gt 0α2gt 0

According to previous research the limit value of theacceleration of the vehicle is 03Gndash075G [30] so themaximum deceleration is set as 70ms2 If an(t)ltminus70ms2then an(t) minus70ms2 Maximum favorite acceleration is setas 30ms2 If an(t)gt 30ms2 then an(t) 30ms2

Because of the simulated time interval the result ofcalculated speed may be negative when the speed is close tozero in numerically updated process us the minimumspeed of the following car is set as V (t) 00ms if Vn (t)lt 00ms Vn (t) 00ms

32 Model Calibration According to the car-followingmodel a total of five parameters need to be calibrated re-sponse time τ DSM lower limit SMDL DSM upper limitSMDH acceleration sensitivity coefficient α1 and decelera-tion sensitivity coefficient α2

e response time is the reaction time of the followingvehicle According to the existing research the reaction timein the car-following process can be determined by com-paring the relative speed curve and the acceleration curve offollowing vehicle [33] According to the theory of thestimulus-response model [34] the acceleration of the fol-lowing vehicle is determined by the relative speed of the twovehicles that is the relative speed change (stimulus) willcause a corresponding change (reaction) of the followingvehiclersquos acceleration after a certain time delay and thisdelay is the car-following reaction time

From the extracted 354 car-following events the reac-tion time of each pair of stimulus-response points wasextracted and the mean value was calculated according towhether or not to use ADAS and driving experience re-spectively When ADAS is off the average response time of

Table 2 ree-way ANOVA results for SMmean

Source Type III sum of squares df Mean square F SigADAS 0000 1 0000 0017 0896Gender 0075 1 0037 2538 0085Driving experience 0016 1 0016 4159 0043lowastADASlowastgender 0002 1 0001 0193 0824ADASlowastdriving experience 0046 1 0046 11841 0001lowastlowastGenderlowastdriving experience 0005 1 0003 0688 0505ADASlowast gender lowast driving experience 0004 2 0002 0454 0636lowastlowastlowastSiglt 0001 lowastlowastsiglt 001 and lowastsiglt 005


unskilled drivers is 15 s and the average response time ofskilled drivers is 13 s is is because without the support ofADAS unskilled drivers need to take more attention re-sources and cause higher workload when handling drivingtasks so the response time is slower than that of skilleddrivers After exposure to ADAS the average response timeof unskilled drivers is 10 s and the average response time ofskilled drivers is 09 s After exposure to ADAS the responsetime of skilled drivers and unskilled drivers will be short-ened and the change of unskilled drivers is more obviousis phenomenon indicates that ADAS has more influenceon skilled drivers than unskilled drivers consistent with theexisting research [35]

e remaining four parameters DSM lower limit SMDLDSM upper limit SMDH acceleration sensitivity coefficientα1 and deceleration sensitivity coefficient α2 cannot bedirectly derived using statistical methods therefore we

denote them as a vectorV (SMDL SMDH α1 α2) etarget of calibration is to obtain a vector V which canminimize the difference between measured and simulatedtrajectories

e genetic algorithm is a nonlinear optimization al-gorithm that simulates biological evolution and has beenwidely used to solve complex nonlinear optimizationproblems It is also used to calibrate the vehicle model [10]erefore we used the genetic algorithm to calibrate theparameter vector V of the car-following model With therelative distance the following vehicle speed and the fol-lowing vehicle acceleration are common indicators used toevaluate the car-following model so we defined the dif-ference parameter F as the fitness function of the geneticalgorithm based on these three parameters e differenceparameter F is calculated as follows

dF(t) |vs(t) minus vr(t)|vr(t)( 1113857 + ds(t) minus dr(t)

11138681113868111386811138681113868111386811138681113868dr(t)1113872 1113873 + as(t) minus ar(t)

11138681113868111386811138681113868111386811138681113868ar(t)1113872 1113873

3

F 1N

1113944

N

t1dF(t)

(8)

where vs(t) represents the simulated speed of the followingvehicle at time t vr(t) represents the real speed of thefollowing vehicle at time t ds(t) represents the simulatedrelative spacing at time t and dr(t) represents the realrelative spacing at time t as(t) represents the simulatedacceleration of the following vehicle at time t ar(t) repre-sents the real acceleration of the following vehicle at time tNrepresents the sampling points number during this car-following event e genetic algorithm is used to find avector p to minimize the fitness function F

According to the definition of fitness function oneparameter vector V can be obtained in one car-followingevent erefore in the extracted 354 car-following events354 parameter vectors V can be obtained of which un-skilled drivers with ADAS OFF have 85 cases skilleddrivers with ADAS OFF have 93 cases unskilled driverswith ADAS ON have 86 cases and skilled drivers withADAS ON have 90 cases In the next section these fourparameters of the parameter vector V will carry out t-testrespectively

As shown in Table 3 the test result of SMDL shows thatthere is a statistically significant difference between the SMDLof skilled drivers and unskilled drivers during naturalisticdriving (ADAS OFF) e SMDL of unskilled drivers issignificantly affected by the ADAS and the SMDL of skilleddrivers is also significantly affected by the ADAS whichindicates that ADAS can significantly affect the driversrsquoSMDL In terms of mean value the SMDL of skilled driverrose from 0718 to 0756 after exposure to ADAS and theSMDL of unskilled driver rose from 0740 to 0752 after

exposure to ADAS indicating that in terms of SMDL ADAShas a greater impact on skilled drivers than unskilled drivers

As shown in Table 4 the test result of SMDH shows thatthere is a statistically significant difference between theSMDH of skilled drivers and unskilled drivers during nat-uralistic driving After exposure to ADAS there is also astatistically significant difference between the SMDH ofskilled drivers and unskilled drivers is shows that skilleddrivers have higher SMDH than unskilled drivers and ADAShas no significant effect on SMDH to both skilled drivers andunskilled drivers

As shown in Table 5 the test result of α1 shows that thereis a significant statistical difference between α1 of skilleddrivers and unskilled drivers during naturalistic drivingAfter exposure to ADAS there is also a statistically signif-icant difference between the α1 of skilled drivers and un-skilled drivers Unskilled drivers have more rapidacceleration due to insufficient control of the throttle so theaverage value of α1 is greater than skilled drivers In terms ofα1 ADAS has no significant effect on skilled drivers andunskilled drivers

As shown in Table 6 the test results of α2 show that thereis a significant statistical difference between α2 of skilleddrivers and unskilled drivers during naturalistic drivingeα2 of unskilled drivers was significantly affected by theADAS Unskilled drivers have more sharp decelerationsthan skilled drivers because of lack of perceived ability sothe α2 is greater than that of skilled drivers during natu-ralistic driving After exposure to ADAS the α2 of unskilleddrivers fall to the same level as skilled driversrsquo It is worth


noting that ADAS has no significant effect on skilled driversin terms of α2

In order to reduce the influence of sampling error on themodel the parameters that have insignificant T test resultsadopt overall meane parameters that have significant T testresults adopt mean of each part e parameter vector is asfollows skilled driver under ADASOFFV1 (13 0718 09276446 12072) unskilled driver under ADAS OFF V2 (150740 0975 6860 12884) skilled driver under ADAS ONV3 (09 0754 0927 6446 12072) and unskilled driverunder ADAS ON V4 (10 0754 0975 6860 12072)

33ModelValidation In this section the proposed model isvalidated in real car-following events data and then com-pared with the Gazis Herman Rothery (GHR) model GHRmodel is an effective car-following model by producing

lower percentile errors for speed and acceleration predic-tions e GHR model is formulated as follows [36]

an(t) cvmn (t)

v(t minus τ)

xl(t minus τ)

(9)

where an (t) is the acceleration of vehicle n (following ve-hicle) implemented at time t Vn (t) is the speed of thefollowing vehicleΔx andΔv refer to the relative distance andspeed between the following vehicle and the (n+ 1) vehicle(leading vehicle) τ is the driver reaction time andm l and crepresent the constants

Four typical types of car-following data (2 (ADAS)lowast 2(driving experience)) were randomly selected from thedatabase e simulation results of the proposed model andthe GHR model were shown in Figure 2 e Root MeanSquare Error (RMSE) was shown in Table 7 From the RMSE

Table 5 T-test result of α1

ADAS OFF ADAS ONSkilled drivers Unskilled drivers Skilled drivers Unskilled drivers

ADAS OFF Skilled drivers (mean value 0926) mdash 0017lowast 0235 mdashUnskilled drivers (mean value 0974) 0017lowast mdash mdash 0314

ADAS ON Skilled drivers (mean value 0929) 0235 mdash mdash 0033lowastUnskilled drivers (mean value 0976) mdash 0314 0033lowast mdash

lowastlowastlowastSiglt 0001 lowastlowastsiglt 001 and lowastsiglt 005



ADAS OFF Skilled drivers (mean value 12021) mdash 0044lowast 0235 mdashUnskilled drivers (mean value 12884) 0044lowast mdash mdash 0045lowast

ADAS ON Skilled drivers (mean value 12075) 0235 mdash mdash 0033Unskilled drivers (mean value 12126) mdash 0045lowast 0033 mdash


Table 4 T-test result of SMDH





Table 3 T-test result of SMDL


ADAS OFF Skilled drivers (mean value 0718) mdash 0026lowast 0035lowast mdashUnskilled drivers (mean value 0740) 0026lowast mdash mdash 0002lowastlowast

ADAS ON Skilled drivers (mean value 0756) 0035lowast mdash mdash 0561Unskilled drivers (mean value 0752) mdash 0002lowastlowast 0561 mdash



of the simulation results it can be seen that the proposedmodel is better than the GHR model

4 Conclusion

In this study a total of 354 car-following events wereextracted from 87 times of FOTs Based on these data weestablished a car-following model using SM as the risk levelquantization parameter based on risk homeostasis theoryFirstly three-way ANOVA was used to analyze the threeindependent variables (ADAS driving experience andgender) e results showed that ADAS and driving expe-rience have a significant effect on the driversrsquo car-following

behavior en according to these two significant factorsthe car-following model was established In the calibrationprocess of the five model parameters (τ SMDL SMDH α1and α2) the statistical method was used to calibrate the firstparameter reaction response τ e remaining four pa-rameters were calibrated using a classical genetic algorithmand the effects of ADAS and driving experience on these fourparameters were analyzed using T-test Finally the proposedmodel was compared with the GHR model which wasadopted by most ACC systems e result showed that theproposed model has smaller RMSE than the GHR modele proposed model is a method for simulating differentdriving behaviors that are affected by ADAS and individual

Table 7 RMSE of the proposed model and the GHR model

ADAS OFF ADAS ONUnskilled driver Skilled driver Unskilled driver Skilled driver

Proposed model 561 239 326 229GHR mode 668 468 472 408

Real valueProposed modelGHR model

05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 511Time (s)

(a)


0

10

20

30

40

50

60

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(b)


05

101520253035

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(c)


05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 91 1011Time (s)

(d)

Figure 2 Simulation results of proposed model and GHR model (a) Skilled driver under ADAS OFF (b) Unskilled driver under ADASOFF (c) Skilled driver under ADAS ON (d) Unskilled driver under ADAS ON


characteristics Considering more driver individual char-acteristics such as driving style is the future researches goal

Data Availability

e data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

e authors declare no conflicts of interest

Acknowledgments

is research was funded by the National Nature ScienceFoundation of China (Nos 51775396 andNo 52072290)Hubei Province Science Fund for Distinguished YoungScholars (No 2020CFA081) and the Fundamental ResearchFunds for the Central Universities (No 191044003 No2020-YB-028)

References

[1] World Health Organization Global Status Report on RoadSafety 2017 World Health Organization Geneva Switzerland2017

[2] J Mar and H-T Lin ldquoA car-following collision preventioncontrol device based on the cascaded fuzzy inference systemrdquoFuzzy Sets and Systems vol 150 no 3 pp 457ndash473 2005

[3] J Wang L Zhang D Zhang and K Li ldquoAn adaptive lon-gitudinal driving assistance system based on driver charac-teristicsrdquo IEEE Transactions on Intelligent TransportationSystems vol 14 no 1 pp 1ndash12 2013

[4] S Panwai and H Dia ldquoComparative evaluation of micro-scopic car-following behaviorrdquo IEEE Transactions on Intel-ligent Transportation Systems vol 6 no 3 pp 314ndash325 2005

[5] C Wang and B Coifman ldquoe effect of lane-change ma-neuvers on a simplified car-following theoryrdquo IEEE Trans-actions on Intelligent Transportation Systems vol 9 no 3pp 523ndash535 2008

[6] E Kometani and T Sasaki ldquoDynamic behavior of traffic with anonlinear spacing-speed relationshiprdquo in Proceedings of theSymposium on eory of Traffic Flow Research LaboratoriesGeneral Motors pp 105ndash119 New York NY USA 1959

[7] R E Chandler R Herman and E W Montroll ldquoTrafficdynamics studies in car followingrdquo Operations Researchvol 6 no 2 pp 165ndash184 1958

[8] S H Hamdar M Treiber H S Mahmassani and A KestingldquoModeling driver behavior as sequential risk-taking taskrdquoTransportation Research Record Journal of the TransportationResearch Board vol 2088 no 1 pp 208ndash217 2008

[9] G J S Wilde ldquoe theory of risk homeostasis implicationsfor safety andHealthrdquo Risk Analysis vol 2 no 4 pp 209ndash2251982

[10] G Lu B Cheng YWang and Q Lin ldquoA car-following modelbased on quantified homeostatic risk perceptionrdquo Mathe-matical Problems in Engineering vol 2013 Article ID 40875613 pages 2013

[11] Y Saito M Itoh and T Inagaki ldquoDriver assistance systemwith a dual control scheme effectiveness of identifying driverdrowsiness and preventing lane departure accidentsrdquo IEEETransactions on Human-Machine Systems vol 46 no 5pp 1ndash12 2016

[12] J Son M Park and B B Park ldquoe effect of age gender androadway environment on the acceptance and effectiveness ofadvanced driver assistance systemsrdquo Transportation ResearchPart F Traffic Psychology and Behaviour vol 31 pp 12ndash242015

[13] C Blaschke F Breyer B Farber J Freyer and R LimbacherldquoDriver distraction based lane-keeping assistancerdquo Trans-portation Research Part F Traffic Psychology and Behaviourvol 12 no 4 pp 288ndash299 2009

[14] S A Birrell M Fowkes and P A Jennings ldquoEffect of using anin-vehicle smart driving aid on real-world driver perfor-mancerdquo IEEE Transactions on Intelligent TransportationSystems vol 15 no 4 pp 1801ndash1810 2014

[15] E Adell A Varhelyi and M D Fontana ldquoe effects of adriver assistance system for safe speed and safe distance-areal-life field studyrdquo Transportation Research Part CEmerging Technologies vol 19 no 1 pp 145ndash155 2011

[16] N Lyu Z Duan L Xie and C Wu ldquoDriving experience onthe effectiveness of advanced driving assistant systemsrdquo inProceedings of the 2017 4th International Conference onTransportation Information and Safety (ICTIS) pp 987ndash992Banff Canada August 2017

[17] N Lyu Z Duan C Ma and C Wu ldquoSafety margins - a novelapproach from risk homeostasis theory for evaluating theimpact of advanced driver assistance systems on drivingbehavior in near-crash eventsrdquo Journal of Intelligent Trans-portation Systems vol 25 no 1 pp 93ndash106 2021

[18] N Lyu C Deng L Xie C Wu and Z Duan ldquoA field op-erational test in China exploring the effect of an advanceddriver assistance system on driving performance and brakingbehaviorrdquo Transportation Research Part F Traffic Psychologyand Behavior vol 65 2018 In press

[19] N Lyu Z Duan and C Wu ldquoe impact of driving expe-rience on advanced driving assistant systemsrdquo Journal ofTransportation Systems Engineering and Information Tech-nology vol 17 no 6 pp 48ndash55 2017

[20] I Engstrome N P Gregersen K Hernetkoski E Keskinenand A Nyberg Jeunes Conducteurs Novices Education ampFormation du Conducteur Etude bibliographique RapportVTI 491A Universite de Turku Turku Finland 2003

[21] G Underwood P Chapman N Brocklehurst J Underwoodand D Crundall ldquoVisual attention while driving sequences ofeye fixations made by experienced and novice driversrdquo Er-gonomics vol 46 no 6 pp 629ndash646 2003

[22] L L D Stasi V Alvarez-Valbuena J J Cantildeas A MaldonadoA Catena and A Antolı ldquoRisk behavior and mental work-load multimodal assessment techniques applied to motorbikeriding simulationrdquo Transportation Research Part F TrafficPsychology and Behavior vol 12 no 5 pp 361ndash370 2009

[23] C Maag D Muhlbacher and H-P Mark ldquoStudying effects ofadvanced driver assistance systems (ADAS) on individual andgroup level using multi-driver simulationrdquo IEEE IntelligentTransportation Systems Magazine vol 4 no 3 pp 45ndash542012

[24] D J Leblanc S Bao J R Sayer and S Bogard ldquoLongitudinaldriving behavior with integrated crash-warning systemrdquoTransportation Research Record Journal of the TransportationResearch Board vol 2365 no 1 pp 17ndash21 2013

[25] L Chong M M Abbas A Medina Flintsch and B Higgs ldquoArule-based neural network approach to model driver natu-ralistic behavior in trafficrdquo Transportation Research Part CEmerging Technologies vol 32 no 4 pp 207ndash223 2013

[26] R Ervin J Sayer D Leblanc S Bogard and M MeffordAutomotive Collision Avoidance System Field Operational Test


Report University of Michigan Ann Arbor TransportationResearch Institute Ann Arbor MI USA 2005

[27] X Wang M Zhu and Y Xing ldquoImpacts of collision warningsystem on car following behavior based on naturalistic drivingdatardquo Journal of Tongji University (Natural Science) vol 44no 7 pp 1045ndash1051 2016

[28] G Lu B Cheng Q Lin and Y Wang ldquoQuantitative indicatorof homeostatic risk perception in car followingrdquo Safety Sci-ence vol 50 no 9 pp 1898ndash1905 2012

[29] G J SWilde ldquoCritical issues in risk homeostasis theoryrdquo RiskAnalysis vol 2 no 4 pp 249ndash258 2010

[30] R Nilsson Safety Margins in the Driver e Faculty of SocialSciences Uppsala University Uppsala Sweden 2001

[31] X Zhang G Lu and B Cheng ldquoParameters calibration forcar-following model based desired safety marginrdquo Interna-tional Conference on Optoelectronics and Image Processing(ICOIP) vol 2 pp 97ndash100 2010

[32] T L Brown J D Lee and D V Mcgehee ldquoHuman per-formance models and rear-end collision avoidance algo-rithmsrdquo Human Factors e Journal of the Human Factorsand Ergonomics Society vol 43 no 3 pp 462ndash482 2001

[33] G S Gurusinghe T Nakatsuji Y Azuta P Ranjitkar andY Tanaboriboon ldquoMultiple car-following data with real-timekinematic global positioning systemrdquo Transportation Re-search Record Journal of the Transportation Research Boardvol 1802 no 1 pp 166ndash180 2002

[34] H Ozaki ldquoReaction and anticipation in the car-followingbehaviorrdquo Transportation and Traffic eory vol 49 no 6pp 2302ndash2306 1993

[35] N Lyu Z Duan and C Wu Evaluated the Effectiveness ofAdvanced Driving Assistant Systems in Near-Crash EventsBased on Safety Margin in Proceedings of the 97st Trans-portation Research Board Annual Meeting Washington DCUSA 2018

[36] M Brackstone and M McDonald ldquoCar-following a historicalreviewrdquo Transportation Research Part F Traffic Psychologyand Behaviour vol 2 no 4 pp 181ndash196 1999


discussed in depth Hamdar et al explained car-followingbehaviors based on the prospect theory and proposed a car-following model by evaluating the gains and losses whiledriving [8] Wildersquos risk homeostasis theory (RHT) anotherrisk-taking theory is also helpful in explaining car-followingbehaviors [9] A car-following model based on risk per-ception which is RHT and stimulus-response mechanismhelps understand car-following mechanisms and facilitatethe simulation of car-following behaviors that differdepending on varied individual characteristics which havedifferent levels of acceptable risk [10]

To improve driversrsquo attention and perceptual abilityvarious Advanced Driver Assistance Systems (ADAS) weredeveloped to provide drivers with correct preaccident hu-man errors ADAS are designed to complement driver ca-pabilities for perception cognition action selection andaction implementation in a dynamic environment [11 12]For the influence of ADAS on driving behavior manyscholars have carried out research from different aspectsBlaschke et al [13] tested the effectiveness of ADAS throughField Operational Tests (FOT) and found that the driver canmore accurately estimate the distance to the leading vehicleafter using ADAS and can maintain a safer time headway(THW) while driving Saito et al [11] conducted a simulateddriving experiment to test the performance of ADASthrough drivers awakening status and lane keeping per-formance e results show that ADAS helps reduce trafficaccidents which is related to fatigue driving Birrell et al [14]tested ADAS through FOT In their tests after using ADASthe driverrsquos fuel efficiency increased by 41 and the averageTHW increased to 23 seconds Adell et al [15] studied theeffects of ADAS on the safety distance and safe speed ofdrivers through FOT e results showed that both positiveand negative effects existed Lyu et al [16] studied the effectof driving experience on the effectiveness of ADAS throughFOT e results showed that ADAS had a positive impacton skilled drivers and unskilled drivers especially for un-skilled drivers in the following vehicle scenario But in thebraking scenario ADAS had a positive impact on unskilleddrivers but a negative impact on skilled drivers Lyu et al[17] evaluated the effectiveness of ADAS in improvingdriverrsquos risk perception in near-crash events using a novelmetric from risk homeostasis theory e results show thatADAS has a positive impact on the low-risk group andmoderate-risk group for all drivers but a negative impact onthe high-risk group for skilled drivers ese studies showthat ADAS can significantly affect the driverrsquos acceptable risklevel so it is necessary to consider the impact of ADAS whenestablishing a car-following model

In addition driver characteristics can significantly affectthe effectiveness of ADAS such as gender [18] and drivingexperience [19] Existing studies had shown that drivingexperience has an impact on driving performance Richdriving experience can make the excellent driving perfor-mance which is related to the driverrsquos learning process andexperience [20] Compared with skilled drivers unskilleddrivers take up more attention resources and cause higherworkload [21] and the accident risk is 2ndash4 times higher [22]In addition gender is one of the most commonly measured

variables in driving behavior researches and it has beenidentified as a key demographic variable that affects drivingperformance [23] erefore the driver characteristicsshould also be considered when establishing a car-followingmodel

is article analyzes which driver characteristics cansignificantly affect the driverrsquos car-following behavior firstlyen we establish the car-following model based on sig-nificant influencing factors

2 Database and Preparation

21 Field Operational Tests Design Driving simulator [11]and Field Operational Tests [14] approaches were employedto study the influences of ADAS to driver behavior With thedevelopment of intelligent vehicles and the application ofvehicle sensors it is becoming a trend to evaluate the effect ofADAS with Field Operational Tests Hence an instrumentedvehicle which is equipped with ADAS was developed tocarry out Field Operational Tests on a variety of roads inWuhan China

44 participants (24 males 20 females) were recruited inthese Field Operational Testseir age ranged from 22 to 55years old (mean 322 SD 82) On average they had 69years of driving experience ranging from 2 to 18 years Itshould be noted that in China many people obtain theirdriverrsquos license but do not obtain actual driving experienceIn order to avoid interfering with the credibility of theexperiment this research used a driverrsquos total drivingmileage rather than hisher driving license age as an indi-cator of proficiency In terms of drivingmileage participantsdrove an average of 110000 kilometers ranging from 400 to400000 kilometers In this study drivers with a total drivingrange of more than 40000 kilometers were defined as skilleddrivers while those with less than 40000 kilometers weredefined as unskilled drivers ere were 22 skilled driversand 22 unskilled drivers in the recruited participants

An instrumented vehicle has been developed to collectcomplete coverage of data on driversrsquo behavior vehiclekinematics and vehicle surroundings e main equipmentof the instrumented vehicle is shown in Figure 1 Mobileyewas used to obtain headway and lane position as well as toalert forward collision and lane departure One video camerawas used to collect vehicle surroundings video informatione INS system was used to obtain the vehiclersquos three-axisacceleration latitude and longitude Lidar was used toobtain the forward target information (distance velocityrelative velocity etc) e CAN bus was used to obtainvehicle data such as vehicle speed accelerator pedal infor-mation brake pedal information and steering wheel angleAll data was synchronized with the master time that wastransmitted by the monitoring software every 01 s

22 Extraction of the Car-following Data Based on LiDARand CAN bus data the car-following segments wereextracted Table 1 summarized the rules used to extract thecar-following segments from existing studies









GAC trumpchi GA3

OXTS RT2500OBD-II

Mobileye M630

MOVON

IBEO LUX4

Microwave









ξ(τ t) V1(t) middot τ + V1(t)1113858 1113859

22a1(t)1113872 1113873 minus V2(t)1113858 111385922a2(t)1113872 1113873

D1(t)

(1)



D1(t) (2)




le 1 minus ξ τ2 t( 1113857 (3)


SM(t) 1 minus ξ τ2 t( 1113857 (4)


a1(t) a2(t) 70ms2 (5)




2141113872 1113873 minus V2(t)1113858 11138592141113872 1113873

D1(t) (6)
















0 else

⎧⎪⎪⎨

⎪⎪⎩(7)















11138681113868111386811138681113868111386811138681113868dr(t)1113872 1113873 + as(t) minus ar(t)

11138681113868111386811138681113868111386811138681113868ar(t)1113872 1113873

3

F 1N

1113944

N

t1dF(t)

(8)













an(t) cvmn (t)

v(t minus τ)

xl(t minus τ)

(9)

























4 Conclusion







05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 511Time (s)

(a)


0

10

20

30

40

50

60

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(b)


05

101520253035

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(c)


05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 91 1011Time (s)

(d)




Data Availability




Acknowledgments


References















































GAC trumpchi GA3

OXTS RT2500OBD-II

Mobileye M630

MOVON

IBEO LUX4

Microwave









ξ(τ t) V1(t) middot τ + V1(t)1113858 1113859

22a1(t)1113872 1113873 minus V2(t)1113858 111385922a2(t)1113872 1113873

D1(t)

(1)



D1(t) (2)




le 1 minus ξ τ2 t( 1113857 (3)


SM(t) 1 minus ξ τ2 t( 1113857 (4)


a1(t) a2(t) 70ms2 (5)




2141113872 1113873 minus V2(t)1113858 11138592141113872 1113873

D1(t) (6)
















0 else

⎧⎪⎪⎨

⎪⎪⎩(7)















11138681113868111386811138681113868111386811138681113868dr(t)1113872 1113873 + as(t) minus ar(t)

11138681113868111386811138681113868111386811138681113868ar(t)1113872 1113873

3

F 1N

1113944

N

t1dF(t)

(8)













an(t) cvmn (t)

v(t minus τ)

xl(t minus τ)

(9)

























4 Conclusion







05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 511Time (s)

(a)


0

10

20

30

40

50

60

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(b)


05

101520253035

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(c)


05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 91 1011Time (s)

(d)




Data Availability




Acknowledgments


References










































ξ(τ t) V1(t) middot τ + V1(t)1113858 1113859

22a1(t)1113872 1113873 minus V2(t)1113858 111385922a2(t)1113872 1113873

D1(t)

(1)



D1(t) (2)




le 1 minus ξ τ2 t( 1113857 (3)


SM(t) 1 minus ξ τ2 t( 1113857 (4)


a1(t) a2(t) 70ms2 (5)




2141113872 1113873 minus V2(t)1113858 11138592141113872 1113873

D1(t) (6)
















0 else

⎧⎪⎪⎨

⎪⎪⎩(7)















11138681113868111386811138681113868111386811138681113868dr(t)1113872 1113873 + as(t) minus ar(t)

11138681113868111386811138681113868111386811138681113868ar(t)1113872 1113873

3

F 1N

1113944

N

t1dF(t)

(8)













an(t) cvmn (t)

v(t minus τ)

xl(t minus τ)

(9)

























4 Conclusion







05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 511Time (s)

(a)


0

10

20

30

40

50

60

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(b)


05

101520253035

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(c)


05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 91 1011Time (s)

(d)




Data Availability




Acknowledgments


References

















































0 else

⎧⎪⎪⎨

⎪⎪⎩(7)















11138681113868111386811138681113868111386811138681113868dr(t)1113872 1113873 + as(t) minus ar(t)

11138681113868111386811138681113868111386811138681113868ar(t)1113872 1113873

3

F 1N

1113944

N

t1dF(t)

(8)













an(t) cvmn (t)

v(t minus τ)

xl(t minus τ)

(9)

























4 Conclusion







05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 511Time (s)

(a)


0

10

20

30

40

50

60

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(b)


05

101520253035

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(c)


05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 91 1011Time (s)

(d)




Data Availability




Acknowledgments


References













































11138681113868111386811138681113868111386811138681113868dr(t)1113872 1113873 + as(t) minus ar(t)

11138681113868111386811138681113868111386811138681113868ar(t)1113872 1113873

3

F 1N

1113944

N

t1dF(t)

(8)













an(t) cvmn (t)

v(t minus τ)

xl(t minus τ)

(9)

























4 Conclusion







05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 511Time (s)

(a)


0

10

20

30

40

50

60

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(b)


05

101520253035

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(c)


05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 91 1011Time (s)

(d)




Data Availability




Acknowledgments


References












































an(t) cvmn (t)

v(t minus τ)

xl(t minus τ)

(9)

























4 Conclusion







05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 511Time (s)

(a)


0

10

20

30

40

50

60

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(b)


05

101520253035

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(c)


05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 91 1011Time (s)

(d)




Data Availability




Acknowledgments


References









































4 Conclusion







05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 511Time (s)

(a)


0

10

20

30

40

50

60

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(b)


05

101520253035

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 911Time (s)

(c)


05

10152025303540

Rela

tive s

paci

ng

11 21 31 41 51 61 71 81 91 1011Time (s)

(d)




Data Availability




Acknowledgments


References









































Data Availability




Acknowledgments


References








































a car-following model based on safety margin considering

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