Simulated safety performance of rear-end andangled vehicle interactions at isolatedintersections

Flavio Cunto and Frank F. Saccomanno

Abstract: This paper applies a calibrated microscopic simulation model to assess the safety implications of signalizationat a stop-controlled isolated intersection. Safety performance is measured in terms of a crash potential index (CPI) thatmakes use of time-specific vehicle parameters, such as deceleration rates, spacing, and speed profiles. Four performancemeasures are obtained: (i) average CPI/vehicle, (ii) CPI 85th percentile, (iii) number of vehicles with CPI > 0 (defined asinteracting), and (iv) number of conflicts (defined in terms of a given CPI threshold). Two types of interactions are consid-ered, namely rear end and angled. For rear-end interactions, CPI/vehicle was found to be significantly higher following theintroduction of fixed signal controls. For angled interactions, CPI/vehicle was found to decrease with signalization. Forboth types of interactions, the CPI 85th percentile was found to decrease nonlinearly with signalization, especially forhigher assumed volumes on the major approach. Rear-end vehicle interactions increased significantly following signaliza-tion and with increasing volume, whereas no such increase was observed for angled interactions. The key observation isthat the number of vehicles subject to angled interactions was found to decrease after signalization.

Key words: safety performance, microscopic simulation, signalized and stop-controlled intersections.

Resume : Cet article applique un modele de simulation microscopique etalonne pour evaluer les implications de securited’une signalisation a un carrefour isole controlee par un arret. Le rendement en matiere de securite est mesure en termesd’indice potentiel de collision (« CPI ») qui utilise des parametres temporels des vehicules tels que les taux de decelera-tion, l’espacement et les profils de vitesse. Quatre mesures du rendement ont ete obtenues : (i) CPI moyen par vehicule,(ii) 85e percentile du CPI, (iii) le nombre de vehicules ayant un CPI > 0 (definis comme interdependants), et (iv) le nom-bre de conflits (defini en termes d’un CPI seuil donne). Deux genres d’interactions sont consideres : par l’arriere et a an-gle. Le CPI/veh. pour les interactions par l’arriere s’est grandement accru apres l’introduction de controles de signauxfixes. Le CPI/veh. pour les interactions a angle diminuait avec la signalisation. Pour les deux types d’interactions, le 85e

percentile du CPI diminuait de maniere non lineaire avec la signalisation, surtout pour les volumes de trafic presumes pluseleves dans l’approche majeure. Les interactions entre vehicules par l’arriere ont augmente considerablement apres la miseen place de la signalisation et avec un volume de trafic superieur; cette augmentation n’a pas ete observee pour les inter-actions a angle. L’observation principale est que le nombre de vehicules sujets a des interactions a angle a diminue apresla mise en place de la signalisation.

Mots-cles : rendement en securite, simulation microscopique, carrefours signales et controles par un arret.

[Traduit par la Redaction]

IntroductionA number of recent studies of crashes for North American

urban roads suggest that over 50% of these reported crashestake place in proximity to intersections. Intersections present

special safety concerns because of unsafe driver actions andmanoeuvres that result in conflicts that could lead tocrashes.

According to the U.S. Federal Highway Administration(FHWA 2004), approximately 3.2 million intersection-re-lated crashes took place in 2002 in the United States, withestimated costs to society in excess of US$100 billion. Thehigh cost of crashes at intersection locations provides strongjustification for the development and implementation ofcost-effective and practicable countermeasures. The micro-scopic model described in this paper serves as an objectivescientific platform for guiding decisions on what type ofcountermeasure to consider, examining the effectiveness ofsuch countermeasures under different traffic conditions, andsuggesting when such countermeasure should be introducedat a given intersection. A number of traffic control strategiescan be considered for stop-controlled intersections, includingsignalization, improvements in signal timings, signage, pri-oritization of movements, and changes in posted approach

Received 18 June 2008. Revision accepted 2 June 2009.Published on the NRC Research Press Web site at cjce.nrc.ca on17 November 2009.

F. Cunto.1 Department of Transportation Engineering,Universidade Federal do Ceara, Campus do Pici S/N, Bloco 703,Departamento de Engenharia de Transportes – CT, CEP.:60.455-760, Fortaleza, CE, Brazil.F.F. Saccomanno. Department of Civil and EnvironmentalEngineering, University of Waterloo, 200, University StreetWest, Waterloo, ON N2L 3G1, Canada.

Written discussion of this article is welcomed and will bereceived by the Editor until 31 March 2010.

1Corresponding author (e-mail: flaviocunto@det.ufc.br).

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speeds. The focus of interest in this paper is on the introduc-tion of fixed signal controls.

A number of researchers have investigated the relation-ship between traffic control and crashes at intersections(Pernia et al. 2002; Abdel-Aty et al. 2005; Hadayeghi et al.2006). Due to a myriad of methodological and empiricalproblems, these studies have not provided the objective plat-form needed for informing decisions as follows: (i) Whenshould such controls be introduced? (ii) What form shouldthese controls take? and (iii) What are the costs and poten-tial safety benefits of these controls?

A major FHWA report authored by Gettman and Head(2003) investigated the feasibility of adopting a microscopicsimulation approach. One of the most attractive features ofmicroscopic simulation models is their potential for investi-gating different safety intervention strategies in a ‘‘virtualworld’’ without incurring high implementation costs or caus-ing traffic disruptions. In general, the use of microscopicsimulation for safety assessments is based on measures ofsafety performance, also known as proximal safety indica-tors or surrogate safety measures. These indicators are de-fined to reflect high-risk events in relation to a projectedpoint of collision based on pairwise vehicular velocity andspacing attributes. The use of safety performance measuresalso constitutes in essence a proactive approach to roadsafety studies because it can detect safety problems whetheror not they result in a subsequent crash (Barcelo et al. 2003;Archer 2005).

Several measures of individual vehicle safety performancecan be extracted from simulation, and these include time-to-collision (TTC), extended time-to-collision (TET), posten-croachment time (PET), and initial deceleration rate (DR)(Hayward 1971; Minderhoud and Bovy 2001; Gettman andHead 2003; Huguenin et al. 2005).

In this paper, a microscopic simulation model has beendeveloped to investigate the safety implications of introduc-ing fixed signal control at a stop-controlled intersection fordifferent traffic conditions. The essence of this model is theuse of vehicle-specific measures of safety performance ob-tained from microscopic traffic algorithms (car following,gap acceptance, and lane changing) to evaluate alternativecountermeasures.

Microscopic simulationThe initial step in the simulation of safety performance is

to choose a simulation platform capable of representing in acomprehensive manner most aspects of driver behaviour, in-cluding late reaction, erroneous judgment of the actual speeddifferential, spacing, and deceleration rate.

Brackstone and McDonald (1999) and Mehmood (2003)presented a comprehensive review of existing car-followingmodels. They identified four types of models: stimulus–re-sponse, safety–distance, psychophysical or action point, andfuzzy logic based models. Psychophysical or action pointcar-following models are based on the assumption that adriver of the following vehicle would be able to ascertain ifhis (her) vehicle was approaching the lead vehicle bychanges in the apparent size of this vehicle and ascertainhis (her) relative speed by changes in the visual angle ofthe lead vehicle. The basic structure of these models was

found to be the most coherent and was best able to describethe natural everyday driver behaviour (Brackstone andMcDonald 1999; Xin et al. 2008). It should be noted that,although these models were not developed explicitly to pre-dict crashes, they can provide sound and accurate estimatesof safety performance.

The simulation model used in this paper is VISSIM ver-sion 4.3, distributed by PTV America. VISSIM is based onpsychophysical driving algorithms developed by Wiedemannand Reiter (1992), whose car-following model considersfour types of regimes where drivers adjust their desiredspacing and speeds through changes in their accelerationand deceleration rates. These four driver regimes are unin-fluenced driving, closing process, following process, andemergency braking (Fig. 1).

The transition between these regimes has been establishedin VISSIM for six different distance–speed thresholds: (i)AX — desired distance for standing vehicles (front-to-frontdistance); (ii) ABX — desired minimum following distanceat low speed differences; (iii) SDV — perception thresholdof speed difference at long distance; (iv) SDX — perceptionthreshold of growing distance in following process; (v)CLDV — perception threshold of small speed differences atshort, decreasing distances; and (vi) OPDV —perceptionthreshold for recognizing small speed differences at short,but increasing distances.

In the uninfluenced driving regime, the following driver istrying to reach the desired speed once there is no lead ve-hicle in a reasonable distance (150 m) or when the distanceis decreasing but the perception threshold of speed differ-ence at long distance (SDV) has not been achieved. Speeddifferential (DV) and spacing (DX) for this regime shouldsatisfy the following conditions: DV < SDV or DX >150 m at each time interval.

When both the distance between the lead and the followingvehicle is less than150 m and the SDV threshold has beensurpassed, the following driver enters the closing-processregime. In this regime, drivers realize that they areapproaching a slower vehicle and, after a given delay, be-gin to decelerate. At this point, drivers intend to decelerate,matching their own desired minimum following distance(ABX). The applied deceleration rate is based on the kine-matics equation for deceleration considering a moving tar-get. An additional error term is added to represent theerror of human estimation that varies for the same driverevery second and a parameter to account for the learningprocess, also updated each second.

In the following process, the following vehicle has almostthe same speed as that of the lead vehicle, and the followingdriver does not consciously react to movements of the leadvehicle. Acceleration and deceleration rates are applied in avery low oscillating level around the average value of0.2 m/s2. The transition from the closing process to the fol-lowing process happens when DV < SDX. The followingprocess is delimited by two perception thresholds for smallspeed differences at short, decreasing and increasing distan-ces (CLDV and OPDV) and two thresholds corresponding tothe minimum desired distance at low speed differences andthe perception of growing distance in the following process(ABX and SDX).

The emergency braking regime happens when drivers

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need to react to avoid a crash and to come back to a dis-tance greater than the minimum desired distance for stand-ing vehicles (AX). The transition to the emergency brakingsituation can happen either from the closing process or fromthe following process. If the vehicle is still in the closingprocess (i.e., DV > SDX) and the spacing between the leadand following vehicles becomes smaller than ABX, then theemergency braking regime begins.

If the vehicle is in the following regime and the lead ve-hicle brakes suddenly, leading to DV > CLDV and DX <ABX, then the emergency regime is also initiated.

The gap-acceptance behaviour for left-turn, right-turn, andcrossing manoeuvres was modeled using the ‘‘conflict area’’feature in VISSIM. Based on intersection geometric charac-teristics as defined by the user, VISSIM automatically de-tects overlapping areas (conflict areas) and the userestablishes which movement should yield the right-of-way.The driver in a lower priority approach evaluates gaps inthe main stream, the situation behind the conflict area, andthe current speed–acceleration profile of the main stream be-fore deciding to proceed or stop at the intersection. Unfortu-nately, there is little information about how the softwareperforms these tests.

Estimating safety performanceSafety-performance measures attempt to capture real-time

vehicle interactions in the traffic stream and hence explaintheir potential for crashes. Safety performance is a more in-clusive expression of high-risk driving behaviour than re-ported crash history, since it also accounts for near misses,which are indicative of lack of safety but do not result inactual crashes. A number of measures of safety performancecan be established, including time-to-collision (TTC), decel-eration rate to avoid the crash (DRAC), and postencroach-ment time (PET), among others (Gettman and Head 2003).

Gettman and Head (2003) and Archer (2005) have explic-itly recognized the relevance of DRAC as a safety–perform-ance measure that considers the role of speed differentialsand decelerations in potential crash occurrence. The conven-tional DRAC measure, however, fails to accurately reflecttraffic conflicts because it does not consider the vehicle’sbraking capability over time for prevailing road and trafficconditions. Hence, a desirable measure of safety perform-ance is one that includes both required deceleration ratesand braking capabilities for individual vehicles.

A crash-potential index (CPI) is established in this paperfrom the perspective of a driver in the traffic stream (re-sponse vehicle, RV) responding to a given stimulus providedby another vehicle (stimulus vehicle, SV). More precisely,CPI is defined in terms of the probability that the DRAC ex-perienced by a given RV exceeds its maximum availablebraking capability (MADR) for every 0.1 s of simulatedtime. DRAC is estimated for each time interval as a functionof the differential speed and spacing between SV and RV us-ing Newtonian physics. The SV is the vehicle responsible forthe initial action (braking for a traffic light – stop sign,changing lanes, and (or) accepting a gap), and the RV is thevehicle immediately affected by SV action and must respondto avoid dangerous interactions. It is worth noting that an RVresponse, whether braking or changing lanes, can also workas a stimulus for the subsequent vehicle in the simulation.

The CPI expression used in this analysis is of the follow-ing form:

½1� CPIi ¼

Xtfi

t¼tii

P�

MADRða1;a2;:::anÞ < DRACi;t

�Dtb

Ti

where CPIi is the crash-potential index for RV i;MADRða1;a2;:::anÞ is a random variable following a normaldistribution according to the vector of traffic and environ-mental attributes a1, a2, . . ., an; DRACi,t is the decelerationrate to avoid the crash for RV i during time interval t; tii isthe initial simulated time interval for RV i; tfi is the finalsimulated time interval for RV i; Dt is the simulation timeinterval (s); b is a state variable (b = 1 if RV is approachingSV (interaction), otherwise b = 0); Ti is the total simulatedtime for vehicle i (s).

A number of other safety-performance measures can beestablished using the CPI expression given by eq. [1]. Onesuch measure is vehicle interaction, defined as the situationwhere a stimulus is presented to the RV such that braking isrequired to avoid a future collision (CPI > 0). In this case,CPI is estimated assuming MADR to be normally distrib-uted, with an average value of 8.45 m/s2 and a standard de-viation of 1.40 m/s2. These values were obtained from fieldtests for different vehicles with initial speeds from 80 to 100km/h coming to a full stop (MOVIT 2006; Neilsen 2007).

Vehicle conflicts, on the other hand, are a subset of inter-actions such that DRAC exceeds MADR. For conflicts, indi-vidual values of MADR are assigned to individual vehiclesentering the simulation, and a conflict is ascribed everytime interval DRAC exceeds MADR. To avoid negativeand unrealistic values of MADR, the normal distributionwas truncated to minimum and maximum values of MADRof 4.2 and 12.7 m/s2, respectively.

Since safety performance in this paper is measured interms of rear-end and angled interactions, separate expres-sions for DRAC need to be defined. For rear-end vehicle in-teractions, DRAC can be expressed as

½2� DRACREARRV;tþ1 ¼

ðVRV;t � VSV;tÞ22½ðXSV;t � XRV;tÞ � LSV;t�

where t is the time interval, X is the position of the vehicles,L is the vehicle length, and V is the velocity.

Angled interactions emerge after vehicles in lower prior-ity manoeuvres accept specific gaps and therefore becomethe SV. Since SV and RV trajectories are not parallel forangled interactions, conflict areas need to be defined for allcombinations of approaching movements. Vehicle speedsand distances to crash zones are used to verify the existenceof a collision course between SV and RV. Figure 2 illus-trates parameter definitions for angled interactions resultingfrom right-turn manoeuvres, with the corresponding expres-sion for DRAC of the form

½3� DRACANGLEDRV;tþ1 ¼ ðVRV;t � VSV;tÞ2

2½XCAm;n� XRV;t�

where XCAm;nis the position of the closest boundary of the

conflict area for SV movement m and RV movement n.

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Vehicles are supposed to apply DRAC to avoid high-risksituations. In reality, combinations of differential speed andspacing are perceived by the RV driver who, after a givendelay or reaction time, will respond in a particular fashion.The simulation algorithm updates DRAC for every time in-terval (0.1 s) based on driver reaction in the previous inter-val. For example, in a given interval (ti) the RV driverapplies a deceleration rate greater than DRAC. In the nexttime interval it is expected that DRAC will be lower, assum-ing that the SV driver did not decelerate, and vice versa.

Intersection and model specificationThe intersection being simulated in this paper consists of

four legs with two lanes in each major approach (westboundand eastbound) and one lane in each minor approach. Alllanes have a fixed width of 3.5 m and an angle between ma-jor and minor approaches of 908.

The simulation experiment was designed to investigatedifferences in CPI-based measures of safety performancecaused by three factors: (i) introduction of fixed signal con-trol to replace a previous stop sign in the minor approach,(ii) changes in traffic volume in the major approach, and(iii) type of vehicle interaction (rear end or angled). In total,10 different traffic volumes were investigated for both stop-controlled and signalized cases. Table 1 summarizes the as-sumed approach volumes and relevant traffic parameters forthe simulation experiment.

It is worth noting that right turns on red have been per-mitted for the signalized intersection. However, the trafficsignal option does not allow for advanced-green left-turnmanoeuvres. Signals are assumed to operate independently

of timings at other adjacent intersections. Semi-actuatedphases have been optimized using Synchro 7. The traffic di-rectional split is assumed to be constant for all approachesduring the simulation period for both signalized and unsign-alized cases (i.e., 5% for left turns, 5% for right turns, 90%through movements).

One of the major steps in applying microscopic simula-tion is to ensure that traffic model inputs (in this case, VIS-SIM input parameters) are accurately calibrated based onobservational vehicle tracking data. Only in this way canwe ensure that simulated measures of safety performanceclosely reflect what can be observed in the ‘‘real world.’’

Cunto and Saccomanno (2008) describe an in-depth heu-ristic procedure for calibrating and validating VISSIM car-following, gap-acceptance, and lane-change parametersbased on observed vehicle tracking data. The data were ob-tained from the Next Generation SIMulation (NGSIM) pro-gram administered by the FHWA (FHWA 2006). Themicroscopic behaviour of road users has been calibrated andvalidated in terms of the CPI for every vehicle in the datasample. This differs considerably from ‘‘conventional’’ cali-bration procedures based on macroscopic traffic attributessuch as average speed, volume, delay, and density. The pri-mary aim of the calibration–validation procedure was to ob-tain values of simulated safety performance based onspecified model inputs that closely matched observed safetyperformance from NGSIM. The results of this calibrationyielded ‘‘best estimate values’’ for those inputs that werefound to be statistically significant in explaining safety per-formance measures as obtained from the simulation. Thesevalues are summarized in Table 2. VISSIM default valueswere used for those inputs not found to be statistically sig-nificant for simulating safety performance.

Each simulation has a 15 min duration plus a 5 minwarm-up interval. To account for variations in different sim-ulation runs for the same traffic volumes, 15 replicates werecarried out for each run using different random seeds. In to-tal, the analysis in this paper involved 300 simulation runs.

Fig. 1. Perception and reaction thresholds and distances in the car-following model (CFM) of Wiedemann and Reiter (1992) (source:PTV 2008).

Fig. 2. Framework to establish CPI for a given time interval.

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Detailed vehicle information for every 0.1 s in the simula-tion was obtained from VISSIM and stored in *.fzp outputfiles. These files were scanned by a search algorithm codedin VisualBasic.net to determine the RV and its correspond-ing SV, as well as DRAC and CPI, in 0.1 s increments forevery vehicle in the simulation.

It has been recognized that microscopic simulation usersshould perform visual inspections during simulation runtime to search for abnormal vehicle behaviour such as sud-den vehicle stoppage and abrupt lane change. Two of thesesituations have been observed during VISSIM simulationsthat would have impacted safety performance measure-ments: (i) ‘‘crashes’’ during gap-acceptance situations, and(ii) vehicles too close during lane-change manoeuvres.Crashes have been observed in VISSIM for complex inter-section environments where a considerably high number ofvehicles and turning manoeuvres exist. These situationsmust be excluded for the analysis because it is consideredthat VISSIM cannot realistically simulate crashes. The algo-rithm is based on a ‘‘crash-avoidance’’ logic.

In this paper, VISSIM output files (*.fzp files) were filteredfor vehicles occupying the ‘‘same’’ space at the same timethroughout a VisualBasic.net application developed for esti-mating CPI, named CPI calculator. Such occurrences wereidentified by unreasonably high DRAC values (>15 m/s2) and(or) very low (or negative) spacing between lead and follow-ing vehicles. In situations where the following vehicle hasstarted to change the lane to improve its travel speed (discre-tionary lane change), the following driver starts to ‘‘look’’ atthe target lane, although for a brief period, say 0.2–0.5 s, thevehicle is still occupying its original lane. In some occasions,especially when the lead vehicle in the original lane is tooclose, this transition yields very low spacing between vehicleswith considerably high speed differentials. In the CPI calcula-

tor VisualBasic.net application, these situations have also beenfiltered by comparing the status of the following vehicle’sVISSIM variable called Lch (direction of current lane change).The signs ‘‘<’’ or ‘‘>’’ in the Lch variable indicate that the ve-hicle has started the lane-change manoeuvre to the left or rightlane, even though the vehicle is still in the original lane.

Simulation resultsThis section presents the major findings from simulation

of safety performance for the two intersection traffic controlstrategies, namely stop control and fixed signal control. Asnoted previously, four parameters based on CPI were usedto reflect changes in intersection safety that result from sig-nalization: (i) CPI/vehicle, (ii) CPI 85th percentile (CPI85),(iii) percentage of vehicles interacting (CPI > 0), and (iv)percentage of vehicles in conflict (DRAC > MADR).

CPI/vehicle is obtained by summing the CPI for all inter-acting vehicles and dividing this by the number of simulatedinteracting vehicles. This measure reflects the average indi-vidual safety performance associated with each traffic sce-nario. CPI85 establishes a threshold for comparing safetyperformance of individual traffic control (value of CPI/ve-hicle that is exceeded 15% of the time). The percentage ofvehicles interacting represents the total number of vehicleswith CPI greater than zero divided by the total of simulatedvehicles. The percentage of vehicles in conflict captures ex-treme traffic interactions where the maximum decelerationrequired to avoid the crash (DRAC) exceeded the brakingcapacity of the vehicle (MADR). This value is also dividedby the total number of vehicles in the simulation.

Table 3 summarizes the simulated average measures ofsafety performance for both stop-controlled and signalizedscenarios. These are based on the average of 15 simulations

Table 1. Intersection approach volumes and traffic attributes.

Volume (vph) Stop-controlled Signalized

Levela Eastbound Westbound Northbound Southbound

MajorapproachLOSb

MinorapproachLOS Cycle (s)

MajorapproachLOS

MinorapproachLOS

1 300 300 100 100 A C 40 A A2 400 400 100 100 A C 40 A A3 500 500 100 100 A D 40 A A4 600 600 100 100 A F 40 A A5 700 700 100 100 A F 40 A A6 800 800 100 100 A F 40 B A7 900 900 100 100 A F 45 B A8 1000 1000 100 100 B F 45 B A9 1100 1100 100 100 B F 50 B B10 1200 1200 100 100 B F 60 B B

aLevels 7–10 satisfy the FHWA Manual of Uniform Traffic Control Devices (MUTCD) warrant 3 for signalization.bLOS, level of service.

Table 2. VISSIM calibrated input parameters.

Input parameter Calibrated DescriptionDesired deceleration –2.6 Maximum deceleration (m/s2) drivers are willing to apply in ‘‘normal’’ (not emergency) situationCC0 3.0 Standstill distance (m); defines the desired distance between stopped carsCC1 1.5 Headway time (s); defined as the minimum time a driver wants to keep from the lead vehicle; the higher

the value, the more cautious the driver; CC0 and CC1 are combined to express the safety distance

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Table 3. Safety performance indicators for stop-controlled and signalized intersections.

Rear-end interactions Angled interactions

Volume levelNo. of simulatedvehicles CPI/vehicle CPI85

Vehiclesinteracting (%)

Vehicles inconflict (%) CPI/vehicle CPI85

Vehiclesinteracting (%)

Vehicles inconflict (%)

Stop-controlled1 198 1.27�10–8 1.48�10–8 19.8 0.00 1.45�10–5 9.98�10–9 4.8 0.032 247 5.87�10–9 6.60�10–9 22.4 0.00 1.98�10–5 2.63�10–8 4.5 0.003 300 1.17�10–8 9.80�10–9 27.7 0.00 8.77�10–5 2.36�10–8 6.2 0.024 347 1.85�10–6 7.44�10–9 31.6 0.02 1.36�10–5 1.42�10–8 6.7 0.025 396 7.48�10–8 5.12�10–9 37.1 0.00 3.14�10–8 1.83�10–8 6.9 0.006 454 9.90�10–6 7.04�10–9 42.7 0.02 6.30�10–5 2.72�10–8 7.1 0.067 506 2.58�10–8 4.51�10–9 47.2 0.00 8.53�10–5 3.16�10–8 7.0 0.048 555 2.64�10–6 4.24�10–9 51.1 0.02 1.82�10–5 3.00�10–8 5.9 0.029 610 1.88�10–6 3.06�10–9 56.5 0.01 1.02�10–4 3.03�10–8 5.1 0.0610 659 1.67�10–6 2.65�10–9 60.5 0.02 1.04�10–4 3.65�10–8 4.2 0.04

Signalized1 199 4.08�10–8 6.35�10–8 27.2 0.00 1.59�10–9 1.59�10–9 0.2 0.002 250 6.22�10–8 5.67�10–8 31.0 0.00 1.68�10–9 3.34�10–9 0.1 0.003 301 2.09�10–7 5.21�10–8 36.5 0.00 1.18�10–8 3.17�10–8 0.4 0.004 349 9.45�10–6 4.29�10–8 42.1 0.06 6.74�10–6 1.35�10–5 0.3 0.005 398 1.32�10–6 4.35�10–8 47.8 0.03 9.15�10–4 1.61�10–3 0.4 0.036 454 6.03�10–6 4.07�10–8 54.1 0.10 6.40�10–4 1.28�10–3 0.5 0.037 506 4.61�10–6 3.65�10–8 59.6 0.09 1.00�10–3 2.20�10–4 0.9 0.068 557 4.84�10–6 3.20�10–8 64.3 0.04 5.27�10–4 1.15�10–3 0.7 0.029 614 1.13�10–5 3.23�10–8 70.4 0.27 3.28�10–4 2.12�10–5 1.0 0.0410 666 1.35�10–5 3.35�10–8 76.1 0.33 5.24�10–4 7.19�10–4 1.1 0.08

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carried out using a different number of seeds. Table 3 alsoprovides results for different major approach volumes andthe two types of interactions of interest (rear end andangled).

Rear-end interactions

When comparing the two traffic control strategies forrear-end interactions, the introduction of signalization con-sistently results in an increase in the average CPI/vehiclevalues, suggesting that signalization may be producing neg-ative safety dividends, and this could be due to disruptionsin traffic flow along the major approach that did not existunder stop control. It should be noted that the introductionof the traffic signal results in an increase in the percentageof vehicles interacting of from 7% to 15%, conditional onincreasing volume.

The relationship between volume and CPI/vehicle and be-tween volume and percentage of vehicles in conflict is notas consistent as the relationship between volume and per-centage of vehicles interacting, and this could be explainedby the high variability in these measures. The influence ofvolume on the percentage of vehicles in conflict seems to

become more apparent for the signalized scenario at highervolumes.

A visual analysis of the results for CPI/vehicle and CPI85(Figs. 3 and 4) seems to support the findings from Table 3.From Fig. 3, a high degree of variability in CPI/vehicle wasobserved with increasing volume (heteroscedasticity). Thissuggests that experiments to detect differences in simulatedCPI/vehicle should be carefully designed to account formore subtle differences in the measure of safety perform-ance and that a large number of simulations may be requiredto enhance confidence in the results. Figure 4 indicates that,for rear-end interactions, CPI85 decreases with an increasein volume regardless of traffic control, stop or fixed signal.This suggests that high-risk drivers are restricted by volumein achieving their desired speeds. Volume in this instanceacts as a kind of speed-dampening effect to discouragehigh-risk behaviour as measured by the 85th percentile.

Figures 5 and 6 provide additional evidence concerningthe influence of volume on number of vehicles in conflictfor stop and fixed signal control, respectively. The previousfigures show that as volume increases, the percentage of ve-hicles not interacting (i.e., CPI = 0) decreases for both stop-controlled and signalized scenarios, and the percentage of

Fig. 3. CPI/vehicle versus volume for rear-end interactions.

Fig. 4. CPI85 versus volume for rear-end interactions.

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vehicles interacting (CPI > 0) increases for both controlstrategies. This result appears to be reasonable, consideringthat at higher volumes the average spacing between vehiclesis reduced with increased interactions requiring braking.

The introduction of the signalization significantly in-creases the percentage of vehicles with a ‘‘high’’ probabilityof DRAC exceeding MADR. For example, for a volume of2600 vehicles per hour (vph), the percentage of vehicleswith CPI between 10–8 and 10–7 increases from 4% to 14%after signalization. This suggests that for rear-end interac-tions there is a shift in the CPI/vehicle distribution to theright, and hence a reduction in safety following the introduc-tion of fixed signal controls.

Angled interactionsFor angled interactions, signalization yields lower CPI/ve-

hicle values at lower traffic volumes. However, no suchtrend was observed at higher volumes. At lower volumes wewould expect greater opportunities for left-turn manoeuvresfrom the major approach, whereas at higher volumes the

presence of a traffic signal creates a kind of ‘‘platooning’’ ef-fect along the major approach, reducing the number of avail-able safe gaps for left-turn vehicles (and hence higheraverage CPI/vehicle). For example, for the stop-control strat-egy at volume level 8, Table 3 suggests that 5.9% of vehiclesare interacting compared with only 0.7% for the signalizedcase. Nevertheless, the 0.7% of vehicles yield CPI valuesfor the signalized case that are considerably higher thanthose for the stop-control case. This suggests that in the ab-sence of an advanced green for left-turn manoeuvres, ahigher proportion of shorter gaps is accepted.

For angled interactions and stop-controlled intersections,the percentage of vehicles interacting increases at low vol-umes until a maximum value of 2000 vph (volume level 7)is reached and decreases thereafter. For signalized intersec-tions, the percentage of vehicles interacting was found to in-crease consistently with an increase in volume. Figures 7and 8 illustrate the frequency of simulated angled interac-tions for different CPI values and volume for stop-controlledand signalized scenarios, respectively.

Fig. 7. Distributions of CPI values for angled interactions in stop-controlled scenario.

Fig. 8. Distributions of CPI values for angled interactions in signa-lized scenario.

Fig. 5. Distributions of CPI values for rear-end interactions in stop-controlled scenario.

Fig. 6. Distributions of CPI values for rear-end interactions in sig-nalized scenario.

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For angled interactions, a key finding of the simulationruns is that the number of vehicles interacting is reducedafter signalization. However, a small number of vehicleswith very high CPI values continue to be present after sig-nalization, especially under high volumes. The signalizationscenario considered in this analysis does not permit ad-vanced-left-turn control, even at high volumes. In practice,an advanced green for left-turn movements would be consid-ered at such volumes, reducing the problem of unsafe gapacceptance and resultant angled interactions.

Analysis of varianceTo statistically verify the influence of volume and type of

control in the average CPI/vehicle, the results in Table 3were grouped into two major categories: (i) low volume(levels 1–3), and (ii) high volume (levels 8–10). A two-wayanalysis of variance (ANOVA) was carried out for rear-endand angled interactions, and the results are summarized inTables 4 and 5, respectively.

The ANOVA results indicate that all main factors(volume and type of control) and their interactions have asignificant effect on average CPI/vehicle for both rear-endand angled interactions. This confirms the findings from vis-ual inspection that the introduction of fixed signal controlsat the stop-controlled intersection can compromise safety byincreasing the potential for rear-end traffic conflicts.

ConclusionsA microscopic simulation model has been presented for

investigating the safety implications of introducing fixedsignal control at a stop-controlled intersection for differenttraffic conditions. The model produces a number of mean-ingful measures of safety performance such as crash poten-tial index per vehicle (CPI/vehicle), value of CPI that isexceeded 15% of the time (CPI 85th percentile, CPI85), per-centage of vehicles interacting, and percentage of vehicles inconflict.

A simulation experiment was carried out by applying themodel to a stop-controlled, four-legged intersection with ma-jor and minor approaches. The analysis investigated differ-ences in CPI-based measures of safety performanceresulting from changes in volume for two types of vehicleinteractions, namely rear end and angled.

For rear-end interactions, the introduction of fixed signalcontrol increased the percentage of vehicles interacting andthe average CPI/vehicle and CPI85. This suggests that sig-nalization could result in an increase in rear-end crash riskwhen compared to a stop-signal control. An increase in vol-ume on the major approach was found to yield higher levelsof vehicles interacting and in conflict with associated highercrash risks.

For angled interactions, the introduction of fixed signalcontrol resulted in a reduction in the percentage of vehiclesinteracting. The effect on safety performance, however, wasnot consistent for all assumed volumes. At low volumes,CPI/vehicle was found to be lower after signalization (i.e.,safety was enhanced), but at high volumes CPI/vehicle wasfound to increase slightly. This inconsistency was due to theabsence of an advanced-green signal for left-turn manoeu-vres from the major approach to the minor approach. Therelationship between CPI/vehicle and signal control and vol-ume was found to be statistically significant at the 5% levelfor both rear-end and angled interactions.

The application of microscopic simulation presented inthis paper provides an alternative ‘‘behavioural’’ platformfor investigating the safety implications resulting from theintroduction of different countermeasures for varying trafficconditions.

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Table 4. Two-way ANOVA of CPI/vehicle for rear-end interactions.

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Note: df, degrees of freedom; F, F statistic; MS, means squared.

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