Brackstone Et Al 2002

7/31/2019 Brackstone Et Al 2002

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Motorway driver behaviour: studies on car following

Mark Brackstone *, Beshr Sultan, Mike McDonald

Department of Civil and Environmental Engineering, University of Southampton, Highfield, Southampton,

Hants SO17 1BJ, UK

Received 8 May 2001; received in revised form 18 November 2001; accepted 20 December 2001

Abstract

This paper will report findings of an instrumented vehicle study aimed at assessing one element of driver

behaviour, that of car following, on UK motorways. The paper (re-) calibrates one of the most successful of

such modelsthe Action Point modelusing dynamic time series data acquired from field tests with an

instrumented vehicle. Probability distributions for a number of parameters from the Action Point model

are produced and a number of modifications made in order to enhance its value for use in traffic flow and

simulation models. Lastly typical headways are compared with existing studies in the area, finding that

current headways are far lower than believed. The rationale behind the adoption of such short headways is

examined. 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Car following; Instrumented vehicle; Driver behaviour; Motorway; Perception

1. Introduction

Understanding the behavioural response of travellers is a key to determining transport system

performance and assessing the ways in which it may be enhanced. The subject has become ofincreasing importance as new technology in the form of intelligent transport systems (ITS) has

begun to offer new and increasingly subtle ways of improving system operations. The opportu-nities are particularly relevant to motorway operations where both in-vehicle and roadside ITStechnologies are developing rapidly, however, assessing the potential effects of any new system

requires a sound base of behavioural understanding. (Establishment of an understanding ofnormative driver behaviour was ranked as the second most important area for development out

of 40 problem statements, by an expert Human Factors-AVCSS panel (ITS America, 1997).)

* Corresponding author. Tel.: +44-2380-593-639; fax: +44-2380-594-152.

E-mail address: [email protected] (M. Brackstone).

1369-8478/02/$ - see front matter

2002 Elsevier Science Ltd. All rights reserved.P I I : S1369- 8478( 02) 00004- 9

Transportation Research Part F 5 (2002) 3146

www.elsevier.com/locate/trf
http://mail%20to:%[email protected]/http://mail%20to:%[email protected]/


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One area in which such an understanding is seen as becoming increasingly important is dy-

namic driver behaviour, such as car following on a motorway, where a driver controls the brakeand accelerator in order to maintain an acceptable distance behind a lead vehicle in the same lane.

To date, research has been undertaken in the collection of time series data describing this processlargely by either using static laboratory simulators (van Winsum & Heino, 1996) or vehicles ontest tracks (Chandler, Herman, & Montroll, 1958). The restrictions are partly due to the lack ofavailability of comparatively cheap measurement technology that allows the operation of suitable

test platforms in real traffic. Although this situation is now being rectified, and a range of in-strumented vehicles exist across the globe (Allen, Magdeleno, Serafin, Eckert, & Sieja, 1997), suchdata is clearly still at a premium.

One instrumented vehicle that has been increasingly used in a range of applications (Brack-stone, McDonald, & Wu, 1997; Brackstone, Sultan, & McDonald, 2000; McDonald, Brackstone,

& Sultan, 1998) is that at TRG Southampton, which over the last three years has been deployedto collect data primarily on car following, in order to conduct calibration and validation of

behavioural models from a microscopic standpoint. It is the findings of one phase of this studythat are reported in this paper.

2. Background

The topic of car following models, i.e. the time series relationships describing the accelerativebehaviour of a driver, a, as a function of their surroundings (typically ground speed, v, in-tervehicle separation, DX and relative speed, DV), has been in place in traffic science for

around 45 years (Chandler et al., 1958), and a wide range of competing models have evolved

(Gipps, 1981; Helly, 1959). (For a review see Brackstone and McDonald, 2000.) These, and otherformulations have been increasingly used both in simulation (Benz, 1994) and theoretical inves-tigations (Del Castillo, Pintado, & Benitez, 1994; Nelson, Bui, & Sopasakis, 1997). However,

comparatively little work has been performed on testing the validity of the underlying model, withthe most common approach being to examine the macroscopic implications of the formulation(May & Keller, 1967) or extract surrogates of microscopic factors from related macroscopic

observables (Hoyer & Fellendorf, 1997).Perhaps the most justifiable formulation is that of the so-called Action Point model, differing

versions of which have been independently derived by a number of researchers since the 1960s.(For a complete exploration regarding the choice of this model over and above others available,

the reader is referred to Brackstone and McDonald (2000), Brackstone, Wu, and McDonald(2001), and McDonald et al. (1998), and it is important to emphasise that it is the calibration of

the model that is the focus of this paper, its choice, although worthy of discussion, is not exploredhere.) Perhaps the earliest contribution to this formulation is due to Michaels (1963) and Todosiev

(1963), who suggested that car-following, in many cases, would be controlled by the presence ofperceptual thresholds. These thresholds, based on changes in distance, relative speed and/or therate of divergence of the apparent visual angle of the vehicle ahead, ht ($DV=DX2), would serveto delineate an area in DX DV space within which the driver of the vehicle would be unable tonotice any change to his dynamic conditions, and would seek to maintain a constant acceleration.Although an equivalent model was later defined by several other researchers using a non-psycho-

32 M. Brackstone et al. / Transportation Research Part F 5 (2002) 3146


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physical basis (Lee & Jones, 1967), the best known subsequent work is perhaps that by Lee

(1976), and most notably by the research team at IfV Karlsruhe in Germany who assembled therange of thresholds into a coherent driver modelling system for the first time. (For a review see,

Leutzbach & Wiedemann, 1986).As stated above, the model is based around four thresholds, the nomenclature for which we

borrow from Leutzbach and Wiedemann (1986):

(a) A minimum desired following distance, ABX, which, measured from the front of the leadvehicle to the front of the following vehicle is given as:

ABXv AX BXpv 1where AX may be seen as the minimum desired spacing between vehicles when stationary (in-cluding L the length of the front vehicle), while BX is the additional spacing required to account

for motion, both of which will vary from driver to driver.

(b) A maximum desired following distance, given as:

SDXv AX BXpv:EX 2typically with EX producing an increase ofSDX (over ABX) of an additional 0.51.5 times the

dynamic speed component.

(c) A threshold for recognizing small negative (closing) relative speeds,

CLDVDX DX2=CX2 3It can be seen that this corresponds to a threshold in the perception of the divergence of the visual

angle according to the constant CX.

(d) A similar threshold for the perception of small positive (opening) relative speeds, with theconstant OP,

OPDVDX DX2=OP2 4On crossing one of these thresholds, a driver may perceive that an unacceptable change in either DX

or DVhas occurred and will execute a change in the sign of his acceleration, typically of the order of

0.2 m/s2 (Montroll, 1959). It is clear that oscillation between these thresholds will produce thecharacteristic spiral plots remarked on by many authors (Gordon, 1971). Although the basis and

structure of this model is now well known, and much similar supporting work is available elsewhere(Evans & Rothery, 1977) little has been attempted regarding its further calibration and expansion.It is the intent of this article to re-examine this model and where necessary amend these thresholds,to ensure that it is able to accurately describe the close following behaviour of UK drivers.

3. Data collection

Data used in this analysis has been collected using an instrumented vehicle, which has beenassembled at TRG Southampton over the last five years (Brackstone, McDonald, & Sultan, 1999).

M. Brackstone et al. / Transportation Research Part F 5 (2002) 3146 33


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The vehicle is equipped with three primary measurement suites. Firstly to measure ground speed,

an Optical Speedometer. Secondly, to measure the relative distance toand the relative speedofsurrounding vehicles, a Radar Rangefinder which can be fitted to either the front or rear of

the vehicle. The unit has an operational range in excess of 100 m, and a measured accuracy of0.2 m in range and 0.4 m/s in relative speed. Lastly, a videoaudio monitoring system allowinga permanent visual record of each experiment to be made, useful both for an analysis of mac-roscopic features, apparent to the driver but not detectable to the sensors (e.g. lane, visual

conditions etc.), and for clarifying potentially confusing radar output. Information from each ofthe sensors is sent to a controller PC at a rate of 10 Hz and recorded in 5 min blocks. Once eachexperimental run has been finished, the logged data is directly transferred to a removable 1 Gb

cartridge, and taken for analysis, where time series data on speed, intervehicle speed and sepa-ration are isolated.

The database was collected during 1997 using the passive mode of collection where the radarwas fitted facing rearward and observation made of following drivers. Data was collected in two

phases. Firstly, experiments were performed during April and May on the M27 three-lane mo-torway in the UK, between junctions 3 and 8 (a total of 13.5 km), chosen due to the relatively highflow levels found during the morning peak between 7 and 8:30 AM. Using this approach, high

speed traffic (60 mph) could be monitored in one direction (heading away from the City ofSouthampton), and peak hour traffic, exhibiting congestion and flow breakdown, monitored inthe other direction to provide data on following at lower speeds. In total the vehicle was deployed

over nine peaks on weekdays, over a three week period with from four to six laps of the test coursebeing conducted during each peak. This yielded, an average, time series of approximately 2 minduration for each of 76 observed following vehicles. Secondly, experiments were performed during

October on the M3 three-lane motorway between junctions 2 and 4a (a total of 22.2 km), during

Fig. 1. A Typical close following spiral.



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the morning peak between 7:30 and 8:30 AM. The vehicle was deployed during three peaks,

during weekdays over a one week period, with from three to four laps of the test course beingconducted during each peak. This yielded an average time series length of a little under 4 min for

each of 33 observed following vehicles. An example of one such trace is given in Fig. 1.

4. Adopted headway and its variation

The first objective to be addressed was to examine the distance keeping behaviour of each driverand to attempt to parameterise the two thresholds ABXand SDX. In doing so, it is first necessary

to identify the specific action or turning points that characterise these thresholds. For ABX, atrace with decreasing DX and negative DV changes to one with increasing DX and positive DV,

while for SDX, a trace with DX increasing and positive DV changes to one with DX decreasingand negative DV (see Fig. 2).

Although identification of these points is straightforward, care must be taken in their deter-mination. All traces associated with each observed driver were grouped together and subject to thesame four stage analysis process. (It is important to note that no effort has been made in this

analysis to distinguish behaviour and parameters according to scenario, for example slowingtraffic, queue formation, or to relate it to measurable macroscopic phenomena, such as localdensities etc. Such an analysis is the subject of ongoing work):

(a) Firstly for each driver, the traces were divided into semi-spirals or half-cycles, that linkeach of the ABXand SDX points and the transition time, as well as the ground speed for each

of the points noted.(b) Next, and in order to ensure only comparatively stable following sequences contributed to

the analysis (i.e. where the relative motion of the follower was not overly effected by large fluc-tuations in lead vehicle speedit is the most common form of car following we seek to exam-

ine) a subjective cutoff was imposed such that any semi-spiral time series, where the magnitudeof the lead vehicles acceleration was larger than 0.6 m/s2, was eliminated.

Fig. 2. Typology of a following spiral. Points ABX and SDX.



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(c) Thirdly, each set was divided according to the speed interval within which each semi-cycletook place, in 10 kph intervals, with a minimum of 10 s worth of time series data being required

from any one driver for inclusion.

(d) The minimum observed value of DX in each interval (or in the case of the analysis ofSDX,the maximum) was identified for each driver, along with its associated ground speed, and de-

fined as that particular drivers value for ABX(or SDX) for that interval. A plot of points pro-duced at this stage is presented in Fig. 3.

This last part of the analysis is particularly important, as it is tempting for statistical reasons toinclude all points for each driver for each interval and not just the absolute max./min. values. The

reason behind this is that not all of the identified points may necessarily be associated with achange in the drivers state (illustrated in several places in Fig. 1). For example, there are several

places where a trace will perform a mini-spiral over a spatial distance of maybe less than 1 m.These spirals are a straightforward result of the natural fluctuations present in traffic and, al-though we are examining the adjustment of a driver to the behaviour of the vehicle in front, it

must be born in mind that the lead vehicle itself is varying its speed as part of its own distancekeeping process to its leading vehicle and so on. (It is to be noted that these mini-spirals are anintrinsic part of the microscopic process and indeed their amplification and propagation may play

an important part in the onset of flow breakdown (Low & Addison, 1995).) The production of asingle point for each speed interval will eliminate all spurious points, with the one point remaining(although potentially not a true action point) being unlikely to be caused through minor fluctu-

ations. This treatment also minimises the effect that any one driver or time series may have on thedistribution, with at most one point being produced for each speed range, and hence producing

effectively a distribution equally weighted over the observed population. (In practice the maxi-

mum number of speed ranges contributed to by any one driver was 8, with on average, two rangesbeing contributed to by most drivers, and four only being exceeded in six of the 109 cases.) The

output of the preceding analysis therefore consists of a distribution of ABX and SDX points

Fig. 3. Distribution ofABX and SDX points by speed.



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across the observed driving population, and the absolute max. and min. for each of these

thresholds for each speed level is shown in Fig. 4.

It is clear from inspection of the above figures that neither of these thresholds obeys a setdeterministic relationship, with r2 values describing the fit of the data to simple relationships, suchas linear, quadratic etc., never rising above 0.36. If we restrict ourselves to describing the data interms of the functional relationships originally proposed for ABX (i.e. including a v1=2 term) we

find best fit values of 3.25 for AX L, 2.96 for BX, as opposed to the initially suggested values of2.5, however these relationships show a degree of fit of no more than of 0.2. (The best fit ob-tainable (r2 0:36) occurs for BX 5:4 with v to the power of 0.43.)

In order to better describe the data therefore, we choose to present these action points as a

function of a probability distribution based on ground speed. In the case of ABX, this probabilityfunction (and its associated smoothed version), given in Fig. 5, demonstrates that as speed in-

creases, the probability of a drivers action point being at a short following distance, decreases,with an increase of action point density at higher distances. This process continues up to a speed

of about 70 kph where the outward progression of the density profile slows, and at around 95 kphstops entirely, with subsequent increases in speed producing a decrease in action point density athigher values of DX. In essence, a three phase distance keeping behaviour would seem to be in

evidence. Firstly an increasing following distance with speed, giving way to a constant valuearound 6575 kph. Such a trend is perhaps unsurprising as it would seem intuitively obvious that

Fig. 4. Minima and maxima of ABX and SDX by speed level.

Fig. 5. Probability plots of minimum desired distance, ABX.



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the faster a vehicle travels, the more space a driver is going to allow to account for stopping

distances, and this has already been observed elsewhere (McDonald, Brackstone, Sultan, &

Roach, 1999). The second transition however may be more surprising with the speed invariantheadway reducing above 105 kph, perhaps reflecting the onset of a more aggressive type of be-haviour.

In the case of SDX a similar procedure has been adopted, however in this case the ratioSDX=ABX has been examined. (Again, low r2 values are found for simple deterministic rela-tionships (


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0.01 DX (in m/s). Although again eliminating high frequency transients, the principal reasonbehind this was to exclude any points where an action was being taken that was not controlled by

the drivers perception of the relative speed. In essence this threshold describes the minimumrelative speed that a driver would be able to detect and use in their decision making process, and

has been derived in several field studies in terms of probability distributions, describing thepercentage chance of a driver being able to perceive the given value of the relative speed

(Brackstone, 2000; Evans & Rothery, 1977). Again, as the data shows a wide scatter (r2 consis-tently


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subsequent minimum for the process, of 2.55 s (TTCmin). Although these experiments do notreally replicate the conditions which we have observed, as all excessive decelerations were removedfrom our analysis, it should in theory be possible to transfer TTC 0 to CLDV. Examination of our

data in the 5060 kph range used in the van Winsum study reveals a far larger set of TTCs ofgenerally 2158 s, and a general consideration of the data would seem to suggest that using TTCas a characteristic would appear to be less valid that the DV approach that we have adopted (a

constant TTC band that would evidence this is lacking due to the speed invariant form dem-onstrated in Fig. 8).

Another equally valid hypothesis is that although we have been attempting to parameterisethresholds according to DV (or a function thereof) it may well be that these thresholds are a

Fig. 8. Probability plots of detection threshold for opening situations (OPDV: upper) and closing (CLDV: lower).



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function of the JND discussed in the previous section, which instead of governing SDX may be

more suited to describing CLDV and OPDV. The reasoning for this is that it is at, or just before,the driver passes these points that they change their state from accelerating to decelerating, or

vice-versa, and must logically therefore have perceived some manner of change. An examinationof the values of OPDV=ABX and 1 CLDV=SDX for consecutive DX and DV action pointswould seem to validate this hypothesis in part with around 60% of the CLDV points, and 55% ofthe OPDV points lying in a range corresponding to commonly held values of a JND (618%,

Evans & Rothery, 1977).It is clear then that several alternative theories are available with which to explain these results,

however it is not possible with our current data to state with any degree of certainty, which of the

processes are the most likely to be taking place. Evidently all the points considered are above abasic perceptual threshold, but this does not imply that it is this perceptual function alone that is

responsible for providing the cues on which driving behaviour is based. Some clarification couldbe obtained by examining those points that had been discarded on the grounds of lying below the

basic optic flow cutoff, or by changing the cutoff to remove those points most likely to have beencaused by a JND change alone. It is important to note that such an examination would be futile aswe are attempting to separate two inputs that could both be used in making the same decision.

However, the ability to use our data in driver behaviour modelling is not limited, as it is thecircumstances surrounding the effect that we are investigating, not the cause, per se.

6. Discussion

Perhaps the most interesting finding from the preceding sections has been the proof that close

following is just that, in many instances, extremely close. Although such a finding is perhapsobvious when faced with the anecdotal evidence from our daily observations as drivers, itsquantitative evaluation has important consequences.

For example, let us examine the proportion of time headways less than a certain value, T,Pt< T, in order that we may conduct a comparison between the advice given to drivers re-garding recommended distances and that which is actually taking place. Before we do so, two

differences should be pointed out between our data and that of others. Firstly all static surveys ofheadways consist of spot measurements in space and time across the driving population, ourshowever contains far more variation, and is not equally weighted across all the observed drivers.(This point has been discussed earlier, and we do not consider that the slight bias toward a small

number of drivers will in practice effect our analysis.) Secondly when examining spot measure-ments, there is no way of telling at exactly which point on a spiral plot the observation has been

made. The observation could be a point close to SDX or ABX, the best that can be hoped for isthat over the course of the study an average between the two can be reached. In order to retain

comparability therefore the average following distance under consideration here has been taken asan average of the observed ABX and SDX points.

An examination of our figures reveals P< 2 (the recommended following distance as set outin Regulation 57 of the UK Highway Code (HMSO, 1993)) to be equal to 95.8%, whileP< 1:4 78:1%, P< 1 47:9% and P< 0:8 29:2%. Other sources have also reported highfigures for short headways. For example, Sumner and Baguley (1978) observed that at low flow



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(approx. one-third the flow levels present in our experiments) on the M4 and M5 in the UK,P< 1 $ 26%, however, due to the level of flow, the number of platoons encountered wasminimal, with a far greater proportion of vehicles with longer headways. Once these readings of

over 2 s are eliminated from their sample, P< 1 increases to 36% on the nearside and 63% on theoffside most lane, with a modal peak around 0.60.7 s (see Fig. 4). Data collected by Parker(1996), on cars driving through a roadworks section gives, we estimate, P< 1 $ 18% with a peakat around 1.21.4 s, while an analysis of distances for a particular set of speeds (6070 kph) gives a

roughly lognormal distribution with the bulk of the distances between 10 and 40 m. An illus-tration of how closely the data collected in our experiments agrees with these, and other sources,including the US California Code (Chandler et al., 1958), Hogema (1996), Huddart and LaFont

(1990) and Xing (1995) is shown in Fig. 9.Some sources disagree with these findings though. Colbourn, Brown, and Copeman (1978), in

investigating driver judgement of safe distances using an instrumented vehicle on a test track,reported an average following time headway of around 2 s at 80 kph (only reducing to 1.7 s at

48 kph). Additionally, Hogema (1996) has reported mean following headways of 2.4 s at 100 kphin simulator experiments. In both cases, there are two possible explanations for the discrepancy.Firstly, the methodology involved the drivers being observed in test vehicles in low risk circum-

stances. Secondly, it may be possible that as these experiments were performed in the absence oftraffic in neighbouring lanes, drivers were content to sit back and follow, whereas in real life, inhigh flow conditions, if one were to leave so large a gap, it is highly likely that a neighbouring

vehicle may move into it, potentially delaying the driver further. These, and other factors, addcredence to the need to collect normative driver behaviour in realistic situations, from within thetraffic stream.

Although we have established the extent of close following, it may also be instructive to ex-

amine potential reasons why this occurs. Let us consider the concept of a safe headway. If thevehicle ahead brakes, then it is clear that the following driver will have a set margin of time in

Fig. 9. Comparison of observed following distances with existing sources.



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which to brake in order to avoid a collision, and from simple Newtonian mechanics we can see

that this time, the braking time, tb DX0=v v1=2a 1=2aL, with a the decelerationadopted by the following driver, and aL, the deceleration adopted by the lead driver triggering the

situation. There also exists a second, reaction time, tr, the time required for the following driver tounderstand that the lead vehicle is decelerating and that a closing speed has developed. Thedifference between the two, tb tr, is the total time the driver has to achieve the correct level ofdeceleration. If we examine this analysis as performed by Lee (1976), where tr was taken as the

time required for the lead vehicle to exceed an angular divergence (or looming) threshold, then wesoon see that for the distances that we have found, decelerating safely would be impossible, with aminimum following distance in excess of 2 s being required in order to avoid collisions in all cases.

There are however a number of flaws with this theory, not the least of which being that it wasassumed that this was a worse case scenario where the brake lights of the lead vehicle would not

activate. It seems unlikely that drivers would in reality drive with this and indeed other-worstcase-safety assumptions in mind. Indeed it is likely that a driver would assume that he would be

able to instantaneously understand the implications of brake lights, and indeed would be able toperfectly match the deceleration of the vehicle in front. The only requirement from a driversviewpoint in such a situation, would be that enough reaction time was present in the time headway

to allow for the activation of braking. Is it thus possible to assume that most drivers have a self-perceived brake reaction time of around 1 s? Certainly this argument would make sense if oneconsiders that typical brake light activation may occur for decelerations in excess of 1.3% of the

ground speed ($0.4 m/s2 at typical speeds) (Ozaki, 1993) and that harsh decelerations may ac-tually be quite rare, even during periods of flow breakdown. (Touran, Brackstone, & McDonald,1999, finds that decelerations above 2 m/s2 comprise less than 0.05% of accelerations exhibitedwhen passing through a total of 8 flow breakdown periods lasting a total of 70 mina total of 1.8

s.) These factors, combined with the oft cited but rarely measured look-ahead factor may leadthe driver to indulge in a certain amount of educated risk taking.

Our findings also have direct implications for the design of new in-vehicle driver aids, as we

have seen, drivers would seem to be comfortable with much lower headways than previouslythought. Although some initial Adaptive Cruise Control prototypes have been investigated tocontrol a vehicle to follow at a headway of 2 s (Broqua, Lerner, Mauro, & Morello, 1991), fromFig. 9 it would seem likely that the public may be quite happy with lower values, such as those

found as the median of typical ABX and SDXs. Clearly the trade-off between customer accep-tance, capacity and safety is a complex issue and further research is essential before any suchpolicy is pursued.

7. Conclusions

In this article we have attempted to parameterise and suggest amendments to the Action Pointbehavioural model that has been used in the simulation of motorway driving, and in doing so,have collected a wide range of novel instrumented vehicle time series data. As indicated in the

introduction, this work has distinct implications to many fields including traffic flow theory, ourunderstanding of human perception, and indeed how drivers comply with the rules of the road.The use of the collected data, does not end with the analysis performed here however, indeed its



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final use, will be within a simulation model currently under test, where model output based on the

calibrated Action Point model, must be compared with empirical time series in order to ensurethat the logic of the model can replicate observed behaviour.

Concerning the future, much work remains to be done before car following can be even par-tially understood. One potential strand of research is to attempt to relate observable performanceto driver background, temperament and psychology (Ohta, 1993; Rajalin, Hassel, & Summala,1997), however in order to come to any conclusions with such an analysis a wide variety of

subjects are required to be monitored as part of a range of rigorous tests. Similarly, behaviourmay be related to macroscopic variable such as local density, travel time etc., and this is thesubject of a forthcoming publication. An alternative strand may be to further examine the dy-

namics of the process, for example although we have obtained an understanding of the bound-aries of car following, we have not looked at their temporal evolution, i.e. how the choice of a

particular value of ABX effects subsequent choices. Perhaps a more meaningful question, highlypertinent to Boltzman type flow modelling, is, what is the maximum velocity of ABX. Such an

examination would involve evaluation and perhaps ARIMA modelling of series of points, andalthough beyond the scope of this article, initial attempts at such an evaluation have revealed thatin stable flow, ABXand SDX can indeed be modelled by a first order autoregressive process. The

most rewarding investigations in the short term however would look to be phenomenologicalstudies based on evaluating the circumstances surrounding the selection of particularly shortheadways (


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Parker, M. T. (1996). The effect of heavy good vehicles and following behaviour on capacity at motorway roadwork

sites. Traffic Engineering and Control, 37, 524531.

Postans, R. L., & Wilson, W. T. (1983). Close-following on the motorway. Ergonomics, 26, 317327.

Rajalin, S., Hassel, S.-O., & Summala, H. (1997). Close following drivers on two-lane highways. Accident Analysis and

Prevention, 29, 723729.

Reiter, U. (1994). Empirical studies as basis for traffic flow models. Proceedings of the second international symposium on

highway capacity (vol. 2, pp. 493502). Sydney, Australia.

Sumner, R., & Baguley, C. (1978). Close following at two sites on rural 2 lane motorways. Transportation Research

Laboratory Report, LR859. Crowthorne, UK.

Todosiev, E. P. (1963). The actionpoint model of driver vehicle system. Engineering Experiment Station, The Ohio State

University, Columbus, Ohio, Report 202 A-3.

Touran, A., Brackstone, M., & McDonald, M. (1999). A collision model for safety evaluation of autonomous

intelligent cruise control. Accident Analysis Prevention, 31, 567578.

Winsum, W., & Heino, A. (1996). van Choice of time headway in car following and the role of time to collision

information in braking. Ergonomics, 39, 579592.

Xing, J. (1995). A parameter identification of a car following model. Proceedings of the second world congress on ITS

(pp. 17391145). Yokohama, Japan.


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Brackstone Et Al 2002