Application of System Dynamics in Car-following Models

Transcription

1 Applicaion of Sysem Dynamics in Car-following Models Arif Mehmood, rank Saccomanno and Bruce Hellinga Deparmen of Civil Engineering, Universiy of Waerloo Waerloo, Onario, Canada N2 3G1 or presenaion a he 20 h Annual Conference of he Sysem Dynamics Sociey, July ABSTRACT Over he pas 50 years, many differen "car-following" models have been proposed o describe he driver behaviour in a raffic sream. A number of inheren assumpions abou human consrains and preferences in exising car-following models hamper heir validiy for use in he design and evaluaion of differen ITS Inelligen Transporaion Sysems echnologies and/or conrols such as ACSS Advanced ehicle Conrol and Safey Sysems. In his paper we inroduce a new Sysems Dynamic SD car-following model ha addresses many of he shorcomings of exising car-following models and provides a more relevan plaform for simulaing driver behavior in all ypes of car-following siuaions subjec o changing raffic condiions. The proposed SD model was developed and validaed based on observed vehicle racking daa. Preliminary resuls sugges ha he proposed model yields speed and spacing profiles for vehicles in "real ime" ha compare well wih hose observed empirically. Keywords: Car-following, Driver behavior, Sysems Dynamics, Microscopic raffic simulaion 1.0 INTRODUCTION Driver behavior involves wo main responses: 1 speed and 2 seering. The primary objecive of mos car-following models is o predic following vehicle speed and spacing profiles based on lead vehicle simuli speeds for a se of roue/raffic condiions and driver characerisics. These models ypically consider a sring of vehicles raveling in a single lane. ane changes are normally no considered wihin he scope of simple car-following algorihms. More complex driver responses considered wihin more exensive microscopic raffic simulaions combine simple car-following 1

2 2 models wih models of oher driver responses i.e. lane changes, rouing, ec. o produce a more pracical opology of driver behaviour in acual raffic siuaions. Given he increasing demand for using new echnologies and echniques in ransporaion secor, i is clear ha a deailed undersanding of driver behaviour under differen ransporaion condiions is now becoming highly imporan. or example, he validiy of car-following models appears o be especially imporan when evaluaing differen ITS echnologies and/or conrols such as, ACSS or ACC Adapive Cruise Conrol. These echnologies are expeced o modify driver behavior in a complex ineracive fashion. rom he perspecive of car-following, hese echnologies also seek o replicae driver behavior hrough parial conrol of he acceleraor, while removing poenial hazards ha may occur hrough mispercepion of disance and oher driver errors. Working prooypes are currenly being invesigaed and will likely be available commercially wihin he nex few years Touran, To assess he impac of ACSS or ACC on safey and raffic flow, i becomes necessary o uilize he resuls of car-following models and he insighs hey provide ino how drivers perceive and reac o variable speeds and separaion disances in acual raffic siuaions. The model inroduced in his paper makes use of Sysems Dynamics SD principles. Sysems Dynamics provides he compuaional plaform for describing and invesigaing he complex process ha reflec driver behaviour in a raffic sream. The SD plaform is characerized by many non-linear relaionships boh heurisic and empirical wih numerous feedback loops. As such, he proposed SD car-following model inroduced in his paper relaxes many of he limiing assumpions of exising car-following models, rendering he process more relevan for microscopic raffic simulaion. This paper has hree basic objecives: 1 review exising car-following models and idenify heir behavioural shorcomings, 2 develop an SD car-following model ha addresses many of hese shorcomings, and 3 compare he SD model o observed vehicle racking daa and assess is abiliy o predic speed and spacing profiles over ime. 2.0 REIEW O CAR-OOWING MODES A comprehensive review of he hisorical developmen of car-following models is available in he lieraure Bracksone and McDonald, In his paper we provide a summary of he imporan models, heir formulaion, and limiaions. Car-following models have been sudied exensively since he early 1950s. The earlies work focused on he principle ha vehicle separaion is governed by safey consideraions by which disance or

3 3 ime headway beween vehicles is a funcion of relaive vehicle speeds. Pipes 1953 developed a car-following model ha assumes ha drivers conrol heir speed o mainain a desired spacing. This spacing is assumed o be linearly dependen on speed. orbes 1958 assumed ha drivers conrol heir speed o mainain a minimum ime headway. This ime headway is a linear funcion of he speed of he lead vehicle. Subsequen models Table 1 have incorporaed facors such as spacing beween vehicles, speed differenial, and driver sensiiviy ino car-following behavior. Car-following models developed by Chandler e al. 1958, Gazis e al. 1959, 1961, Edie 1961, Newell 1961, Herman and Rohery 1962, and Bierley 1963 all assume ha following vehicle drivers respond solely o changes in speed and posiion of he lead vehicle essenially he vehicle immediaely in fron. ox and ehman 1967, and Bexelius 1968 have suggesed ha insead of considering only he vehicle immediaely in fron, drivers should also ake ino accoun he speed and posiion of oher lead vehicles a leas wo downsream. This suggess a more reasonable percepion of driver behaviour where following vehicle drivers ake a longer range view of he raffic condiions downsream in seing heir respecive speed and spacing over ime. A common feaure of mos of he car-following models in Table 1 is he assumpion ha he following vehicle driver s responses are based on spacing and differenial speed beween he following and he lead vehicles. The underlying assumpion for hese models is ha he following vehicle driver can accuraely perceive spacing and differenial speed beween he following and he lead vehicles. A larger number of sudies have focused on calibraion of parameers á, m, and l in he GHR model he model developed by Gazis, Herman and Rohery, 1962 and i varians. Among hese he mos noable examples of are: May and Keller 1967, Heyes and Ashworh 1972, Treierer and Myers 1974, Ceder e al. 1976, Aron 1988, Ozaki, According o Bracksone and McDonald, 1999 no wihsanding considerable work on calibraion and validaion he general level of agreemen on parameer values has led o is general demise. Anoher class of models, called psychophysical or acion poin models, also exiss. These models have been developed in he basis ha drivers perceive relaive speed by deecing changes in he apparen size of he downsream vehicles. The hreshold for his percepion, which is well known, deermines wheher or no a driver can perceive a change in relaive speed or spacing. Several exising microscopic raffic simulaion programs including Paramics and Mission incorporaed acion poin car-following models. The difficuly wih hese models is he lack of objecive calibraion of he individual parameers and hresholds, and consequenly of he models as a whole.

4 4 Table 1: Seleced car-following model algorihms. Source: Corresponding Car-following Model Chandler e al [ ] 2 a = + α Gazis e al. 1959, 1961 [ ] a = + α Edie 1961 ] [ ] [ a = + α Newell 1961 [ ] 2 G a n = + Herman and Rohery, 1962 ] [ ] [ ] [ 2 2 a l m = + α Bierley 1963 [ ] [ ] 2 2 a + = + β α ox and ehman = ] [ ] [ ] [ ] [ W W a α Bexelius 1968 [ ] [ ] 1 2 a + = + β α Rockwell e al [ ] 2 2 a a β α + = ead 1 ead 2 ollower Where: a +Ä = Acceleraion rae of ollowing ehicle driver a ime + Ä a 2 = Acceleraion rae of ead ehicle 2 driver a ime, 1, 2 = Speed of ollowing, ead ehicle 1 and ead ehicle 2 a ime, 1, 1 = Posiion of ollowing, ead ehicle 1 and ead ehicle 2 a ime = Curren simulaion ime seconds Ä = Percepion-reacion ime seconds or simulaion inerval G n = Empirical relaionship beween velociy and headway for acceleraion/deceleraion á,â,m,l,w 1,W 2 = Model parameers

5 5 There are four basic assumpions inheren in many exising models ha end o resric heir abiliy o explain and predic driver behaviour in acual raffic siuaions: 1. The vas majoriy of car-following models assume ha following vehicle drivers can accuraely perceive relaive speed of he lead and following vehicles, absolue speed and/or acceleraion of lead vehicle a any poin in ime. These assumpions are unrealisic given he recilinear naure of vehicles moving in a single lane, and problems of deph percepion and differences driver reacions wih facors such as, ageing, impairmen, disabiliy, ec Boer, Many exising car-following models assume ha following vehicle drivers respond only o he lead vehicle immediaely in fron wihou observing oher vehicles downsream. A number of researchers have observed ha in acual raffic siuaions, drivers ake a more exensive view of raffic condiions ahead which may include several lead vehicles in seing he following vehicle desired speeds and spacing ox and ehman, 1967; Bexelius, 1968, Ozaki, 1993, and Toruran, Many exising car-following models, paricularly he GRH models, assume a mahemaical expression ha is empirically based bu fails o explain acual behaviour in a mechanisic fashion cause-effec. Bes fi expressions fail o clarify or explain, why cerain relaionships are specified as hey are Winsum, These expressions have lile, if any, basis on acual behaviour, and he model parameers have no obvious connecion wih idenifiable driver and vehicle rais ha explains behaviour Gipps, Many exising car-following models assume symmerical driver responses o changing raffic simuli involving lead vehicles. To illusrae, we consider wo cases, one wih a posiive relaive speed i.e. lead vehicle is ravelling faser and he oher wih a negaive relaive speed lead vehicle slower. or he same magniude of speed difference, he following vehicle driver in he firs insance will increase his or her speed wihou incurring higher collision risks. In he laer insance, he following vehicle driver will need o decelerae o avoid a poenial collision, since boh vehicles are moving closer o each oher. rom a safey perspecive, we would expec he acceleraion/deceleraion rae in he firs case o be less han he acceleraion/deceleraion rae in he second case. Many exising car-following models assume he magniude of acceleraion/deceleraion o be he same. This siuaion is normally ouside he scope of exising car-following models and is explained using separae collision avoidance algorihms euzbach, When boh he lead and following vehicle are raveling a he same speed, many exising

6 6 car-following models assume zero following vehicle deceleraion/acceleraion raes regardless of he spacing beween vehicles. This assumpion is clearly unrealisic Chakrobory and Kikuchi, PROPOSED SD CAR-OOWING MODE The car-following siuaion considered in his paper assumes a sring of hree vehicles wo lead vehicles and one following vehicle raveling along a single lane. I is assumed ha all vehicles ravel in he same lane and only adjusmens in speed are permied for all drivers involved. The profile of he firs lead vehicle is deermined exogenously based on predominan raffic condiions. The speed and spacing profiles for he second lead and he following vehicle are deermined inernally. One of he basic differences beween he proposed model and he exising car-following models is ha in exising car-following models following vehicle drivers consider only one lead vehicle ahead, while in he proposed model following vehicle drivers consider all vehicles ravelling ahead wihin heir comfor zone. or example, in case of hree vehicles siuaion considered in his paper he following vehicle driver would perceive informaion eiher from boh lead vehicles 1 s and 2 nd or from only second lead vehicle, depending on wheher one or boh lead vehicles are ravelling wihin his/her comfor zone. The comfor zone of a driver is defined based on his/her curren speed and percepion of crash risk. Unlike many exising car-following models, he proposed model assumes ha in a recilinear ravel sysem wih variable speeds and condiions, following vehicle drivers do no have he required deph percepion o accuraely ascerain spacing, differenial speeds, and/or acceleraion of lead vehicle a any poin in ime. In addiion o his own speed and safe comfor zone, he following vehicle driver can only ascerain his or her spacing o he vehicle immediaely in fron he second lead vehicle, and possibly he spacing beween boh lead vehicles if hey are sufficienly close. We noe ha in he proposed model he speeds and/or acceleraion of he lead vehicles are no required as inpus in seing he following vehicle acceleraion/deceleraion raes and spacing. This assumpion differs from many exising car-following models and can be viewed as being more parsimonious han hese models in esimaing he following vehicle speed and posiion over ime. Underlying assumpions The proposed SD model differs from exising car-following models in several imporan aspecs:

7 7 1. A simplified acceleraion/deceleraion rule is used for following drivers ha includes only spacing and rae of change in spacing beween he lead and he following vehicle. 2. The informaion from more han one vehicle ahead is used for decision-making process of following vehicle drivers. 3. The proposed model permis changes in percepion/reacion ime of following vehicle drivers o accoun for supplemenary lead vehicle simuli, such as, he saus of lead vehicles brake lighs. 4. The concep of a comfor zone for he following vehicle driver is inroduced o reflec his/her desired speed and spacing for differen driving condiions. igure 1 illusraes he dynamic relaionships inheren in he proposed SD car-following model. or every decision inerval, a driver ses a unique "safe comfor zone". This comfor zone reflecs speed and spacing saus ha he driver considers o be safe over ime and changing raffic condiions. Here we assume ha he desired speed is based on he curren spacing and rae of change in spacing wih respec o he lead vehicle immediaely in fron. If he curren spacing is shorer han ha dicaed by he driver's comfor zone and is decreasing in lengh, he following vehicle driver will decelerae o achieve a desired comfor zone or separaion disance. Conversely, if he curren spacing exceeds ha se by he driver s comfor zone, and he vehicle is ravelling a a speed below desired speed, he following vehicle driver will accelerae. The proposed model assumes ha he level of alerness of a driver affecs he percepion/reacion ime componen of he acceleraion/deceleraion rae. If a driver is aler, less ime is needed o perceive and reac o a given siuaion. In he proposed SD car-following model, he following vehicle driver will modify his or her personal percepion/reacion ime wih respec o he saus of he lead vehicle brake lighs. In he proposed SD model, we assume ha he following vehicle driver becomes more aler wih reduced percepion/reacion imes when he lead vehicle brake lighs are on and he lead vehicle is wihin he following vehicle driver comfor zone. The saus of he brake lighs can be ascerained inernally. Ozaki 1993 suggess ha brake ligh saus can be deermined as a funcion of vehicle deceleraion raes, such ha: if deceleraion rae < imes he speed of he vehicle, hen brake lighs are assumed o be li.

8 8 As indicaed in igure 1, he following vehicle driver considers boh he firs and second lead vehicle posiion in changing his/her speed. The quesion is how o balance he simuli beween he firs and second lead vehicles in seing he following vehicle driver response. While boh lead vehicles provide simuli o he following vehicle driver, he imporance ha he following vehicle driver places on one lead as compared o he oher depends on he spacing beween he following vehicles and he lead vehicle immediaely in fron, driver comfor zone for prevailing speed, and he spacing beween he wo lead vehicles. Model ormulaion The proposed car-following model consiss of four secors: 1 he firs lead vehicle, 2 he second lead vehicle vehicle immediaely in fron of following vehicle, 3 he following vehicle, and 4 he spacing secor. The sock flow diagram for he proposed model is given in igure 2 a and b. Each secor performs cerain funcions o produce speed and spacing profiles for individual vehicles in he hree-vehicle sring. uncions in each secor inerac wih funcions in he oher secors hrough feedback links. This reflecs how he speed and spacing of one vehicle acs o affec he speed and spacing of anoher vehicle in he sring. The firs lead vehicle secor is specified exogenously and prescribes he lead vehicle arge condiions for inpu ino he second lead and following vehicle secors. The acceleraion/deceleraion rae, speed and spacing of he second lead and following vehicles are deermined wihin he model, subjec o rules and assumpions pre-scribed in he following paragraphs. Road geomery, pavemen condiions, and weaher condiions are se exogenously. The process describing he second lead vehicle secor is similar o ha associaed wih he following vehicle secor. The only difference is ha he following vehicle driver ses his or her spacing and rae of change in spacing on he basis of spacing beween he firs and second lead vehicle and beween he second lead vehicle and iself. The second lead vehicle driver on he oher hand considers only is spacing wih he firs lead vehicle in seing his/her spacing and speed. The assumpion here is ha we are dealing wih a hree vehicle sring. This can be exended o include longer srings, wih an appropriae number of lead vehicle secors. The acceleraion/deceleraion rae of he following vehicle depends on he driver s percepion reacion ime, curren and desired speed. The desired speed depends on wo facors: 1 curren spacing beween he following vehicle and lead vehicle immediaely in fron, and 2 rae of change in spacing beween he following vehicle and he lead vehicle immediaely in fron. In he SD model,

9 9 he former facor is calibraed based on observed individual vehicle racking daa, while he laer is a non-linear funcion of rae of change in spacing beween second lead and following vehicles. This relaionship is based on a heurisic undersanding of he siuaion as opposed o empirical resuls from observed field daa. The boundary limis of his non-linear funcion are se so as o saisfy he exreme limis of a driver's percepion reacion ime as repored by Ozaki The produc of facors 1 and 2 above yields he desired speed of he following vehicle. The percepion reacion ime of he following vehicle driver depends upon his/her level of alerness. Alerness is defined in erms of driver's percepion reacion ime as modified by brake ligh saus, as discussed above. When he value of alerness level is one, he percepion reacion ime is assumed o be 2.5 sec Olson, The percepion reacion ime decreases as he vehicles ge close o each oher and he brake lighs on he lead vehicles are li Ozaki,1993. In igure 2b, a fourh secor is defined ha reflecs vehicle spacing separaion disance profiles, beween he firs and second lead vehicles, and beween he second lead and following vehicle. The facors such as pavemen condiions, pavemen fricion, road geomery, and raffic condiions can affec he disance ravelled by a vehicle a a paricular speed. or his paper, we have assumed ideal weaher and pavemen condiions. 4.0 CAIBRATION AND AIDATION USING SAE DATA The major componen of he proposed car-following model relaionship beween curren spacing and desired speed is calibraed based on observed individual vehicle racking daa obained from he SAME Sysem for Assessmen of ehicle Moion Environmen daabase Ervin, The Universiy of Michigan Transporaion Research Insiue UMTRI developed his SAME daabase for he Naional Highway Traffic Safey Adminisraion. This daabase provides a complee microscopic record of rajecories and disance headway observed for individual vehicles in a raffic sream over a period of ime. The SAME daabase conains 18 hours of vehicle rajecory daa represening over 30,500 vehicles. All daa were colleced during dayligh hours. Trajecory daa for a random sample of 132 vehicle pairs raveling in he shoulder lane were exraced from he SAME daabase. or each pair of vehicles, he speed of he following vehicle and he spacing were exraced. or each observed speed, he mean disance headway from all vehicles observed o ravel a his speed was compued. The resuls are illusraed in igure 3 as he desired speed versus mean spacing. To ensure realisic behavior a he boundaries of relaionship

10 10 shown in igure 3, consrains are incorporaed such ha he desired speed mus be non-negaive and no greaer han he maximum assumed speed of 70 f/sec 77 Km/h. The relaionship illusraed in igure 3 is consisen wih he daa obained from a Newcasle Universiy research eam in he Unied Kingdom May, ike SAME daabase, he daa colleced by a research eam a Newcasle Universiy also ends o demonsrae a fairly aggressive car-following behaviour a shor spacing and less aggressive car-following behaviour a longer spacing, as illusraed by igure 3. Observaions in SAME sugges ha desired speed for a given spacing differs beween drivers. This is likely due o individual driver differences of age, gender, risk aking propensiy, skills, vehicle size and performance characerisics. Moreover, he siuaional facors such as ime of day, day of week, road geomery, raffic condiions, weaher and road condiions also influence he desired speed of a driver for a given spacing. As an iniial sep, we have assumed ideal roadway condiions and individual driver differences and siuaional facors are no explicily considered ino he proposed car-following model in his paper. 5.0 EAUATION O PROPOSED SD CAR-OOWING MODE The microscopic evaluaion of he proposed model is conduced by comparing model esimaes of speed and spacing for he second lead and he following vehicle o hose observed in he SAME daabase. The rajecories of firs lead vehicles were randomly seleced from he SAME daabase. The rajecories of he wo vehicles following he seleced lead vehicle second lead and following were also exraced from he SAME daabase and were used o compare o he model oupus. The rajecory of he firs lead vehicle, he iniial speed and posiion of he second lead and following vehicles were provided as inpus o he proposed car-following model. The model was hen used o esimae he behavior of he second lead and following vehicle in response o he known behavior of he firs lead vehicle. igure 4 illusraes he observed and model prediced resuls for he firs daa se exraced from he SAME daabase. igure 4a illusraes observed and prediced speed and spacing associaed wih he second lead vehicle. igure 4b illusraes he same for he following vehicle. As indicaed by he resuls illusraed in igure 4 a and b, he speed and spacing profiles prediced by he proposed carfollowing model closely follow hose in he observed field daa. Tweny samples of hree-vehicle srings were exraced from SAME daabase. or each sample he roo-mean-squared RMS error associaed wih he predicion of speeds and spacing of second and

11 11 following vehicle was esimaed as given in Table 2. The average RMS error associaed wih he predicion of second lead and following vehicle speed for he weny samples was found o be 3.68 Km/h and 4.7 Km/h respecively. The RMS error associaed wih he predicion of second lead and following vehicle spacing was 2.56 m and 2.87 m respecively. Table 2: RMS error associaed wih weny sample applicaions Sample Observed Average Observed Average Roo-Mean-Squared-Error Speed Km/h Spacing m Speed Km/h Spacing m 2 f S2 Sf 2 f S2 Sf Average = Second lead vehicle speed f = ollowing vehicle speed S2 = Spacing beween firs and second lead ehicle Sf = Spacing beween second lead and following ehicle

12 12 A one-way ANOA was carried ou o assess he saisical significance of he RMS error wih respec o he following vehicle speed and spacing. The resuls of ANOA are given in Table 3. or his analysis he variaion in observed mean speed of following vehicle was grouped ino hree classes < 50Km/h, Km/h, and > 60 Km/h. Table 3: ANOA resuls, RMS error versus following vehicle speed and spacing. ariable P-value Remarks f Significan Sf No significan As indicaed in Table 3, he ANOA suggess ha he mean speed of following vehicle f has a saisically significan effec on he RMS error of following vehicle speed. The P-value for he following vehicle spacing Sf shows he variaion in observed mean speed of following vehicle speed lacks saisical significance a he 5% level. To furher invesigae he performance of he proposed model in predicing he speed of following vehicle, he RMS error of following vehicle speed is ploed agains observed mean speed of following vehicle igure 5. As shown in igure 5, he RMS error of following vehicle speed a higher observed mean speed is less han he RMS error a lower observed mean speed. A his poin we canno speculae on he reason for his relaionship. A regression analysis of prediced and observed speed and spacing of following vehicle was carried ou for he sample applicaion. The resuls are shown in igures 6 and 7. igure 6 shows he plo of prediced versus observed speed of he following vehicle. igure 7 shows he plo of prediced versus observed spacing of he following vehicle. The resuls indicae significan agreemen beween he prediced oupu from he model and he observed field daa. While hese resuls are based on a limied comparison beween he proposed SD car-following esimaes and observed SAME daa, hey sugges ha he proposed model can closely reflec observed speed and spacing profiles for seleced hree-vehicle srings, where following vehicle drivers consider boh wo lead vehicle simuli in seing speeds and spacing over ime.

13 CONCUSIONS In his paper we have discussed a number of exising car-following models and have idenified several common shorcomings. We have presened a revised car-following model based on Sysem Dynamics principles, which aemps o address many of hese shorcomings. The proposed model assumes ha drivers adjus heir speed based on he curren spacing and rae of change in curren spacing o nex downsream vehicle. The model also akes ino accoun he driver's desired speed and disance headway in relaion o increased risk of collisions. The proposed model assumes ha drivers are capable of esimaing he spacing beween heir own vehicle and he nex downsream vehicle. The model, unlike many exising car-following models, does no make unrealisic assumpions abou drivers' abiliy o esimae he speed of downsream vehicles. In his paper we have compared he model esimaes of speed and spacing profiles for he following and second lead vehicle o he speed and spacing profiles of observed vehicles. These comparisons sugges ha he proposed car-following model yields realisic resuls in replicaing he behavior of he following vehicle driver from an observed vehicle racking daabase. In he proposed model drivers seek o mainain he speed and spacing ha is consisen wih heir undersanding of he risks involved for any raffic siuaion. ACKNOWEDGEMENTS The auhors are graeful o he researchers a UMTRI, and in paricular Drs. Rober Ervin and Jeff Walker, for providing he SAME daabase.

14 14 REERENCES Aron, M "Car-following in an urban nework: simulaion and experimens". In Proceedings of Seminar D, 16 h PTRC Meeing 29-39pp. Bexelius, S "An exended model for car-following". Transporaion Research Bierley, R "Invesigaion of an iner vehicle spacing display". Highway Research Record 25: Boer, E.R "Car following from he driver's perspecive" Transporaion Research Par Bracksone, M. and McDonald, M " Car-following: a hisorical review" Transporaion Research Par Ceder, A "A deerminisic raffic flow model for he wo regime approach". Transporaion Research Record, 567, 16-30pp. Chandler, R.E., Herman, R., and Monrol, E.W "Traffic dynamics: sudies in car-following". Operaion Research. 6, 2, pp. Chakrobory, P. and Kikuchi, S "Evaluaion of he General Moors based car-following models and a proposed fuzzy inference model" Transporaion Research Par C Edie, "Car-following and seady sae heory for non-congesed raffic". Operaion Research Ervin, R., MacAdam, C., ayda, A., and Anderson, E "Applying he SAME Daabase on Iner-ehicle Kinemaics o Explore he Naural Driving Environmen". Presened a 80 h Annual Meeing of he Transporaion Research Board, Washingon D.C. orbes T.W., Zagorski, H.J., Holshouser, E.., and Deerline, W.A "Measuremen of driver reacions o unnel condiions". Highway Research Board Proceedings pp. ox, P. and ehman,.g "Safey in Car-following. A Compuer Simulaion". Newark College of Engineering. Newark. New Jersey. 173pp. Gazis, D.C., Herman, R., and Pos, R.B "Car-following heory of seady sae flow". Operaion Research 7 4, pp. Gazis, D.C., Herman, R., Rohery, R.W "Nonlinear follow-he-leader models of raffic flow". Operaion Research. 9 4, pp. Gipps, P.G "A Behavioural Car ollowing Model for Compuer Simulaion". Transporaion Research-B. 15B pp. Herman, R. and R.W. Rohery "Microscopic and Macroscopic Aspecs of Single ane Traffic low". Operaion Research, Japan, 74pp. Heyes, M.P., and Ashworh, R "urher research on car-following models". Transporaion Research, 6, pp. euzbach, W Inroducion o he Theory of Traffic low. Springer-erlag, May, A.D., Traffic flow fundamenals, Englewood Cliffs, New Jersey: Prenice Hall.

15 15 May, A.D, and Keller, H.E.M " Non ineger car-following models". Highway Research Record, 199, 19-32pp. Newell, G "Nonlinear Effecs in he Dynamics of Car-following". Operaion Research Olson, P.., and Michael S "Percepion-Reacion Time o Unexpeced Roadway Hazards". Human acors pp. Ozaki, H "Reacion and anicipaion in he car-following behaviour". In Proceedings of he 13 h Inernaional Symposium on Traffic and Transporaion Theory pp. Pipes,.A "An operaion dynamics of raffic dynamics". Journal of Applied Physics 24 3, Rockwell, T.H. and Treierer, J "Sensing and communicaion beween vehicles". Naional Cooperaive Highway Research Program Repor 51. Highway Research Board. Washingon D.C. Treierer, J., and Myers, J.A "The hyseresis phenomenon in raffic flow". In Proceedings of he Sixh Inernaional Symposium on Transporaion and Traffic Theory, Sydney, 13-38pp. Touran, A., Bracksone, M.A., and McDonald, M "A collision model for safey evaluaion of auonomous inelligen cruise conrol". Acciden Analysis and Prevenion. 21, pp. Winsum, W "The human elemen in car-following models". Transporaion Research Par. 2: pp.

16 igure 1: Dynamics hypohesis of proposed car-following model 16

17 igure 2a: Sock-flow diagram of 1 s and 2 nd lead vehicle secor 17

18 igure 2b: Sock-flow diagram of following vehicle and spacing secor 18

19 Mean of observed poins Relaionship used in model Desired speed f/sec Spacing f igure 3: Calibraed relaionship beween spacing and desired speed

20 Speed f/sec Observed-2 Model oupu Observed imesec Speed f/sec Observed-f Model oupu-f Observed ime sec Spacing f Observed-S2 Model oupu-s Observed Timesec Spacing f Observed-Sf Model oupu-sf Observed Time sec a second ead ehicle b ollowing ehicle igure 4: Comparison of Prediced and Observed vehicle speeds and spacing Daa Se 1

21 21 12 RMS error of following vehicle speed Km/h Observed mean speed of following vehicle Km/h igure 5: RMS error s Observed mean speed of following vehicle Km/h

22 22 Prediced f Km/h y = x R 2 = Observed f Km/h igure 6: Predicaed s Observed speed of following vehicle for weny samples n = 1055 Prediced Sf m y = 0.883x R 2 = Observed Sf m igure 7: Predicaed s Observed spacing of following vehicle for weny samples n = 1055