Minderhoud and Bovy 2001

Accident Analysis and Prevention 33 (2001) 89–97

Extended time-to-collision measures for road traffic safetyassessment

Michiel M. Minderhoud 1, Piet H.L. Bovy *Delft Uni6ersity of Technology, Faculty of Ci6il Engineering and Geosciences, Traffic Engineering Section, PO Box 5048,

NL-2600 GA Delft, The Netherlands

Received 7 July 1999; received in revised form 1 March 2000; accepted 7 March 2000

Abstract

This article describes two new safety indicators based on the time-to-collision notion suitable for comparative road traffic safetyanalyses. Such safety indicators can be applied in the comparison of a do-nothing case with an adapted situation, e.g. theintroduction of intelligent driver support systems. In contrast to the classical time-to-collision value, measured at a cross section,the improved safety indicators use vehicle trajectories collected over a specific time horizon for a certain roadway segment tocalculate the overall safety indicator value. Vehicle-specific indicator values as well as safety-critical probabilities can easily bedetermined from the developed safety measures. Application of the derived safety indicators is demonstrated for the assessmentof the potential safety impacts of driver support systems from which it appears that some Autonomous Intelligent Cruise Control(AICC) designs are more safety-critical than the reference case without these systems. It is suggested that the indicator thresholdvalue to be applied in the safety assessment has to be adapted when advanced AICC-systems with safe characteristics areintroduced. © 2000 Elsevier Science Ltd. All rights reserved.

Keywords: Safety assessment; Time-to-collision; Autonomous intelligent cruise control

www.elsevier.com/locate/aap

1. Introduction

Most car manufacturers are currently developing in-vehicle systems aimed at improving driver comfort,which possibly also may affect traffic flow characteris-tics as well as traffic safety. The traffic safety aspect issubject of this article. Recent technological develop-ments in the field of driving task automation, such asthe development and careful introduction of Au-tonomous Intelligent Cruise Control (AICC) or Colli-sion Avoidance Systems, justify safety impactassessments. It is expected that the introduction of newvehicle technologies will have both positive and nega-tive impacts on traffic safety.

We can distinguish direct safety benefits (such asenhanced driving performance and mitigation of crash

consequences) and indirect safety benefits (e.g. reducedexposure, reduced driver stress and fatigue, reducedconflicts and variance in behavior). Also, direct safetyrisks (driver distraction, overload, reduced situationawareness) and indirect safety risks (behavioral adapta-tion, loss of skill, etc.) can be distinguished. Resultingimpacts largely depend on the extent to which thesupport system meets drivers’ needs and is compatiblewith human capabilities and limitations.

Since intelligent driver support systems are not yetwidespread present in the car traffic flow, direct safetymeasures such as accident and fatality frequencies cannot be obtained in many cases. Since empirical collec-tion of accident data is not yet an option, other meth-ods for safety assessment are needed.

Among these are ex ante assessments with which thesafety consequences of different vehicle fleet composi-tions relative to a base (do-nothing) case can be esti-mated. To this end, microscopic simulation is a usefulapproach. With the application of microscopic simula-tion tools a variety of traffic safety indicators can beadopted, such as the headway distribution, time-to-col-

* Corresponding author. Tel.: +31-2781681; fax: +31-2783179.E-mail addresses: [email protected] (M.M. Minderhoud),

[email protected] (P.H.L. Bovy).1 Present address: Hague Consulting Group, Surinamestraat 4,

NL-2585 GJ, The Hague, The Netherlands.

0001-4575/00/$ - see front matter © 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 0 0 1 -4575 (00 )00019 -1

M.M. Minderhoud, P.H.L. Bo6y / Accident Analysis and Pre6ention 33 (2001) 89–9790

lision (TTC) distribution, or number and severity ofshock waves. The comparison of headway distributionsat a cross-section gives an indication about the positiveor negative shifts in traffic safety, assuming that smallheadways are relatively unsafe. Also, a comparison oftime-to-collision distributions can be made to evaluatesafety changes. Other safety indicators can be used aswell, such as the number of shock waves (see e.g.VanArem and DeVos, 1997), time-to-accident (TTA),post-encroachment-time (PET), deceleration-to-safety-time (DTS) (see e.g. Hyden, 1996; Topp, 1998). Abso-lute safety effects are hard to derive with suchcomparative analyses. It may also be clear that trafficsafety analyses with microscopic traffic simulation havea number of restrictions. Most important, driver behav-ior in real road traffic is more diverse and less pre-dictable than can be implemented within a model.Generally, microscopic simulation models developedfor traffic flow analyses require less detail with respectto driver errors modeling than required for safetyanalyses. Furthermore, microscopic simulation modelsmostly neglect parts of the lateral driving tasks, such askeeping the vehicle on the roadway. Despite theselimitations, simulation can give valuable insights intorelative changes of traffic flow safety. In many cases, itis the only way available in ex ante assessment ofexpected future conditions.

In assessing the safety impacts of future intelligentin-vehicle devices interacting with the driver, adequatesafety indicators should be applied which express thelevel of safety into a comparative and understandablevariable. Focus of this article is the specification andapplication of such new safety measures based on thetime-to-collision notion. This implies that the lateralsafety concerns are not taken into account. The time-to-collision indicator expresses only indirect safety con-cerns related to the execution of the longitudinaldriving task which should be interpreted with this limi-tation in mind.

Section 2 will introduce the time-to-collision notionfollowed by Sections 3 and 4 presenting refined indica-tors, respectively the TET (Time Exposed Time-to-colli-sion indicator) and the TIT (Time IntegratedTime-to-collision indicator). Calculation of these safetyindicators is outlined in Section 5, followed by anexample of application in Section 7. Section 8 gives asummary and some implications of the investigation.The presented safety indicators are especially (but notexclusively) suited for application in microscopic simu-lation studies of traffic, in which much more informa-tion is available about individual vehicle movementsthan usually is the case in empirical studies.

2. Time-to-collision notion

2.1. Definition

The time-to-collision notion has been applied benefi-cially as a safety indicator in safety analyses. Thetime-to-collision (TTC) concept was introduced in 1971by the US researcher Hayward. A TTC value at aninstant t is defined as the time that remains until acollision between two 6ehicles would ha6e occurred if thecollision course and speed difference are maintained, seee.g. Hyden (1996). The time-to-collision distributionhas been applied in several studies to identify trafficsafety impacts (among others Fancher et al., 1997;VanArem and DeVos, 1997).

The time-to-collision of a vehicle-driver combinationi at instant t with respect to a leading vehicle i−1 canbe calculated with:

TTCi=Xi−1(t)−Xi(t)− li

X: i(t)−X: i−1(t)ÖX: i(t)\X: i−1(t) (1)

where X: denotes the speed, X the position, and l thevehicle length.

The time-to-collision notion is illustrated with twovehicle trajectories in Fig. 1. Depicted is a situation inwhich the lead vehicle i−1 brakes. After a reactiontime t, subject driver i starts a control action. Accord-ing to expression (1), a time-to-collision value can onlybe calculated when a positive speed difference betweenthe vehicles exists. Fig. 1 shows the TTC-value atinstant t, the moment driver i starts braking.

For calculation of a TTC-value, the speed differentialat instant t is assumed to remain constant during thehypothetical collision trajectories of the vehicles untilinstant t % (shown by the straight dashed lines). Thehigher a TTC-value, the more safe a situation is.

2.2. Critical time-to-collision 6alue

Safety-critical approach situations are characterizedby small TTC-values. In applying the developed, im-Fig. 1. Time-to-collision notion illustrated with vehicle trajectories.

M.M. Minderhoud, P.H.L. Bo6y / Accident Analysis and Pre6ention 33 (2001) 89–97 91

Fig. 2. Trajectories of vehicles observed over road length L duringtime period H.

Our proposal combines the two approaches whichresults into two new safety indicators (called TET andTIT). Instead of a single cross-section a specified roadlength is considered for safety analysis. With this ap-proach, the occurrences of small time-to-collision val-ues of all traffic participants, at any moment, can betaken into account.

3. A road-section based time-to-collision profile

In establishing the improved safety measures, let usconsider a road section between X1 and X2. Exampletrajectories of vehicles driving at a road section areshown in Fig. 2. The considered road section length isdenoted with L, the duration of the time period be-tween T1 and T2 with H. It is now possible to determinethe time-to-collision profile over time, TTCi(t) for eachof the vehicles i that use the road section, using expres-sion (1). Such a time-to-collision value profile over timeis shown in Fig. 3.

Shown in Fig. 3 (upper part) is the movement of adriver on a motorway lane. At instant t=0 the driverapproaches a slower driving vehicle, so the time-to-col-lision value decreases with time. At a certain moment t1

the subject decides to make a lane change. The driver isconfronted with a new leader at a smaller gap distance.The time-to-collision values are smaller and reach quiteunsafe values. The driver adapts his speed to increasethe gap distance and reduce the speed differential.Between t2 and t3 no positive TTC values are apparent.The lead vehicle is thus driving with a higher speed.However, at t3 the subject approaches another leadvehicle. Drivers’ car-following behavior exhibits thisoscillatory behavior constantly, switching from a nega-tive to a positive speed difference, in order to maintaina minimum desired gap distance. At t6, the lead vehiclereturns to the right lane, and a new lead vehicle isobserved by the driver. The subject approaches this newleader without speed adaptations, so the TTC valuedecreases.

In Fig. 3 (upper part) a constant TTC thresholdvalue (TTC*) is indicated (horizontal line), togetherwith shaded areas if drivers’ TTC values drop belowthis threshold value. The TTC threshold value is atime-to-collision value that can be applied to distin-guish safe and safety-critical approach situations.

From the example, we observe that the time-to-colli-sion values for a single driver may strongly vary overtime. Based on such TTC-profiles, a number of morerefined safety indicators will be derived in the sequel.An analysis approach is developed in which the individ-ual time-to-collision profiles are used in the determina-tion of a useful time-to-collision exposition distribution.A full description of the developed safety indicatorsTIT and TET is given in the following sections.

proved safety indicators, a critical or threshold 6alueshould be chosen to distinguish relatively safe andcritical encounters. Hirst and Graham (1997) reportthat a time-to-collision measure of 4 s could be used todiscriminate between cases where drivers unintention-ally find themselves in a dangerous situation from caseswhere drivers remain in control. The study furtherdescribes a laboratory experiment of the design of aCollision Warning System. The results show that aTTC warning criterion of 4 or 5 s results in too manyfalse alarms. The study shows that a TTC-value of 3 sproduced the least number of alarms although in somecases critical situations were observed. Hogema andJanssen (1996) studied the driver behavior at an ap-proach of a queue for non-supported and supporteddrivers in a driving simulator experiment. They found aminimum TTC value of 3.5 s for the non-supporteddrivers, and 2.6 s for supported drivers. The 2.6 s valueis regarded as a safety concern. VanDerHorst (1990)reports even lower critical TTC values, based on ap-proaches at intersections.

2.3. Approaches for determining time-to-collision 6alues

Basically, two approaches can be observed in litera-ture to determine time-to-collision values for safetyassessments (see previous paragraph). One approachfocuses on time-to-collision values of vehicles passing across-section of a roadway. This method is mostly usedin empirical traffic flow studies and in microscopicsimulation studies. The other approach deals with sub-ject drivers driving during a certain time period orfollowing a specific route in real-life traffic conditionsor under controlled conditions in a driving simulator.The driving performance of the subjects (includingtime-to-collision) is continually measured, so that after-wards minimum time-to-collision values can bedetermined.


4. Definition of two TTC-based road traffic safetyindicators

Two safety indicators are derived using the trajecto-ries and time-to-collision profiles of all vehicles, ob-served over road section length L during time periodH. Fig. 3 shows a trajectory profile of a driver (upperpart) as well as the principle of the two safety indica-tors we developed (lower part). The definition of thetwo indicators is given below, after which calculationprocedures are described based on measured TTC-frequencies.

4.1. The TET indicator

The first indicator we will specify is called TET,which stands for Time Exposed Time-to-collision. Theduration of exposition to safety-critical time-to-colli-sion values over specified time duration H is used hereas safety indicator. It is a summation of all moments(over the considered time period) that a driver ap-proaches a front vehicle with a TTC-value below thethreshold value TTC*, the latter is considered to bethe boundary between safe and safety-critical ap-proaches. Thus, the lower the TET value, the moresafe the situation (on average over period H). Thissafety measure does not take into account the varia-tion in safety levels of different time-to-collision valuesbelow the threshold value.

Calculation of the TET indicator requires collectionof the position and speed of all vehicles entering andleaving the specified road section between X1 and X2,over time period H, from which trajectories (Fig. 2)and time-to-collision profiles can be established. How-ever, since data mostly is collected in discrete time, theTTC values will also be determined at discrete timemoments (determined by time scan interval tsc). For

calculation purposes it is assumed that the measuredTTC-values at an instant t do not change during asmall time step tsc (e.g. 0.1 s). For the considered timeperiod H, there are T=H/tsc time instants t takeninto account in the calculation (t=0… T).

From Fig. 3, it can be concluded that the TET*indicator for a subject i can be expressed by:

TETi*= %T

t=0

di(t) · tsc

di(t)=!0 else

1 Ö 05TTCi(t)5TTC*(2)

in which d is a switching variable. Its value is 1 incase a driver i at instant t experiences a TTC-valuebetween 0 and the specified threshold value TTC*,otherwise, its value is 0.

The TET indicator is expressed in seconds. The su-perscript * should be interpreted as ‘indicator valuecalculated with respect to the threshold value’. It caneasily be understood that for a population of N driv-ers (i=1 … N), the total TET* is equal to:

TET*= %N

i=1

TETi* (3)

The TET indicator can also be calculated separatelyper user class, e.g. trucks and passenger cars, orequipped and non-equipped vehicles, by adding anextra index and summation per user class.

4.2. The TIT indicator

One disadvantage of the TET indicator is that theTTC-value if it is lower than the threshold does notaffect the TET indicator value. However, according tothe theory, it may be expected that an extremely small

Fig. 3. Example time-to-collision profile of a driver-vehicle-combination i in motorway traffic (lightly shaded areas represent safety-criticalapproach conditions).


TTC-value (e.g. smaller than 0.5 s) represents an ap-proach situation with a relatively high probability of acollision compared to higher TTC-values (e.g. 2 or 3 s).For example, the approach situation between t1 and t2

in Fig. 3 can be considered to be more dangerous thanthe approach between t5 and t6. To take the impact ofthe TTC-value into account in the safety assessment, theTIT indicator has been developed.

The TIT (=Time Integrated Time-to-collision) indi-cator uses the integral of the time-to-collision profile ofdrivers to express the level of safety (in s2). In continu-ous time:

TIT*= %N

i=1

& T

0

[TTC*−TTCi(t)]dt

Ö 05TTCi(t)5TTC* (4)

The lightly shaded areas in Fig. 3 represent situationsin which the driver approaches the front vehicle withTTC-values below TTC*. Since low TTC-values repre-sent more dangerous situations, it holds that the smallerthe shaded area, the higher the risks of collisions. To beconsistent with the TET-indicator, the shaded areashould be subtracted from the area below the thresholdvalue, resulting in a time integral with an interpretablemeaning. This area is shown in Fig. 3 by a dark surface.A high TIT value means a large exposition time toduration-weighted unsafe TTC-values, which is negativefor road safety. The individual TIT for subject i indiscrete time can be calculated with:

TITi*= %T

t=0

[TTC*−TTCi(t)] · tsc


Summation over all vehicles (i=1… N) present in theinvestigation during time period H, results in the follow-ing discrete-time aggregate TIT definition (expressed ins2):

TIT*= %N

i=1

TITi* (6)

The aggregate indicator values (3) and (6) hold for thepopulation of all observed vehicles N, and depend onthe considered time period H. The population size Ndepends on the beginning and ending of the timehorizon, see Fig. 2. One should consider the number ofvehicles already present on the road section at momentT1, as well as the number of vehicles still present on theroad section at the end of the considered period, at T2.

From the aggregate TET and TIT indicators, otherindicators can be derived, such as corresponding aver-age values per vehicle, as well as the probability ofsafety-critical situations per time unit (see Section 5). Inorder to calculate the various indicators in practicalcircumstances it is advantageous to use frequency distri-butions of measured TTC-values.

5. Calculation procedures of TET and TIT indicators

For the construction of a TTC-frequency distribu-tion, which is useful for visual inspection and analysis ofthe impact of the threshold value on the indicator value,we distinguish TTC-classes denoted with index k. As-suming an equal size of the classes set at a and TTC-val-ues ranging from 0 to MAX seconds, the boundaries ofthe TTC classes in the frequency distribution then aredefined by TTCk= (k−1) · a, where k=1… MAX/a.

The summed exposition time with TTC-values withina particular TTC-class k over period H is calculated by:

TETk= %N

i=1

%T

0

d ik(t) · tsc

d ik(t)=

!0 else1 Ö TTCk5TTCi(t)BTTCk+1 (7)

From Eq. (7) it follows that the TET* indicator (3) canbe determined by:

TET*= %k�

k=1

TETk Ö k=1…k* (8)

where k* represents the index of the class correspondingwith a TTC-value equal to the threshold value TTC*.The class index k* can be calculated from k*=TTC*/a.

Given the TET-values per class k, the aggregate TITindicator (6) can easily be derived. Firstly, it should beobvious that holds:

di(t)= %k�

k=1

d ik(t) (9)

since from Eq. (2) it follows that a subject i with atime-to-collision value below TTC* at instant t corre-sponds to a switching variable value of di(t)=1. Thetime-to-collision value is also element of the TTC-fre-quency distribution; the time instant will be assigned toone of its classes k. Summation of d i

k(t) over index k willresult in the same value as found for the switchingvariable di(t).

The aggregate TIT* indicator (6) can be derived fromthe TTC-frequency distribution. Graphically, it can beobserved that for TIT* holds:

TIT*=N · T · TCC* · tsc− %N

i=1

%T

t=0

TTCi(t) · tsc


where the first part of the equation represents the areabelow TTC* for time instants with a TTC-value meetingthe condition 05TTCi(t)5TTC*, and the second partrepresenting the area below the curve (see Fig. 3) fortime instants meeting the same condition. This subtrac-tion of areas results in the TIT* indicator; it is equal tothe area below the threshold value and above theTTC-profile, again for time instants meeting the


Fig. 4. Exposition time versus time-to-collision (two-lane motorwaywithout AICC-equipped vehicles).

It is the expected average duration that a vehicleencounters an unsafe situation.

TIT*=TIT*

N(s2/vehicle) (13)

The average TIT* per vehicle expresses the expectedduration-weighted exposition to unsafe TTC-values(over time period H).

These average indicators still include the time periodover which the indicator value has been determined. Toovercome this dependency, an indicator P* can beestablished, expressing the probability that a vehicleencounters a safety-critical approach situation, which isdefined as a moment with a TTC-value between 0 andTTC* second. The TET* probability per vehicle istherefore:

TET P*=100 ·TET*

H(%) (14)

The probability indicator can be interpreted as thepercentage of time that a random driver on averagedrives with TTC-values below the threshold TTC*. Thisindicator is calculated by dividing the average indicatorvalue of Eq. (7) by the maximum attainable time period(thus H).

Analogously, the TIT* probability indicator can becalculated with:

TIT P*=100 ·TIT*

TTC* · H(%) (15)

in which the TIT* is divided by the theoretically maxi-mum attainable TIT indicator value per vehicle (thusH · TTC*).

The following section presents an example of thefrequency distribution of the TET indicator, and con-centrates on the impact of the chosen threshold valueon the TET indicator values.

6. Illustration of derived TET indicator: aTTC-frequency distribution

Dividing the time-to-collision range in classes witha=0.25 s, a TTC-frequency distribution of the aggre-gate indicator value TET per class k can be calculatedaccording to Eq. (7).

Fig. 4 shows the calculated TTC-frequency distribu-tion for simulated traffic on a 5 km long two-lanemotorway stretch with an on-ramp bottleneck (seeMinderhoud, 1999; Minderhoud and Bovy, 1999a,b).Only the traffic on the two mainline lanes is consideredin the analysis. On the x-axis the TTC range between 0and 7 s is depicted, on the y-axis the exposition timeper TTC class is shown. For a class k, the expositiontime (TET indicator) is calculated according to Eq. (7).

previous mentioned condition. Eq. (10) can be formu-lated also using the TET indicator by substitutingTTCi(t) · tsc according to the following relationships:

TCCi(t) · tsc=%k

TTCik · tsc

=%k

d ik(t) · TTCk·tsc

=%k

TETik · (k−1) · a (11)

The TIT* calculation with the aid of the TTC-fre-quency distribution is less exact than using the vehicletrajectory approach (Sections 4–6) since the expositiontime of unsafe TTC-values are aggregated into classesof TTC-values defined by class width parameter a, thuslosing information of the precise TTC-value observed.Nonetheless, the method simplifies the data collectioneffort while the estimated indicator value is sufficientlyaccurate for assessing safety impacts.

5.1. Related specific safety indicators

We developed two related time-to-collision safetyindicators which can advantageously be applied in theanalysis of traffic safety. For comparative purposes it isdesirable to standardize the indicator values relative tothe sample size and duration of the observations.

We may standardize the aggregate TET and TITindicator values into an average value per vehicle,denoted with TET* and TIT*, respectively:

TET*=TET*

N(s/vehicle) (12)


Also shown in Fig. 4 is the cumulative exposition tounsafe TTC-values. For the cumulative distribution, thevalues on the y-axis correspond with the aggregateTET* indicator value, assuming a threshold TTC-valueon the x-axis.

The three-second threshold is considered an adequatelevel for discriminating dangerous approach situationsfrom acceptable situations, as has been observed byHirst and Graham (1997). In our example, the safetyindicator TET* with a threshold TTC-value TTC* of 3results in a value of approximately 19.5 s. Nevertheless,other TTC-threshold values can be applied.

The calculated aggregate TET indicator value of 19.5s implies that during the 2.5-h simulation run onlyabout 19 s of potential dangerous situations have oc-curred with TTC-values below 3 s. Assuming a total of10 000 vehicles generated in the simulation, the averageexposition time of safety-critical TTC-values is 19.5×10−4 s per vehicle.

The probability (denoted with TETP*) that a driveris confronted with an unsafe situation is relativelysmall. In our example, the simulation time is 9000 s andabout 10 000 vehicles traversed the observed motorwaysegment. The percentage of time that a random vehiclein the given simulation experienced unsafe conditions isthen 2.2×10−7 on average. This probability is quitesmall. Even if a driver experiences a situation with asmall time-to-collision value, this will mostly not resultin a rear-end collision.

The TET indicator value is especially useful in acomparative analysis of scenarios. The TIT indicator,while being more adequate, is more complex to deter-mine and more difficult to interpret its meaning. Inaddition, the threshold value adopted in studies differslargely, affecting the safety assessment substantially.Although the TIT measure is theoretically a preferableindicator, the TET indicator is preferred for use incomparative studies in which simulation tools are ap-plied to generate trajectories. Due to the simplificationsand uncertainties in modeled driver behavior, the addi-tional benefits of the more complex TIT approach seemsmall.

7. Application to intelligent driver support systems

We will illustrate the use of the developed safetyindicators by showing the impact of different vehiclefleet compositions on the TET* safety indicator values.Let us assume a future situation in which vehicles areequipped with intelligent driver support systems. Theso-called AICC is able to actively support the driver indistance keeping and speed adaptation, thus enhancingdriver comfort while it interacts on driver performance.One of the expected safety benefits of AICC use is thatthe system is able to perform the longitudinal drivingtask without temporarily decreasing the attention level,without moments of arousal, or other temporarily inat-tentive behavior. A safety decrease is also possible,since the gap distance can be shorter, whereas driverintervention is required in some cases. It is important tounderstand the decisive role of the applied simulationtool in the analysis of safety impacts. The appliedmicroscopic simulation tool consists of a state-of-the-art model of individual driving behavior on multilanemotorways (including car following, speed choice, lanechanging, etc.), extensively calibrated and validatedwith empirical data, where even the driver behaviorwith respect to handling of the AICC-equipment in hiscar is modeled in detail (see for details Minderhoud,1999; Minderhoud and Bovy, 1999a,b). The modelrepresents AICC behavior quite well, but does notmodel driver errors and assumes constantly alert driv-ers. This affects the outcome of the safety indicators,probably overestimating the safety of non-supporteddriving.

It can be hypothesized that traffic safety can beincreased with some AICC designs that fully assist thedriver, even if it is observed that the frequency of smallTTC values increases compared to the reference casewithout AICC. The resulting indicator values of thevarious scenarios can not be compared easily due to thedifferent driving characteristics in case of a fully con-trolled and manually controlled vehicle. We expect thatlower TTC-threshold values may be applied for theseadvanced driver assistance systems (for e.g. a 2 s TTC-threshold) because of their more adequate responsebehavior in case of dangerous situations.

Table 1Estimated TET indicator values for a sample of AICC scenario’s as function of threshold value

TTC*=2 s TTC*=3 sTTC*=1 s

Left lane Right laneLeft lane Right lane Left lane Right lane

12.8 19.58.0 00 0Reference13.18.4 183.9050% AICC-partial 0.3

0 5.2 4.4100% AICC-partial 11.5 634 93.644.2019.300 6.550% AICC-complete

0 10.8 3.4 26.2 4.7100% AICC-complete 69.9


Fig. 5. Exposition time versus time-to-collision (two-lane motorwaywith 100% AICC-partial equipped vehicles).

The table shows that the safety-critical time-to-colli-sions are mainly found on the right lane, since mergingvehicles from the on-ramp enter the mainline on theright lane. Fig. 5 shows the frequency distribution ofthe AICC-partial at 100% penetration, from which theimpact of the selection of a threshold value can beobserved graphically. It is observed that large and safeTTC-values (e.g. 8 s) are more frequently encounteredthan safe-critical small values (e.g. 2 s).

From Fig. 5, the impact of the threshold value on theexposition time is obvious. The smaller the TTCthreshold value, the smaller the overall exposition timeTET* (indicated by the cumulative distribution).

It is speculated that AICC-systems will improve thedriving performance and reduce the safety risks due toquick response behavior, less errors, etc. so we mayselect a smaller threshold value that expresses the at-tainable safety levels realistically. The adequatethreshold value depends on the design characteristics ofthe AICC-system and how the traffic safety level even-tually will be influenced by these features. However,determining such a system-dependent threshold value isdifficult since empirical data is not yet available. There-fore another simplified approach is followed. It is de-cided to adapt the threshold value belonging to certainsystem types to the safety level found in the do-nothingcase. For the AICC-partial it appears that the 2 sboundary results in an indicator value that approxi-mates the reference. The 1 s threshold fits better for theAICC-complete at 100% penetration. The AICC-com-plete is more advanced than the AICC-partial, so itappears logical that safety analysis of the AICC-com-plete should adopt a lower threshold value.

In the example, the safety indicator has been deter-mined per lane, which resulted in the conclusion thatthe right lane contributes largely to the safety-criticalsituations. The analysis could be easily extended byintroducing user class specific indicator values, givingthe possibility to compare the performance betweenuser classes (e.g. equipped and non-equipped vehicles).This could give essential information about the safety-critical behavior of particular groups of users.

8. Summary and implications

In this article we described two new safety indica-tors based on extensions of the time-to-collision safetymeasure. In contrast to the classical TTC-indicator,these extensions can take the full course of vehiclesover space and time into account. The extended indi-cators therefor can give a more complete and compre-hensive picture of the safety level on a particularstretch of road during a particular period of time. Thedeveloped TET indicator expresses the exposition timeto safety-critical approach situations, whereas the de-

Table 1 gives an overview of the TET* safety indi-cator values found in the simulation experiments of a5 km long two-lane motorway stretch with on-rampbottleneck (see Minderhoud, 1999). A high TET*value means a high exposition duration to safety-criti-cal approach situations. A value of 0 implies thatthere is no safety concern (with respect to the selectedthreshold value for distinguishing between safe anddangerous approaches). A comparison is made of thesafety indicator values estimated for two AICC-de-signs (partial and complete, respectively) at two pene-tration levels (50 and 100%, respectively). In addition,three threshold values are considered: 1, 2 and 3 s.The AICC systems are characterized by the following:1. AICC-partial: driver must intervene if the speed

drops below 30 km/h or needed deceleration arrivesat −3 m/s2. The system has a target headwaysetting of 0.8 s.

2. AICC-complete: driver is fully supported. The sys-tem has a target headway of 0.8 s.

From Table 1 it can be seen that the AICC-partial at100% penetration has extreme large indicator values ifapplying the 3 s threshold value, which is a safetyconcern. The high TET* value is caused by the neededdriver intervention as drivers approach the bottleneck,while speeds below 30 km/h are not supported. Afterdriver intervention, drivers expand their gap distance totheir normal preferred distance, which is larger than thetarget 0.8 s headway the AICC-system maintained. It isapparent that this leads to shock waves (especially onthe left lane) and safety-critical time-to-collision values,nonetheless, no rear-end collisions were observed in thesimulation.


veloped TIT indicator additionally takes into account theencountered TTC-values during these safety-critical ap-proaches. The safety assessment approach can be appliedfor a single driver, a specified user class, or all vehiclesthat pass the road segment during a time period, and candistinguish impacts per lane. Advantage of the TET andTIT safety measures above the conventional time-to-col-lision measure is the inclusion of time-dependent time-to-collision values of all subjects that use a road sectionduring a time period. This means that the occurrence ofsmall TTC-values, which can hardly be measured at asingle cross-section of the roadway, will be included aswell.

These new measures appear to be fruitful safetymeasures that can be used most beneficially in micro-scopic simulation studies focusing on safety impacts suchas of intelligent driver support systems. However, themethodology presented can also be applied to empiricaldata, if available. A threshold value should be specifiedin accordance with the design characteristics of theAICC-devices in order to make valid comparisons of thesafety impacts.

Acknowledgements

The authors are grateful to two anonymous refereeswhose comments were very helpful in improving the text.

References

Fancher, P., Koziol, J., Baker, M., 1997. Preliminary results from theIntelligent Cruise Control field operational test in SoutheasternMichigan. Proceedings of the 4th Annual World Congress onIntelligent Transport Systems, Berlin.

Hirst, S., Graham, R., 1997. The format and presentation of collisionwarnings. In: Noy, N.I. (Ed.), Ergonomics and safety of IntelligentDriver Interfaces.

Hogema, J.H., Janssen, W.H., 1996. Effects of intelligent cruise controlon driving behavior. TNO Human Factors, Soesterberg, TheNetherlands, Report TM-1996-C-12.

Hyden, C., 1996. Traffic conflicts technique: state of the art. In: Topp,H.H. (Ed.), Traffic safety work with video processing. UniversityKaiserslautern, Transportation Department, 1996, Green SeriesNo. 37, pp. 3–14.

Minderhoud, M.M., 1999. Supported driving: impacts on motorwaytraffic flow. Delft University Press, Delft, The Netherlands, 1999,TRAIL Thesis Series T99/4.

Minderhoud, M.M., Bovy, P.H.L., 1999. Impact of AICC design onmotorway capacity. In Transportation Research Record no. 1679,1999a, pp. 1–9.

Minderhoud, M.M., Bovy, P.H.L., 1999b. Development of a micro-scopic simulation model for AICC. Proceedings of the 6th AnnualWorld Congress on Intelligent Transport Systems, Toronto.

Topp, H.H. (Ed.), 1998. ViVa traffic: video verkehrs analyse in derpraxis (in German). University Kaiserslautern, TransportationDepartment, 1998, Green series No.43.

VanArem, B., DeVos, A.P., 1997. The effect of a special lane forintelligent vehicles on traffic flows. TNO-INRO Report 1997-02a.Delft, The Netherlands.

VanDerHorst, A.R.A., 1990. A time-based analysis of road userbehavior in normal and critical encounters. Dissertation DelftUniversity of Technology, The Netherlands.

Documents

Minderhoud and Bovy 2001