COMPARING SIMULATED ROAD SAFETY PERFORMANCE TO OBSERVED CRASH FREQUENCY AT SIGNALIZED INTERSECTIONS

Transcription

1 COMPARING SIMULATED ROAD SAFETY PERFORMANCE TO OBSERVED CRASH FREQUENCY AT SIGNALIZED INTERSECTIONS Janailson Q. Souza Research Assisan, Deparmen of Transporaion Engineering, Universidade Federal do Ceará, CE, Brazil, Marcos W. Sasaki Research Assisan, Deparmen of Transporaion Engineering, Universidade Federal do Ceará, CE, Brazil, Flávio J. C. Cuno, Ph.D Assisan Professor I, Deparmen of Transporaion Engineering, Universidade Federal do Ceará, CE, Brazil, Submied o he 3 rd Inernaional Conference on Road Safey and Simulaion, Sepember 14-16, 2011, Indianapolis, USA ABSTRACT Microscopic raffic simulaion has been developed and applied over he pas wo decades wih he main focus owards he design and operaions of ransporaion sysems. Recenly, due o advancemens in daa collecion echniques and microscopic algorihms, he poenial of microscopic simulaion as a ool for safey assessmens has been under considerable debae. This ype of approach may allow beer knowledge regarding he chain of evens preceding crash occurrences; herefore, leading o a more comprehensive mehodology for safey sudies when compared o radiional observaional sudies. This paper presened a validaion effor beween observed rear-end collisions and simulaed raffic conflics, as refleced by hree Safey Performance Measures (SPM) namely: Time o Collision (TTC), Deceleraion Rae o Avoid he Crash (DRAC) and Crash Poenial Index (CPI). Three years of acciden daa ( ) for wo-hour peak (7:00AM - 9:00AM) and off-peak (9:00AM - 11:00AM) were compared o he esimaed number of raffic conflics as obained by a microscopic simulaion experimen. The resuls suggesed ha simulaed SPM did no reflec he apparen decrease in observed rear-end crashes for peak and off-peak periods. This migh be due o he inherenly rare random characerisic of raffic accidens and he somewha simplified microscopic environmen provided by curren algorihms. On he oher hand, all esed SPM were capable of capuring differences in he number of accidens among he hree differen sudy sies. Keywords: surrogae safey measures, road safey, microscopic simulaion, ime o collision. 1

2 INTRODUCTION The use of microscopic raffic simulaion over he las wo decades has essenially focused on he analysis of he efficiency of ransporaion infrasrucure, such as signalized inersecions, arerial neworks and freeway corridors. The poenial of microscopic simulaion in raffic safey and raffic conflic analysis was iniially recognized by Darzenas e al (1980) and has gained ineres mosly due o recen developmens in human driver behavior modeling and advancemens in real-ime vehicle daa acquisiion. In heory, microscopic raffic models have he poenial o accoun for imporan facors ha heavily influence crash occurrences, including differen behavioral aspecs of drivers and individual pair-wise vehicular ineracions in real-ime. This would provide a plaform for he developmen of safey sudies ha apply a more microscopic mechanisic approach o improve he knowledge of crash occurrence. However, some mehodological aspecs of his approach need o be fully invesigaed including: Tradiional microscopic car-following, gap accepance, and lane changing algorihms have no been developed specifically o accoun for he full range of facors explaining he poenial for crashes. Models should allow errors o occur as he resul of less-han-perfec percepion, decision-making, and acion, hereby causing differen levels of risk in he ineracions beween road-users and he environmen (Archer, 2000; Archer, 2005; Xin e al., 2008). An objecive link beween simulaed safey performance and observed high risk raffic evens can enhance he scope of microscopic modeling as a ool for safey assessmens of ransporaion sysems. Safey performance measures (SPMs), also known as proximal safey indicaors or surrogae safey measures, have been calculaed from microscopic simulaion packages o reflec high risk evens involving a leas one vehicle in relaion o a projeced poin of collision. The mos commonly documened SPMs are TTC-ime o collision (Hayward, 1972), DRAC-deceleraion rae o avoid he crash (Cooper and Ferguson, 1976), PET-pos encroachmen ime (Cooper, 1983), CPI-crash poenial index (Cuno and Saccomanno, 2008) and ohers. The usefulness of microscopic simulaion for assessing safey depends on he abiliy of hese measures o capure complex behavioural relaionships ha could lead o crashes and o esablish a link beween simulaed safey measures and observed crash risk. The main objecive of his paper is o presen a SPM relaive validaion effor by comparing observed rear-end crashes and simulaed TTC, DRAC and CPI for hree urban arerial signalized inersecions in he ciy of Foraleza, Brazil. The underlying premise is ha if simulaed SPM reflecs high risk behaviour in he raffic sream, hen crashes end o occur more frequenly when hose indicaors are consisenly higher. Conversely, i is expeced ha in non-crash siuaions hese measures would be closer o he average for he prevailing raffic condiions and locaion. 2

3 SIMULATED SAFETY PERFORMANCE MEASURES Simulaed safey performance is usually expressed in erms of proximal safey indicaors defined o reflec high risk evens in relaion o a projeced poin of collision. These measures are usually based on pair-wise vehicular speed and spacing aribues. The main assumpion underlying he use of safey performance measures is ha if one is able o deec high risk siuaions ha occur considerably more frequenly han crashes, hen saisically reliable resuls will be possible wihou he need of hisorical crash daa. The use of safey performance measures also consiues in essence a proacive approach o road safey sudies since i is able o deec safey problems before hey resul in crash (Barceló e al., 2003; Dazenas e al., 1980; Perkins and Harris, 1968). Three basic caegories of SPM have been idenified in he lieraure as follows (Cuno, 2008): ime based measures, required braking power measures and safey indices. Time based measures are esimaed according o a projeced ime of a poenial collision assuming vehicles mainaining heir curren speeds and rajecories. The mos common ime based measures found in he lieraure are ime o collision (TTC), ime o acciden (TTA), posencroachmen ime (PET), encroachmen ime (ET), and gap ime (GT) (Hayward, 1972; FHWA, 2003). A problem ha limis he applicaion of his safey measure is ha several combinaions of speed and disance can produce he same measure; herefore, inferences abou crash severiy become more cumbersome. The differenial speeds of vehicles a he momen of impac plays a major role in crash severiy due o he kineic energy of he sysem immediaely before he collision. Safey measures based on he required rae of speed reducion or braking power of vehicles have a heoreical formulaion o provide good esimaes of poenial conflics, as well as o produce an objecive plaform for safey sudies on which severiy is a major facor. Two safey performance measures based on vehicles require braking power while in conflics are: deceleraion rae o avoid he crash (DRAC) and proporion of sopping disance (PSD) (Brian e al., 1978; Archer, 2005; Cooper and Ferguson, 1976; Darzenas e al., 1980; Geman and Head, 2003). Recen developmens in real-ime daa acquisiion echniques and increasing use of microscopic simulaion in safey sudies have fosered he developmen of safey indices ha incorporae a emporal dimension o radiional SPMs. The fundamenal assumpion underlying he use of safey indices is ha he conflic severiy and he corresponden ime exposed o such conflic can provide a beer measure of safey ha a single measuremen, such as he lowes TTC, he highes DRAC, ec. Among he safey indices are ime exposed ime o collision (TET), ime inegraed ime o collision (TIT), he unsafey densiy parameer (UD) and he crash poenial index (CPI) (Barceló e al., 2003; Minderhoud and Bovy, 2001; Cuno, 2008). This paper invesigaes one indicaor of each caegory of SPM by esimaing he number of rearend conflics obained from measures of he TTC, DRAC and CPI simulaed for hree insolaed signalized inersecions for shor incremens of ime (0.1s). TTC can be esimaed using an expression of he form 3

4 ( X X ) L = (1) i 1, i, i 1, TTC i, ; Vi, > Vi 1, Vi, Vi 1, where = ime inerval X = posiion of he vehicles (i = following vehicle, i-1 = lead vehicle) L = vehicle lengh V = velociy The deceleraion rae o avoid he crash or DRAC can be defined using ime-space relaionships applied o a given vehicle pair as he deceleraion required by he following vehicle o come o a imely sop or aain a maching lead vehicle speed in order o avoid a rear-end crash. This can be expressed as DRAC i, ( Vi, Vi 1, ) = (2) ( X X ) L i 1, i, i 1, The CPI index can be obained using an expression of he form (Cuno, 2008): CPI i = fi = ii P ( a1, a2,..., an ) ( MADR DRAC ) T i i, b (3) where, CPI i = crash poenial index for vehicle i i i = iniial ime inerval for vehicle i f i = final ime inerval for vehicle i DRAC i, = deceleraion rae o avoid he crash (m/s 2 ) for vehicle i in ime MADR i = maximum available deceleraion rae (m/s 2 ) for vehicle i given condiions (a 1,...a n ) = observaion ime inerval (sec) T i = oal simulaed ime for vehicle i (sec) The parameer b in he above equaion denoes a binary sae variable, 1 if DRACi, >0 and 0 oherwise. Thresholds for he definiion of a rear-end raffic conflic have been assumed according o sudies elsewhere (Van der Hors, 1990; Hydén, 1996 and Cuno, 2008). For TTC and DRAC, a raffic conflic has been assigned for vehicle ineracions resuling on TTC values lower han 1.5s and DRAC values exceeding 3.35m/s 2. Defining conflics using CPI requires assumpion on he maximum available deceleraion rae (MADR) for each vehicle and esimaes (simulaion environmen) of DRAC over ime. For every vehicle in he simulaion an individual MADR value was assigned from a runcaed normal disribuion for cars and rucks separaely (Table 1). The values on Table 1 were obained from field ess for differen vehicles wih iniial speeds from 80 o 100km/h coming o a full sop 4

5 (Neilsen, J., 2007; MOVIT, 2007). DRAC values, on he oher hand, were obained from rearend vehicle ineracions as represened by a combinaion of geomeric and raffic aribues and heir relaionships according o microscopic car-following, gap-accepance and lane change algorihms. In his case a raffic conflic is deeced when a given vehicle required braking effor is greaer han is assigned maximum braking capabiliy, i.e., DRAC>MADR. Table 1 Assumed runcaed normal disribuion parameers for MADR MADR disribuion parameers Car Trucks and Buses Average (m/sec 2 ) Sandard Deviaion (m/sec 2 ) Upper Limi (m/sec 2 ) Lower Limi (m/sec 2 ) Max. Conflic Disance (m) SIMULATED SPM AND CRASHES COMPARISON FRAMEWORK The framework for he ess o explore he relaive validaion beween observed crashes and simulaed safey performance is illusraed in Figure 1. This framework consiss of seven seps: 1) Defining sies (inersecions) and respecive area of ineres o be invesigaed, 2) Obaining crash daa for sudy areas, 3) Geomeric and raffic aribues daa collecion, 4) Microscopic nework coding, 5) Calibraion and validaion of microscopic algorihms, 6) Esimaing safey performance measures for seleced sies, and 7) Spaial and Temporal SPM/Crash comparison. Figure 1 Framework of he seps on he relaive validaion process of he SPM. 5

6 Defining Inersecions and Areas of Ineres The validaion exercise discussed here is based on he analysis of hree inersecions seleced based on he following crieria: ype of raffic conrol, parking condiions and influence of oher inersecions. The seleced inersecions are signalized wih acuaed signal conrollers o faciliae he daa collecion process since raffic flow, average delay and oher informaion are easily obained from loop deecors and he SCOOT (Spli Cycle Offse Opimizaion Technique) sysem. The influence of parking condiions on rear-end crashes was considered o be a poenial source of bias since curren microscopic algorihms do no consider explicily hese maneuvers in heir formulaion. Consequenly aemps were made o selec only inersecions wih no parking spaces and driveways wihin he area of ineres on every approach. The hird selecion crierion was relaed o raffic arrival and spaial dependence of inersecions. In his case inersecions wih a considerable disance from oher signalized inersecions (>200meers) were seleced o avoid vehicle plaooning from upsream inersecion and he inroducion of a spaial crash dependency (bias) beween eniies. These facors would produce an exra level of effor o be adequaely considered by curren microscopic raffic algorihms. Figure 2 illusraes he seleced inersecions, namely: Inersecion #168 (Dedé Brasil Avenue and dos Expedicionários Avenue), Inersecion #243 (Murilo Borges Avenue and Rogaciano Leie Avenue) and Inersecion #250 (Murilo Borges Avenue and Raul Barbosa Avenue). All sudy areas are four-legged signalized arerial inersecions wih cenral medians and wo o hree lanes per approach. INTERSECTION 168 INTERSECTION 243 Ineres area Occupied area Green area River INTERSECTION 250 N N N Figure 2 Seleced Inersecions and Area of Ineres. Areas of ineresed have been defined for every inersecion o encompass he average queue lengh measured from he sop line for every approach during peak (7:00AM-9:00AM) and offpeak (9:00AM-11:00AM) periods. The average queue lengh obained from SCOOT/ASTRID hisorical daabase ranged from: 140 o 150 meers on Inersecion #168; 90 o 160 meers on Inersecion #243; and 80 o 200 meers on Inersecion #250. 6

7 Crash Daa for Areas of Ineres In his sudy, hree years of acciden daa ( ) were colleced from he municipal acciden informaion sysem (SIAT-FOR) o be compared o he simulaed SPM. A series of filers were hen applied o selec rear-end crashes only, ime of he analysis, vehicle ype and spaial configuraion of he observed collisions. In order o minimize random flucuaions due o differen driving behavior observed on weekends, accidens recorded on Saurdays and Sundays have been removed from he daase. An imporan aspec observed in many Brazilian ciies is he considerable use of moorcycle for commercial purposes. This inroduces a significan number of collisions involving hose users ha may no be adequaely represened in microscopic raffic algorihms; herefore his ype of crash was also removed from he daase. Finally, o consider arge accidens wihin he areas of ineress, wo ypes of acciden locaion have been invesigaed, as follows: 1) Accidens wihin inersecion area and 2) Accidens wihin he area encompassed by he average queue lengh (segmens). To idenify he acual locaion of accidens observed on segmens wo ypes of informaion have been applied: he building number as recorded by he police and reference poins provided by he SIAT sysem. Table 2 presens a summary of he recorded and valid crashes for he hree years of he analysis. Table 2 Toal of recorded and valid crashes ( ) # TOTAL OF CRASHES # REAR END CRASHES INT 168 Peak INT 168 Off-peak INT 243 Peak INT 243 Off-peak 9 4 INT 250 Peak INT 250 Off-peak Geomeric and Traffic Aribues The geomeric aribues for nework coding were colleced using he sofware Google Earh and complemened by field measuremens o confirm geomeric aspecs such as he number and lane widh, cenral median widh and inersecion angles. The basic raffic inpu daa obained from he adapive raffic conrol sysem (ATCS) SCOOT/ASTRID daabase include average raffic flow aggregaed over 15 minues per approach, cycle lengh and average delay. Table 3 presens a sample of he raffic aribues as obained from he ATCS for inersecion #168. Inersecion approach Table 3 Sample of raffic aribues for inersecion #168 Average Average Day Dae Sar Time End Time Flow Delay (dd-mmm-yyyy) (hh:mm) (hh:mm) (veh/h) (veh) 7 Average Vehicle Delay (s) 00168:a FR 6-Mar :00 07: :a MO 9-Mar :00 07: :a TU 10-Mar :00 07: :a WE 11-Mar :00 07:

8 The daase used for esimaing raffic aribues was obained from a sample of 80 ypical days from he year of Similar o he collision daase, he raffic sample was filered and compiled for he monhs, days and hours of he sudy period. Addiionally he daase was saisically reaed o idenify ouliers and missing observaions using box plo ools as proposed by Oliveira (2004). Using ATCS CCTV cameras, four hours of raffic survey (7:00AM - 11:00AM) were performed for each inersecion o esimae he percenage of heavy vehicles (rucks and buses), as well as raffic direcional spli. Table 4 presens a summary of he operaional aribues used for he seleced inersecions on he simulaion experimen. Flow Peak (veh/h) Table 4 Summary of he Traffic Aribues Inpu Flow Off-peak (veh/h) Movemen (%) Lef Fron Righ Trucks and Buses (%) Cicle Time Peak (s) Cicle Time Off-peak (s) 00168:a :b :c :d :a :c :d :a :b :c :d Plaform for Esimaing Safey Performance Measures The simulaion plaform for esimaing safey performance measures used in his research (VISSIM ) is based on psychophysical driving algorihms. In paricular, VISSIM s carfollowing model considers four ypes of regimes where drivers adjus heir desired spacing and speeds hrough changes in heir acceleraion/deceleraion raes. I has been recognized ha despie is limiaions o reflec real crashes, hese algorihms are able o generae a large variey of driving ineracions reflecing a considerable heerogeneiy in he raffic sream (FHWA, 2003; Archer, 2005; Cuno, 2008). Geomery and raffic aribues were coded in VISSIM for every inersecion during he wo hours peak and off-peak periods. The average raffic flow for every approach was considered a 15 minues inervals (8 inervals for each period) o accoun for raffic variabiliy using he informaion described in he previous secion. Cuno and Saccomanno (2008) presen a sudy for calibraing and validaing VISSIM carfollowing, gap-accepance, and lane-change parameers based on observed CPI as obained from vehicle racking daa. The resuls of his calibraion/validaion exercise yielded bes esimae values for hose inpus ha were found o be saisically significan in explaining safey 8

9 performance measures as obained from he simulaion. These values were assumed for his research and are found summarized in Table 5. VISSIM defaul values were used for hose inpus no found o be saisically significan for simulaing safey performance. Table 5 Calibraed VISSIM inpu parameers (Cuno, 2008) Inpu parameer Calibraed Descripion Desired deceleraion 2.6 Maximum deceleraion (m/s2) drivers are willing o apply in normal (no emergency) siuaion CC0 3,0 Sandsill disance (m); defines he desired disance beween sopped cars CC1 1,5 Headway ime (s); defined as he minimum ime a driver wans o keep from he lead vehicle; he higher he value, he more cauious he driver; CC0 and CC1 are combined o express he safey disance A oal of six simulaion scenarios, wo for each inersecion has been considered. For each inersecion scenario 10 simulaion runs were performed using differen number seeds o esimae he variabiliy among TTC, DRAC and CPI measures. Individual vehicle informaion o esimae SPMs, such as vehicle coordinaes, vehicle ype, speed, lengh, acceleraion/deceleraion rae, headway, leading vehicle, preceding vehicle and ohers, have been recorded for every 0.1second ime inerval. These individual vehicle variables were compiled and processed using a visual basic applicaion o obain esimaes of TTC, DRAC and CPI for every 0.1 seconds and recording raffic conflics as described earlier in he manuscrip. SIMULATION RESULTS For his validaion exercise, he average number of rear-end conflics resuling from 10 simulaion runs using differen number seeds for each scenario (2 hours peak and off-peak period) was compared o rear-end crashes recorded for he same wo hours inervals during hree years ( ) for each inersecion. The average number of conflics was normalized o provide an esimae of he oal number of conflics for he same ime period of he crash daa (739 days). Table 6 presens he number of observed crashes and respecive average number of conflics and conflic/flow raio for each SPM, followed by he average raffic flow and he flow of simulaion. Scenario Table 6 Number of crashes, average flow and average simulaion resuls # Crashes Average flow (veh/h) #Simulaed vehicles # Conflics (hree years) # Conflics/vehicle (x10³) (coefficien of variaion) TTC DRAC CPI TTC DRAC CPI INT#168 Peak (0.06) 5.0 (0.15) 0.5 (0.53) INT#168 Off-peak (0.06) 4.7 (0.16) 0.6 (0.44) INT#243 Peak (0.11) 3.9 (0.13) 0.2 (1.08) INT#243 Off-peak (0.09) 4.8 (0.13) 0.3 (0.73) INT#250 Peak (0.07) 7.6 (0.08) 1.1 (0.38) INT#250 Off-peak (0.05) 6.9 (0.08) 1.1 (0.33) 9

10 In he analysis for peak and off-peak periods i has been noed ha he apparen decrease observed in acciden daa was no direcly refleced on he number of conflics regardless of he SPM esed. Simulaed conflics appear o be consisen wih small changes presened in raffic flows beween peak and off-peak scenarios (50 o 221veh/h) alhough hese indicaors did no adequaely reproduced he downward rend in collisions as saed before. Par of his inconsisency can be accredied o he rare random naure of accidens as well as o he somewha simplified simulaion environmen. When comparing he hree SPM i can be noed ha TTC and DRAC hresholds (1.5s and 3.35m/s 2, respecively) yielded considerably more vehicles in conflics when compared o CPI. Furhermore, he resuls have indicaed ha CPI based conflics presened he highes variabiliy among he indicaors. This variabiliy can be aribued o he fac ha his indicaor has wo sochasic componens, he firs being associaed wih he process of generaion of vehicles in he simulaion (random seed generaion) and second associaed wih he disribuion for MADR shown in Table 1. A paired -es showed no saisical difference for any of he indicaors beween peak and offpeak periods. In his case, anoher possible analysis can be done by esimaing he conflic/flow raio o he combined peak and off-peak periods (Table 7). Table 7 Number of crashes and average simulaion resuls combined scenarios # Crashes #Simulaed # Conflics/vehicle (x10³) vehicles TTC DRAC CPI INT# INT# INT# The comparaive analysis beween inersecions suggess a fairly reasonable consisency beween he esimaed numbers of conflics and observed number of crashes. In general, higher levels of observed crashes have implied on higher number of raffic conflics for all he hree esed SPM. Similar rend has been observed wih respec o average flow, crashes and SPM, hus reinforcing he generally acceped noion ha accidens and raffic conflics end o increase wih exposure. The resuls from Table 7 also sugges ha Inersecion #243 presened he lowes number of conflics per vehicle regardless he safey indicaor when comparing o he oher inersecions. This can be explained by wo facors, namely: 1) The exisence of only hree approaches a Inersecion #243 resuling in less rear-end ineracions a he sudy area; and 2) There is a proeced righ-urn movemen (island) on he souhbound herefore resuling on a lower number of rear-end ineracion on ha approach. CONCLUDING REMARKS This paper presened a validaion effor beween observed rear-end collisions and simulaed raffic conflics as refleced by hree Safey Performance Measures (SPM), namely: Time o Collision (TTC), Deceleraion Rae o Avoid he Crash (DRAC) and Crash Poenial Index (CPI). Three isolaed signalized arerial four-legged inersecions from Foraleza ciy, Brazil 10

11 were seleced for his sudy. Three years of acciden daa ( ) for he morning peak (7:00AM - 9:00AM) and off-peak (9:00AM - 11:00AM) periods were compared o esimae he number of raffic conflics as obained by a microscopic simulaion experimen. The resuls sugges ha simulaed SPM did no reflec he apparen decrease in observed rear-end crashes for peak and off-peak periods. This migh be due o he inherenly rare random naure of raffic accidens which causes considerable overdispersion in raffic couns and he somewha simplified microscopic environmen provided by curren algorihms. On he oher hand, he all esed SPM were capable of capuring differences in he number of accidens among he hree differen sies. Anoher imporan facor in he analysis was he behavior of he CPI index which had lowes number of conflics beween he hree indicaors. This resul can be credied wih he fac ha he calculaion of his indicaor is influenced by wo disinc random componens. Addiionally, CPI was found o presen he highes variabiliy among he esed measures, hus, i is expeced ha when using CPI one may need o increase he number of simulaions on he experimen o obain meaningful resuls. The overall resuls indicae a poenial for applicaion of microscopic simulaion ool for analyzing he performance of road safey. I is recommended however o expand he number of inersecions and he period of analysis as well as o consider oher componens such as he presence of parking los and a wider range of vehicle ypes. Anoher imporan aspec o be considered is he use of safey performance models o provide beer esimaes of he expeced number of crashes o every inersecion hus reducing he naural overdispersion found on hisorical crash daa. ACKNOWLEDGEMENTS The auhors would like o acknowledge he Brazilian Council for Scienific and Technological Developmen (CNPq) for funding his research and Mr. David Duong for providing valuable commens and suggesions o his manuscrip. REFERENCES Archer, J. (2000). Developing he poenial of micro-simulaion modelling for raffic safey assessmen. In Proceedings of he 13 h ICTCT Workshop. Archer, J. (2005). Indicaors for raffic safey assessmen and predicion and heir applicaion in micro-simulaion modelling: A sudy of urban and suburban inersecions. PhD hesis, Royal Insiue of Technology. Barceló, J., Dumon, A., Monero, L., Perarnau, J. and Torday, A. (2003). Safey indicaors for microsimulaion based assessmens. In 82 nd Annual Meeing of he Transporaion Research Board. 11

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13 Van der Hors, A.R.A. (1990). A Time-based Analysis of Road User Behaviour in Normal and Criical Encouners. PhD hesis, Delf Universiy of Technology, Xin, W., Hourdos, J., Michalopoulos, P. and Davis, G. (2008). The less han-perfec driver: A model of collision-inclusive carfollowing behavior. In Proceeding of he 87 h Annual Meeing of he Transporaion Research Board. 13