Motorway driver behaviour: studies on car following - CiteSeerX

Transportation Research Part F 5 (2002) 329–344 www.elsevier.com/locate/trf

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 models—the Action Point model—using 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. Ó 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 of increasing 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 opportunities are particularly relevant to motorway operations where both in-vehicle and roadside ITS technologies are developing rapidly, however, assessing the potential effects of any new system requires a sound base of behavioural understanding. (Establishment of an understanding of ‘normative’ 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).)

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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 Ó 2002 Elsevier Science Ltd. All rights reserved. PII: S 1 3 6 9 - 8 4 7 8 ( 0 2 ) 0 0 0 0 4 - 9

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M. Brackstone et al. / Transportation Research Part F 5 (2002) 329–344

One area in which such an understanding is seen as becoming increasingly important is dynamic driver behaviour, such as car following on a motorway, where a driver controls the brake and 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 process largely by either using static laboratory simulators (van Winsum & Heino, 1996) or vehicles on test tracks (Chandler, Herman, & Montroll, 1958). The restrictions are partly due to the lack of availability 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 instrumented vehicles exist across the globe (Allen, Magdeleno, Serafin, Eckert, & Sieja, 1997), such data is clearly still at a premium. One instrumented vehicle that has been increasingly used in a range of applications (Brackstone, McDonald, & Wu, 1997; Brackstone, Sultan, & McDonald, 2000; McDonald, Brackstone, & Sultan, 1998) is that at TRG Southampton, which over the last three years has been deployed to 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 study that are reported in this paper.

2. Background The topic of car following models, i.e. the time series relationships describing the accelerative behaviour of a driver, ‘a’, as a function of their surroundings (typically ground speed, ‘v’, intervehicle 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 other formulations have been increasingly used both in simulation (Benz, 1994) and theoretical investigations (Del Castillo, Pintado, & Benitez, 1994; Nelson, Bui, & Sopasakis, 1997). However, comparatively little work has been performed on testing the validity of the underlying model, with the 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 explored here.) 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 of perceptual thresholds. These thresholds, based on changes in distance, relative speed and/or the rate of divergence of the apparent visual angle of the vehicle ahead, ht (DV =DX 2 ), would serve to delineate an area in DX DV space within which the driver of the vehicle would be unable to notice 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-


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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 the range 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 lead vehicle to the front of the following vehicle is given as: p ABX ðvÞ ¼ AX þ BX v ð1Þ where AX may be seen as the minimum desired spacing between vehicles when stationary (including 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: p S DX ðvÞ ¼ AX þ BX v:EX

ð2Þ

typically with ‘EX’ producing an increase of S DX (over ABX) of an additional 0.5–1.5 times the dynamic speed component. (c) A threshold for recognizing small negative (closing) relative speeds, CL DV ðDX Þ ¼ DX 2 =CX 2

ð3Þ

It 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 the constant ‘OP’, OP DVðDX Þ ¼ DX 2 =OP2

ð4Þ

On crossing one of these thresholds, a driver may perceive that an unacceptable change in either DX or DV has 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 the characteristic ‘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 been assembled at TRG Southampton over the last five years (Brackstone, McDonald, & Sultan, 1999).

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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 to—and the relative speed of—surrounding 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 of 0.2 m in range and 0.4 m/s in relative speed. Lastly, a video–audio monitoring system allowing a permanent visual record of each experiment to be made, useful both for an analysis of ‘macroscopic 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 of the sensors is sent to a controller PC at a rate of 10 Hz and recorded in 5 min blocks. Once each experimental 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 separation are isolated. The database was collected during 1997 using the ‘passive’ mode of collection where the radar was 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 motorway in the UK, between junctions 3 and 8 (a total of 13.5 km), chosen due to the relatively high flow levels found during the morning peak between 7 and 8:30 AM. Using this approach, ‘high speed’ traffic (60 mphþ) could be monitored in one direction (heading away from the City of Southampton), and peak hour traffic, exhibiting congestion and flow breakdown, monitored in the 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 course being conducted during each peak. This yielded, an average, time series of approximately 2 min duration 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 being conducted 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 driver and to attempt to parameterise the two thresholds ABX and S DX . In doing so, it is first necessary to identify the specific action or turning points that characterise these thresholds. For ABX, a trace with decreasing DX and negative DV changes to one with increasing DX and positive DV , while for S DX , a trace with DX increasing and positive DV changes to one with DX decreasing and negative DV (see Fig. 2). Although identification of these points is straightforward, care must be taken in their determination. All traces associated with each observed driver were grouped together and subject to the same 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 slowing traffic, queue formation, or to relate it to measurable macroscopic phenomena, such as local densities 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 link each of the ABX and S DX 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 fluctuations in lead vehicle speed—it is the most common form of car following we seek to examine) a subjective cutoff was imposed such that any semi-spiral time series, where the magnitude of the lead vehicles acceleration was larger than 0.6 m/s2 , was eliminated.

Fig. 2. Typology of a following spiral. Points ABX and S DX .

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(c) Thirdly, each set was divided according to the speed interval within which each semi-cycle took 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 of S DX , the maximum) was identified for each driver, along with its associated ground speed, and defined as that particular drivers’ value for ABX (or S DX ) for that interval. A plot of points produced at this stage is presented in Fig. 3. This last part of the analysis is particularly important, as it is tempting for statistical reasons to include 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 a change 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, although 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 distance keeping process to its leading vehicle and so on. (It is to be noted that these mini-spirals are an intrinsic 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 a single 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 fluctuations. This treatment also minimises the effect that any one driver or time series may have on the distribution, 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 maximum number of speed ranges contributed to by any one driver was 8, with on average, two ranges being 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 S DX points

Fig. 3. Distribution of ABX and S DX points by speed.


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Fig. 4. Minima and maxima of ABX and S DX by speed level.

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 set deterministic relationship, with r2 values describing the fit of the data to simple relationships, such as linear, quadratic etc., never rising above 0.36. If we restrict ourselves to describing the data in terms 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 of 2.5, however these relationships show a degree of fit of no more than of 0.2. (The best fit obtainable (r2 ¼ 0:36) occurs for BX ¼ 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 probability function (and its associated smoothed version), given in Fig. 5, demonstrates that as speed increases, the probability of a driver’s 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 kph stops entirely, with subsequent increases in speed producing a decrease in action point density at higher 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 value around 65–75 kph. Such a trend is perhaps unsurprising as it would seem intuitively obvious that

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

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Fig. 6. Probability plots of ratio of maximum to minimum desired distance (S DX =ABX ).

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 invariant headway reducing above 105 kph, perhaps reflecting the onset of a more aggressive type of behaviour. In the case of S DX a similar procedure has been adopted, however in this case the ratio S DX =ABX has been examined. (Again, low r2 values are found for simple deterministic relationships (