Itersectios Cotrol ad Safety 143 Traffic coflicts at roudabouts: risk aalysis uder car-followig coditios G. Guido, A. Vitale & V. Gallelli Departmet of Tow ad Coutry Plaig, Uiversity of Calabria, Italy Abstract Roudabouts have had a remarkable spread sice the 80s of the twetieth cetury, especially i Europe. Compared to the covetioal itersectio s layout, traffic cotrol systems based o roudabouts are suitable for improvig road safety ad urba desig. Nevertheless, much research has addressed ivestigatig safety issues related to the traffic coflicts of iterestig roudabouts traffic flows. The focus of this paper is o the aalysis of safety levels at roudabouts as regards the rear-ed vehicles iteractios i carfollowig coditios. Levels of safety are evaluated o the basis of a traffic coflict techique applied to vehicles trajectories obtaied experimetally from a frame-by-frame aalysis of video-taped traffic data. I order to estimate traffic coflicts, reactios of followig vehicles were observed at a roudabout case study, ad the were compared to the estimated oes obtaied from a carfollowig model, based o a properly calibrated stimulus-respose fuctio. Keywords: driver behaviour, roudabout, car-followig, road safety. 1 Itroductio Itersectios ca be cosidered as the most sesible part of the road etwork due to the fact that itersectio accidets costitute a sigificat portio of total crashes [1]. I may coutries i the world, i order to icrease road safety ad capacity at the same time, may itersectios have recetly bee coverted ito roudabouts. Roudabouts, ideed, elimiate or chage the dyamics of coflict types, reducig crash severity ad drivers speeds [2]. Therefore, more studies ad research i this sector could provide additioal iformatio o the safety o roudabouts, ad, cosequetly, suggest helpful solutios for plaers ad doi:10.2495/978-1-84564-764-3/ WIT Trasactios o State of the Art i Sciece ad Egieerig, Vol 6, 6 013
144 Itersectios Cotrol ad Safety desigers i idetifyig existig deficiecies ad i refiig their desig cocepts. This paper presets a risk aalysis at a roudabout with particular attetio to rear-ed iteractios amog vehicles. With the help of a video image processig techique ad a frame-by-frame aalysis, more tha 500 trajectories were observed at a roudabout case study, determiig the istataeous speed ad acceleratio of vehicles. This trajectories sample allows the authors to calibrate a car-followig model able to replicate rear-ed iteractios of the traffic stream. For each couple of vehicles (lead ad followig vehicle) a risk aalysis was performed usig traffic coflict techique [3 6]. I particular, for each couple of lead ad followig vehicles Deceleratio Rate to Avoid the Crash (DRAC) was determied, idetifyig potetial coflict scearios. Fially, the authors compare the coflict scearios derived from the direct observatio of vehicles maoeuvres with those obtaied applyig a properly calibrated car-followig model. 2 State of the art of car-followig models I car-followig theory, the followig vehicle (fv) decelerates or accelerates as a respose of the stimulus iduced by leadig vehicle (lv). The differet models vary accordig to the defiitio of the stimulus that, geerally, may iclude the velocity ad the acceleratio of the lv, the relative velocity ad spacig betwee lv ad fv. Chadler et al. [7] formulated a first car-followig model i which the stimulus is specified as the relative velocity betwee lv ad fv. The fuctioal form of the model is: frot a V (1) where, = perceptio time of driver ; a (t) [respose] = acceleratio applied by driver at time t; V frot (t- ) [stimulus] = speed differece betwee user ad the precedig vehicles i the same lae at time t- ; [sesitivity] = costat. O the basis of this first formulatio, Gazis et al. [8], i 1959, suggested a model takig ito accout the relative spacig betwee two successive vehicles: frot a t V X (2) where, X (t- ) is the relative spacig betwee lv ad fv at time t-. I 1960, Edie [9] modified the model cosiderig that the velocity of vehicle itself iflueces driver behaviour. I cosequece, the model ca be more geerally expressed as: a t V frot V t (3) X t WIT Trasactios o State of the Art i Sciece ad Egieerig, Vol 66,
Itersectios Cotrol ad Safety 145 where, V (t) speed of the driver at time t-. May calibratios of the model were carried out from 1959 [10,11], usig various approaches ad o differet scales (microscopic ad macroscopic). Therefore, the formulatios defied by Chadler et al. [7] ad by Gazis et al. [8] ca be cosidered special cases derived from the above-metioed model. The recet developmets i sesor techologies led to the defiitio of more geeral models ad differet combiatios of ad [12 14]. I 1996, Subramaia [15] proposed a formulatio based o the GMN model, i which a radom term appears associated with the -th user at time t. This term is ormal distributed while perceptio ad reactio time is cosidered as a radom variable trucated logormal distributed: a t V frot V (4) X t I 1999, Ahmed [16] formulated a ew expressio of the GMN model, cosiderig the effect of flow s desity (K (t- )) i the sesitivity fuctio ad suggestig a o-liear relatioship betwee acceleratio ad the stimulus fuctio (V frot (t- )). a t V frot K t V t (5) X t i which ((0;1)) is a parameter that describes the -th user s perceptio of the cogestio level. Besides the above-described models, based o the stimulus-respose fuctio, there are other types of car-followig models, some of them based o the cocept of brakig distace [17 19], as well as models based o liear relatios [20 23], psychophysical models [24 27], models based o fuzzy logic [28 31], ad other models based o ITS systems [32 34]. 3 Aalysis of traffic coflicts uder car-followig coditios: case study Traffic flow was aalysed at a roudabout placed ear the motorway turoff of Coseza, a medium-sized tow i souther Italy, i order to calibrate the GMN car-followig model revised by Subramaia [15], ad evaluate the potetial coflict scearios for rear-ed vehicles iteractios. 3.1 Data collectio The test area is close to the Coseza North motorway turoff, which is a importat ode i the local road etwork because of the presece, i the eighbourhood, of the Arcavacata Uiversity campus, the most importat regioal uiversity complex. Cosiderable traffic flows use this roudabout, WIT Trasactios o State of the Art i Sciece ad Egieerig, Vol 66,
146 Itersectios Cotrol ad Safety because it is located alog the oly corridor that coects both the railway statio ad the highway with the uiversity campus. The geometric features of the itersectio have bee obtaied by prelimiary surveys: this is a sigle-lae roudabout (the iscribed circle diameter varies betwee 68 ad 80 meters) with four etries. Afterwards the roudabout was video-taped by a camera durig the afteroo peak hour, betwee 1:00 pm ad 2:00 pm. This survey allowed us to obtai the O/D matrix durig the peak hour, to idividuate the busiest etries of the roudabout ad to evaluate the traffic flow i the circulatory roadway (Figure 1). Figure 1: Traffic flows (veh/h) durig peak hour. The car-followig coditios occur for distaces of less tha 75 metres i accordace with the theory of Ayci ad Beekohal [35]; ideed, for distaces greater tha this critical value, user behaviour is ot iflueced by precedig vehicles i the same lae. The roudabout moitored was divided ito further truks i order to determie the most importat parameters for the defiitio of the car-followig model. The aim of this discretizatio is to carry out the istataeous dyamic features of each vehicle. The followig data were extracted from the recordig stage: V (t), speed of the user (fv) at istat t; V (t- ), speed of the user (fv) at istat t- ; V -1 (t- ), speed of the user s predecessor (lv) at istat t-. WIT Trasactios o State of the Art i Sciece ad Egieerig, Vol 66,
Itersectios Cotrol ad Safety 147 I order to determie the perceptio ad reactio time () of the users, it was used a experimetal relatioship suggested by Italia rules [36], i which: V 2.8 0. 01 (6) The determiatio of the reactio (acceleratio or deceleratio) applied by the - th user at istat t was carried out usig the followig equatio: a t V V 3.2 Data aalysis ad calibratio of the model (7) The aalysis of the trajectories recorded through the video-tapig stage suggested that a higher percetage of the maoeuvres were carried out i deceleratio coditios, hece the authors calibrated a geeral deceleratio model i car-followig coditios. A statistical aalysis was carried out to determie the correlatio amog the observed parameters useful to describe the car-followig model. The deceleratio applied by the -th user at istat t proved to vary liearly both with velocity V ad with V, whereas the relatioship betwee the same parameter (a ) ad the distace headway X is better characterized by a expoetial fuctio (Equatios (8), (9) ad (10)). a a a t X 2.004 0. 062 V (8) 0.026 0. 065 V (9) 1.436 exp 0. 041 (10) The parameters of the model (α, β, γ) were estimated through the Noliear Least Square Aalysis, whose umerical solutio was provided by the damped least-squares (DLS) method, or Leveberg-Marquardt algorithm. The geeral expressio of the model assumes the followig shape: a t 2.498 V frot 0.001 V (11) 0. X t 481 The calibratio of the model shows that parameters ad have order of magitude correspodig to that obtaied by other studies [12, 15, 16, 37]. Differeces i the estimatio ca be ascribed to differet calibratio ad testig cotexts. Ideed, almost all the car-followig models are calibrated o straight stretches of road, i which drivers behaviour is differet from that observed at roudabouts. Radom terms of the model ( (t)) are ormally distributed with a mea equal to -0.047 (m/s 2 ) ad stadard deviatio equal to 0.237 (m/s 2 ). Further iformatio about the model ad the estimated parameters are described i Guido ad Vitale [38]. WIT Trasactios o State of the Art i Sciece ad Egieerig, Vol 66,
148 Itersectios Cotrol ad Safety 3.3 Risk aalysis I order to estimate traffic coflicts, reactios of followig vehicles were observed i specified sectios of the roudabout ad the were compared to the estimated oes obtaied from the model. These reactios, expressed i terms of deceleratio rate, were aalyzed o the basis of the expected values of Deceleratio Rate to Avoid the Crash (DRAC). DRAC was defied i terms of the speed differetial betwee followig vehicle ad lead vehicle divided by their closig time [39], ad for rear-ed iteractios this ca be expressed as: V 1 X t L 1 V DRAC t (12) DRAC values were classified accordig to Hydé [40] to idetify brakig levels ad verify if the observed ad the estimated reactios were properly applied by users. Therefore, six coflict levels were established depedig o DRAC values: 1) DRAC equal to 0 m/s 2 evasive actio ot ecessary; 2) DRAC ragig from 0 to 1 m/s 2 adaptatio ecessary; 3) DRAC ragig from 1 to 2 m/s 2 reactio ecessary; 4) DRAC ragig from 2 to 4 m/s 2 cosiderable reactio ecessary; 5) DRAC ragig from 4 to 6 m/s 2 heavy reactio ecessary; 6) DRAC greater tha 6 m/s 2 emergecy reactio ecessary. No coflict is expected for the first two levels. Table 1 shows the umber ad the percetage of vehicles that applied observed ad estimated reactios accordig to the expected levels of DRAC. 2 Table 1: Number ad percetage of vehicles accordig DRAC ad observed/estimated reactios. Level of coflict DRAC (m/s 2 ) # veh. 1 % veh. 2 # obs. veh. 3 % obs. veh. 4 # est. veh. 5 % est. veh. 6 1 2 1 Number of vehicles havig DRAC accordig to coflict levels. 2 Percetage of vehicles havig DRAC accordig to coflict levels. 3 Number of observed vehicles applyig deceleratio accordig to coflict levels. 4 Percetage of observed vehicles applyig deceleratio accordig to coflict levels (colum five/colum three). 5 Number of estimated vehicles applyig deceleratio accordig to coflict levels. 6 Percetage of estimated vehicles applyig deceleratio accordig to coflict levels (colum seve/colum three). WIT Trasactios o State of the Art i Sciece ad Egieerig, Vol 66,
Itersectios Cotrol ad Safety 149 A first observatio cocers the high percetage of observed vehicles (94.31%) that are ot i traffic coflicts accordig to DRAC classificatio above described; however, 93.21% of vehicles should adapt their coditio to the leader vehicles behavior. The differece foud betwee the observed ad the estimated umber of vehicles havig deceleratio ragig from 0 to 1 m/s 2 is justified cosiderig the fact that the lower limit of this level of coflict is equal to 0 m/s 2, ad may observed reactios (acceleratios ad deceleratios) are close to this value. Therefore, the model provided reactios with more occurreces of deceleratio compared to those observed, eve if the average reactios values are close to the real oes. It should also be emphasized that model replicates well the expected reactios based o the DRAC values. Ideed, for the secod level of coflict (DRAC ragig from 0 to 1 m/s 2 ), the model forecasts reactios of followig vehicles i terms of deceleratio with a percetage equal to 71.46%, while oly 22.44% of observed users react applyig deceleratio, although a ecessary adaptatio is expected [40]. Cocerig the levels of coflict 3, 4, 5 ad 6, there are o appreciable differeces betwee the observed values ad the estimated oes. 4 Coclusios The aalysis of safety at a roudabout itersectio was performed o the basis of traffic coflict techique. Rear-ed vehicles iteractios were evaluated from a frame-by-frame aalysis of a video-taped sample of trajectories. This aalysis allowed the authors to calibrate a car-followig model able to replicate rear-ed iteractios of the traffic flow. The calibrated behavioural model provided estimates of the users reactio to a stimulus produced by the precedig vehicles i the traffic stream. Furthermore, followig ad lead vehicles pairs were idetified from the observed trajectories to assess coflict levels accordig to Deceleratio Rate to Avoid the Crash, a surrogate safety performace measure based o the differetial speeds ad spacig associated with each vehicle s pair. I car-followig coditios, potetial coflict scearios occur whe the followig vehicle reacts with a deceleratio lower tha a threshold correspodig to a certai value of DRAC. However, the authors classified the levels of coflict o the basis of DRAC [40], ad established whether drivers should have applied a suitable reactio. Coflict scearios derived from the direct observatio of vehicles reactios were compared with those obtaied applyig the carfollowig model. From the aalysis it emerged that 94.31% of observed vehicles were ot i traffic coflicts accordig to DRAC classificatio, ad o reactio was expected, but 93.21% of vehicles should have adapted their coditio to the leader vehicles behavior beig i secod level of coflict. For DRAC ragig from 0 to 1 m/s 2 the model forecasts that vehicles adapt their movemet with more occurreces of deceleratio compared to those WIT Trasactios o State of the Art i Sciece ad Egieerig, Vol 66,
150 Itersectios Cotrol ad Safety observed; however, sice o coflict is expected, observed drivers apply their adaptatios with safety margi. Regardig the levels of coflict requirig reactios (levels 3 to 6), there are o appreciable differeces betwee the observed umber of vehicles reactig ad the estimated oes. Future developmets of the research could be addressed to the trasferability of the car-followig model ad to the aalysis of differet roudabout s cofiguratios i order to better ivestigate safety issues ad, cosequetly, suggest helpful solutios for plaers ad desigers. Refereces [1] Neuma, T.R., Pfefer, R., Slack, K.L., Hardy, K.K., Harwood, D.W., Potts, I.B., Torbic, D.J. ad Kohlma Rabbai, E.R., NCHRP Report 500: Guidace for Implemetatio of the AASHTO Strategic Highway Safety Pla, vol. 5: A Guide for Addressig Usigalized Itersectio Collisios. Trasportatio Research Board, Washigto, DC, 2003. [2] FHWA, Roudabouts: A Iformatioal Guide. Publicatio FHWA-RD- 00-067, Washigto, DC, 2000. [3] Guido G., Saccomao F.F., Vitale A. ad Cuto F., Comparig Safety at Sigalized Itersectios ad Roudabouts Usig Simulated Rear-Ed Coflicts, Trasportatio Research Record, Joural of the Trasportatio Research Board, Vol. 2078, pp. 90 95, 2008. [4] Guido G., Saccomao F.F., Vitale A., Astarita V. ad Festa D.C., Comparig safety performace measures obtaied from video capture data, Joural of Trasportatio Egieerig, ASCE, Vol. 137, N 7, pp. 481 492, 2011. [5] Guido G., Astarita V., Giofrè V. ad Vitale A., Safety performace measures: a compariso betwee microsimulatio ad observatioal data, Procedia Social ad Behavioral Sciece, 20, pp. 217 225, 2011. [6] Praticò F. G., Vaiaa R. ad Gallelli V., Trasport ad traffic maagemet by micro simulatio models: operatioal use ad performace of roudabouts, Urba Trasport 2012, WIT Press, ISBN: 978-1-84564-580-9. DOI: 10.2495/UT120331, A Coruña, Spai, 2012. [7] Chadler R., Herma R., ad Motroll E., Traffic dyamics; studies i car followig, Operatios Research 6, 165+, 1958. [8] Gazis D., Herma R. ad Potts B., Car-followig theory of steady state traffic flow, Operatios Research 9, 449+, 1959. [9] Edie L. C., Car followig ad steady state theory for o-cogested traffic. Operatios Research, 9(1), pp. 66 76, 1961. [10] Herma R., Motroll E. W., Potts B. ad Rothery R. W., Traffic dyamics: aalysis of stability i car followig, Operatios Research, 7, pp. 86 106, 1959. [11] Motroll E.W., Acceleratio ad clusterig tedecy of vehicular traffic, i Proceedigs of the Symposium o Theory of Traffic Flow, Research Laboratories, Geeral Motors, pp. 147 157, New York: Elsevier, 1959. WIT Trasactios o State of the Art i Sciece ad Egieerig, Vol 66,
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