category: literaturenote citekey: martinrelationshipbetweencrashrate2002 title: Relationship between crash rate and hourly traffic flow on interurban motorways authors: "Martin, Jean-Louis" year: 2002 date: 2002-00-00 2002 doi: 10.1016/s0001-4575(01)00061-6 publication: "Accident Analysis & Prevention" url: "https://doi.org/10.1016/s0001-4575(01)00061-6" zotero_key: 3MW7H8KU zotero_storage: PT8EARZW collections: transpordi_planeerimine folder: 001_artiklid/Road Safety Indicators firstAuthor: "Martin, Jean-Louis"

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Accident Analysis and Prevention 34 (2002) 619–629

Relationship between crash rate and hourly traffic flow on interurban motorways

Jean-Louis Martin *

Institut National de Recherche sur les Transports et leur Se´curite´, ²⁵ a. Franc¸ois Mitterrand, ⁶⁹⁶⁷⁵ Bron, France Received 14 November 2000; received in revised form 18 April 2001; accepted 24 April 2001

Abstract

This paper describes the relationship between crash incidence rates and hourly traffic volume and discusses the influence of traffic on crash severity, based on observations made on 2000 km of French interurban motorways over 2 years. Incidence rates involving property damage-only crashes and injury-crashes are highest when traffic is lightest (under 400 vehicles/h). These incidence rates are at their lowest when traffic flows at a rate of 1000–1500 vehicles/h. For heavier traffic flows, crash incidence rates increase steadily as traffic increases on 2- and 3-lane motorways and inflect on 2-lane motorways when traffic increases to a level of 3000 vehicles/h. For an equivalent light traffic level, the number of crashes is higher on three-lane than on 2-lane motorways and higher at weekends (when truck traffic is restricted) than on weekdays. In heavy traffic, the number of crashes is higher on weekdays. We found no significant difference between the number of daytime and night-time crashes, whatever the traffic. No difference was observed in crash severity by number of lanes or period in the week for a given level of traffic. However, severity is greater at night and when hourly traffic is light. Compared to the number of vehicles on the road, light traffic is a safety problem in terms of frequency and severity, and road safety campaigns targeting motorway users to influence their behavior in these driving conditions should be introduced. © 2002 Elsevier Science Ltd. All rights reserved.

Keywords: Hourly traffic flow; Incidence rate; Interurban motorway; Modeling; Negative-binomial regression; Relationship; Road accident; Severity

1. Introduction

When you consider road crashes, it seems normal to try to correlate the number of crashes occurring in a given zone during a given observation period with the number of vehicles in this zone at the same period and exposed to a risk of crash.

Some authors have already examined this problem (Satterthwaite, 1981), although there are not many recent references. There is an abundant literature on traffic modeling from the traffic flow point of view (for regulation or forecasting, for example), but few studies simultaneously address the relationship between road traffic and crash occurrence. Some articles discuss traffic–crash relationships for a geographical area as a

* Tel.: +33-4-7214-2512; fax: +33-4-7214-2520 E-mail address: jean-louis.martin@inrets.fr (J.-L. Martin). whole on all the various types of roads (Jadaan, 1992). They use average traffic calculated on an annual (Turner and Thomas, 1986; McGuigan, 1987) or hourly basis (Gwynn and Baker, 1970; Ceder and Livneh, 1982; Zhou and Sisiopiku, 1997; Hall and Pendleton, 1990), which significantly influences the type of phenomenon demonstrated.

Other authors have developed models to predict crashes and traffic, using the V/C ratio (volume of traffic divided by the theoretical capacity of the road observed) to characterize the infrastructure used and its theoretical capacity to handle given traffic (Frantzeskakis and Iordanis, 1987). Others have tried to derive a Safety Performance Function to predict the effect of a change of exposure on the number of crashes (Mensah and Hauer, 1998) and to group together very different highway types. Most authors only consider injury-crashes.

This study is based on the observation of all crashes involving damage to vehicles and structures and all crashes causing injuries, occurring on most of the French motorway network. Knowledge about damageonly crashes enables the study of crash frequency and crash severity (as observed inside all vehicles involved), as a function of traffic. More specifically, as traffic flows are considered to be uninterrupted, the objectives of this study were: (1) firstly, to describe the relationship between the observed crash rate and hourly traffic volume and to examine the effects of the few exposure measurements we possess; and (2) to address the influence of traffic on the crash severity.

2. Material

Most French interurban motorways are toll roads. The data used in this study concerns crashes which occurred on the motorways managed by the Socie´te´ des Autoroutes du Sud de la France (ASF). This network comprises approximately 2000 km of motorways located in plains. Two thirds of these roads have two lanes in each direction and one third have three lanes. Average traffic is between 10,000 and 60,000 vehicles per day, 10–20% of which is trucks.

A crash report form is completed whenever a vehicle on or off the motorway pavement cannot resume its journey, without being towed away, after a crash. This is how we were able to obtain data concerning injurycrashes and damage-only crashes. For all these crashes, the crash circumstances, the condition of the vehicle occupants and a detailed description of the damage incurred following between-vehicle collisions and crashes into infrastructures are recorded.

Data relates to 2 years of observation—1997 and 1998. We identified 92 motorway sections considered homogeneous in terms of traffic between two motorway entry points and for which we possess hourly traffic measurements. The counting stations measure traffic flow at a point on each of these sections every 6 min, but only the average hourly figures are archived for the year. When no crash occurs on a section, we use the average hourly traffic volume. However, when a crash occurs, we replace this volume with the traffic volume noted on the 6-min traffic count recorded before the crash occurred This ensures that the traffic value is not modified by the crash, which would not be the case if 'uninterrupted' hourly rates were used. In what follows, in both cases we will call the result the hourly traffic flow. As the two traffic streams are considered separately, and as hourly traffic measurements are insufficiently reliable for only very few hours on some motorway sections, the study relates to over 2,900,000 'section-hour' observations.

3. Method

We addressed traffic flows per motorway rather than by lane. The V/C ratio frequently used for traffic management to combine different network types, seems less relevant for crash studies. In fact the assumption that the number of crashes is proportional to the number of lanes for a given volume of traffic on each lane does not seem very realistic as the traffic conditions are not always identical and crash typologies can be different. This leads us to distinguish between 2-lane and 3-lane motorways for one part of the analysis. A first stage of the study underlines the existence of a correlation between the average number of crashes and average corresponding traffic. We are then more specifically interested in the relationship between the hourly traffic flow and the incidence rates of all crashes as well as of vehicles damaged in these crashes (Hauer, 1995). Incidence rates are obtained by adding together, for all the hours during which a certain volume of traffic is measured, the number of events as the numerator, and the number of vehicles multiplied by the number of km as the denominator. For each traffic section, the 95% confidence interval (CI) around the average incidence rate (IR) is calculated by the conventional formula: IRVAR(IR), with variance of IR, var(IR) esti-

mated by the number of events (the number of vehicles×km)² . This estimate is valid as the number of events is very low according to the number of vehicles exposed, and we can therefore assume that the number of events is Poisson distributed (Rice, 1995).

Some graphs presented were smoothed with cubic spline functions as the objective is to give their form, but not to use them subsequently for predictive purposes. The method utilizes a selected parameter value, making it possible to obtain a solution closest to the mean points while smoothing the curve as much as possible (Reinsch, 1967).

The relationship between traffic flow and the crash incidence rate is examined by the number of lanes per motorway and by the two other 'continuous' dimensions available, relating to traffic volume and traffic conditions: the day–night and weekend–weekday variables.

A regression model was then used to include these different variables simultaneously. The systematic component of the model used to explain the number of crashes (na) on each section and taking account of the number of vehicles exposed (nve) has the form (with and ^k as the parameters to estimate): Ln(na)= Ln(nve)++k k=1kxk.

Conventionally the random component is supposed to have a Poisson distribution (Nicholson and Wong, 1993) and the model used is a Poisson regression. This law of distribution supposes the equality of the mean and the variance of the outcome. For a correctly specified model, the ratio obtained by dividing the deviation by the number of degrees of freedom must be close to 1. The fact that all values for adjusted models exceed 1 means that the data present an overdistribution (Mc-Cullagh and Nelder, 1989). To take account of this, the random component of the model is assumed to have a negative binomial distribution (Miaou, 1994; Maher and Summersgill, 1996; Poch and Mannering, 1996). This model of negative-binomial regression enables a 'best fit' to our data with a theoretical variance varying with the mean although it is necessary to estimate an additional parameter : Var(na)=E(na)+E(na)² .

It should also be noted that the assumption of an underlying Poisson distribution is only valid if the events considered are independent. This is not always the case for two crashes occurring at the same time in the same section, either because one crash causes another or two crashes are both caused by the same specific traffic conditions. However, as this problem concerned under 4% of all the crashes we observed, we can consider our working distribution hypothesis as valid. All the calculations were carried out with SAS (1999) software and STATA (1999) software for the negative binomial regression.

After addressing the influence of traffic on crash occurrence, we go on to describe crash severity and the traffic observed when the crash occurred based on the same factors as above. To explain the probability, P, of observing at least one injury-crashes in a crash we use a logistic regression with the form: Ln(P/(1−P))= + -K k=1kxk, the random component having a binomial distribution. In the different types of regression used, the contribution of each variable is tested by the ratio of the likelihood *L*1 of the model containing the variable and of the likelihood *L*0 of the model without it. The test is based on the property that the expression −2Ln(*L*1/*L*0) has a ² distribution with a number of degrees of freedom equal to the difference in the number of parameters between two nested models (McCul-

Fig. 1. Crash number and traffic flow versus time of day for 1997 and 1998.

lagh and Nelder, 1989). Only significant variables (-5%) are included in the final model.

We then address severity and the number of vehicles involved in the crash.

4. Results

During 1997 and 1998, our observations covered 2,937,886 motorway sections×hours and 33.8 billion vehicles×km. During this period 11,172 crashes occurred, involving 17,448 vehicles. Approximately 15% of the crashes injured people.

Fig. 1 shows, for each hour in the day, the annual average traffic flow and the annual number of crashes observed on the corresponding sections.

As expected, variations throughout a day between the least busy and most busy hours is high—from under 400 up to 1400 vehicles/h, and the average number of crashes follows this variation extremely closely.

Fig. 2 identifies each motorway section observed (1 point per direction) and shows the number of crashes observed per kilometer and traffic flow averaged over 1 year.

The linear trend is very clear, except for some specific sections where the number of crashes appears abnormally high. These are very specific sections like ring roads around large cities with a high number of access spurs used by vehicles on long and medium length trips as well as people travelling from their homes to work, for example. All are retained to ensure the continuity of the analysis as the impact of these sections is negligible within the complete set of observations.

Fig. 3 shows the distribution of the number of crashes per hour and per number of lanes.

Crashes observed on 2-lane motorways generally occur at traffic flows of under 1000 vehicles/h, with a definitely skewed distribution, whereas crashes on 3 lane motorways occur at different traffic flow rates with a flatter distribution and a mean of 1500 vehicles/h. This corresponds to a specific feature of the observed network, as the major highway from Lyon to the Spanish border constitutes the main part of the 3-lane motorways in our data, with a higher traffic flow than the rest of the network, and a higher percentage of trucks (about 20%).

⁴.1. Incidence rate and hourly traffic flow

Fig. 4 highlights the relationship between the crash rate, calculated as the ratio between the number of crashes involving damage-only and injury crashes on 10⁸ times the number of vehicles×km and traffic per hour. The continuous line corresponds to the confidence intervals represented by rectangles and the dotted line corresponds to the intervals symbolized by seg-

Fig. 2. Number of crashes per kilometer for each motorway section versus average hourly traffic flow over 1 year.

Fig. 3. Number of crashes per number of lanes versus hourly traffic flow.

ments. This convention applies to all the following graphs.

Several points of interest emerge: (1) the relationship is non-linear and the curve passes through a minimum, approximately 1000 vehicles/h for the 2-lane, and 1500 vehicles/h for the 3-lane, i.e. identical values in terms of volume/capacity; (2) the crash rate is significantly higher on 3-lane motorways when traffic is light. This remains true from a volume/capacity point of view too; and (3) the curve for 2-lane motorways inflects beyond 3000 vehicles/h. This could indicate the beginning of saturation phenomena, although this assertion should be considered with prudence given the confidence intervals (impact of the small number of crashes observed when traffic is heavy, as shown in Fig. 3).

As the number of vehicles involved in a crash tends to increase with traffic flow, it is also interesting to examine the incidence of crashed vehicles (Fig. 5).

As expected, the gradient is steeper with, for example, an average number of damage-only vehicles twice as high at 4000 than at 1500 vehicles an hour on 3-lane sections. Fig. 6 shows that the number of vehicles involved in a crash increases with traffic flow.

To some extent the shape of the graph in Fig. 5 appears to result from the overlay of the two curves in Fig. 6, as previously described by some authors as Ceder and Livneh (1982) or Zhou and Sisiopiku (1997).

The number of vehicles involved is one variable characterizing a crash, but many others vary with traffic flow. Fig. 7 shows the distribution, and traffic flow, of five identified crash types: crashes involving a single vehicle in the right-hand lane; crashes involving a

Fig. 4. Crash incidence rates (crashes/100 million vehicles×km) and hourly traffic flow.

Fig. 5. Crashed vehicles incidence rates (crashed vehicles/100 million vehicles×km) per hourly traffic flow.

Fig. 6. Crash incidence rates for crashes involving one vehicle and crashes involving two or more vehicles per hourly traffic flow.

Fig. 7. Distribution of five crash types per hourly traffic flow.

single vehicle in the left-hand or central lane if any; crashes involving two vehicles in the same lane; crashes involving two vehicles in different lanes and crashes occurring at motorway entrances and exits (all the other categories being in running sections).

As expected, crashes only involving one vehicle decrease as traffic flow increases and are replaced by crashes involving several vehicles and, more specifically, at the highest traffic peaks, by crashes involving vehicles in different lanes.

Two other exposure factors related to crash incidence rates and traffic flows are also known for all our observations—the sections-hours: day/night and weekday/weekend.

As Fig. 8 shows, when hourly traffic is considered the crash rate is not appreciably different by day and by night below 3400 vehicles/h. The part of the graph describing the trend for night-time crashes cannot be interpreted for traffic flows over 3400 vehicles/h as there are so few observations available.

Fig. 9 shows a slightly higher crash rate in light traffic at weekends, whereas the rate increases during the week as traffic builds up. The distinction between periods in which trucks are forbidden to use motorways and periods in which they are authorized was also addressed (in France from Saturday 22:00 h to Sunday 22:00 h, plus specific days when very heavy traffic is expected). The result is very close to the weekend–weekday distinction, which includes the previous one: weekend traffic with few trucks and, more generally, fewer professional drivers. This combination of dimensions—vehicle type and driver type—makes Fig. 9 difficult to interpret. No precision concerning the proportion of trucks in traffic were available from the data. The influence of trucks in the traffic flow on crash occurrence will be studied more specifically in a later work.

Fig. 8. Accident incidence rates per night and day versus hourly traffic flow.

Fig. 9. Accident incidence rates per weekend-weekday periods versus hourly traffic flow.

Table 1 Crash incidence rate ratios fitted by negative-binomial regression (with significant figures in bold type)

Traffic flow (vehicles/h)	Weekdays and 2-lanes	3-lanes	Weekend
1–400	1.61	2.43	2.05
400–800	1.03	1.41	1.28
800–2000	1.00	1.01	0.92
2000–3000	1.27	1.16	1.23
3000+	1.40	1.55	1.02

Table 2 Accident severity expressed as a percentage of accidents with injuries and relative risks (RR) of severity according to different variables

Factor	%	RR	95% CI
Night	16.9	1.17	1.06–1.28
Day	14.5	1
Weekend	15.1	1.0	NS
Weekdays	15.1	1
2×3 lanes	15.6	1.07	NS
2×2 lanes	14.7	1
1–400 vehicle/h	16.3	1.14	1.01 –1.28
400–800 vehicle/h	15.7	1.10	NS
800–2000 vehicle/h	14.3	1
2000–3000 vehicle/h	15.2	1.06	NS
3000+ vehicle/h	14.2	0.99	NS

⁴.2. Multiariate analysis

Prior to the introduction in a negative-binomial regression, the traffic flow was made discrete and split into five traffic flow classes to make it possible to avoid the linear constraint underlying the use of the continuous variable. This split is made because the relationship studied is roughly U-shaped, and because this will help for interpretation. The reference class selected is the mean traffic flow (800–2000 vehicles/h).

The traffic flow is then introduced in the model and the likelihood ratio test shows its significant contribution. We then introduce each of the three variables already analyzed in a univariate way. The variable night and day period is not significant and is not kept in the model. On the other hand, number of lanes and weekend–weekday period variables are significant both separately and together. As the main effects are significant, we introduce class 1 interactions—number of lanes×traffic flow class—and then weekend–weekday×traffic flow class. The likelihood ratio test shows the significant contribution of both interactions which leads us to present the complete model in Table 1 below. The Risk Ratios are the exponential of the parameter estimates.

This model confirms the two separate analyses of Figs. 4 and 5. As the reference class is a flow of traffic from 800 to 2000 vehicles/h on a 2×2-lane motorway on weekdays, Table 1 shows that, for example, the crash incidence rate is multiplied, on average, by 2.43 in light traffic (1–400 vehicles/h) on 3-lane motorways and by almost 5 (2.43×2.05) at weekends on 3-lane motorways. Similar results are obtained if the model is used to determine the number of damaged vehicles rather than the number of crashes as the outcome, with higher incidence ratios at higher traffic flows.

⁴.3. Accident seerity

The preceding analysis concerns crash incidence rates. The same analysis was also carried out on injurycrash incidence rates alone. It reveals similar trends, but the shapes of the curves obtained are difficult to interpret for the lightest and heaviest traffic densities, because the small number of injury-crashes generate very wide confidence intervals. However, knowledge about damage-only crashes makes it possible to break down the probability of observing an injury-crash when one is exposed to a risk of crash in a two- term product:

injury crashes vehicles×km ⁼ injury crashes injuries+damage only crashes ^× injuries+damage only crashes vehicles×km .

The first part of the analysis addresses the second term, i.e. the probability of observing a crash and the number of vehicles exposed. The second part of the analysis addresses the other term, i.e. the probability of observing at least one injury-crash or fatality once the crash has occurred, and traffic density at the time of the crash. We examined crash severity and traffic density using this method and the same variables as above the number of lanes, the day–night difference and the weekend–weekday difference. Table 2 shows the proportions of injury-crashes according to these three dimensions and traffic density.

No significant difference in severity is observed according to the number of lanes or the period of the week. On the other hand, crashes are 1.17 times more serious at night and 1.14 times more serious in light traffic, when separated into five classes, as above. A logistic regression is then used to model the probability that a crash involves injury-crashes. The explanatory variables are the day–night difference, the traffic and the interaction between these two factors. This relationship is not significant, which means that the increase in severity observed at night does not seem to depend on traffic density. The same test made with the two other factors used above and their interaction with traffic, does not reveal a significant difference.

In all the analyses, the statistical unit considered was the crash and not the damage-only vehicle. For this reason the number of vehicles involved in a crash is directly related to the severity criterion used. For example, the probability of observing injury-crashes in a crash involving two vehicles is equal to k times the probability of observing injury-crashes in each vehicle, with k=2 if we assume that severity is appreciably the same whether the crash involves another vehicle or any other obstacle, even if the vehicle overturns on the road. Using the same method as above, the logistic regression shows that severity increases with the number of vehicles involved (one, two and three or more), and differently with traffic density (the term expressing the interaction of the number of vehicles×traffic is significant). This is illustrated in Fig. 10.

For average traffic of 800 to 2000 vehicles/h, the proportion of injury-crashes depends on the number of vehicles involved (10% for crashes involving a single vehicle, 20% if two vehicles are involved, 29% per three vehicles and more). This multiplying factor is smaller for high traffic flows, and much higher for light traffic flows, with a severity 45% greater for crashes involving at least three vehicles and a volume of traffic of under 400 vehicles/h.

5. Discussion

Given the importance of traffic fluctuations inside 1 day, the time scale used appears especially relevant when studying the impact of traffic on crash occurrence. However it does not seem to be precise enough to highlight some extreme phenomena. For example, there are no observations of zero traffic during 1 h (for which the number of crashes could be only null) which means the crash/traffic flow rate should pass through the origin point of the graph. More problematically, the hourly traffic count does not make it possible to demonstrate total saturation (i.e. with total immobilization of all vehicles), although this would probably be possible with the original 6 min traffic count. Traditionally, traffic management studies address three dimensions considered as essential (May, 1990): traffic flow Q, speed U (average speed of all the vehicles on the road) and traffic density k. Fundamental relationships exist between these variables (TRB Highway Capacity Manual, 1994). For our study, only 'uninterrupted' traffic flow was available and the other dimensions were only determined from spot estimates. The fundamental relationship between volume and density shows that density increases in a nonlinear way with traffic up to a saturation threshold. However, on the motorway sections observed, hourly flows showing saturated traffic (during the great summer migrations) are very rare, and it seems likely we are always in the part of the graph in which traffic flow increases when the traffic density increases. In the same way, the threshold beyond which traffic flow starts to decrease at the same time as the average all-vehicle speed decreases is seldom reached in an hourly traffic count. In practice, the lack of data for these two dimensions does not prevent interpretation of the relationship between traffic flow and crash incidence rates, but does eliminate reasoning from a 'level of service' point of view.

Of the three factors examined during the analysis, only the day–night distinction does not appear to influence the crash incidence rate if hourly traffic is taken into account. In other words, crash frequency is not higher at night than during the day at equal traffic flows. Let us note that this study concerns only motorways, which means, compared to the rest of the network, a better visibility at night, and less problems with alcohol during long journeys (as is often the case on motorways). The proportion of injury-crashes is, on the other hand, higher by a little over 15%. A partial

Fig. 10. Accident severity and hourly traffic flow versus the number of vehicles involved.

explanation of higher severity at night is probably that it corresponds to a specific crash typology, with, in particular, crashes due to driver drowsiness or falling asleep, often leading to crashes at full speed.

The difference between the incidence rate—traffic curves and the period of the week is more difficult to interpret. At weekends, the crash rate is higher than in the remainder of the week for light traffic, but relatively stable beyond 1000 vehicles/h. Conversely, during the week, it rises regularly after 1500 vehicles/h. Perhaps one explanation of this rise is the increase in crash-generating configurations when traffic flow increases with a high proportion of trucks.

Finally, the impact of the number of lanes on crash incidence rates was analyzed carefully. It appears that when traffic is light, crashes are more frequent on 3-lane motorways. This remains true, although less significantly so, if V/C is considered. This result may appear surprising because the possibilities of crash avoidance are higher than on 2-lane motorways, but may also be due to higher average speeds or more unfavorable crash configurations. This issue will be studied in another work as the hourly traffic speed should soon be available.

We have prioritized the crash dimension rather than the damage-only vehicle dimension by analyzing data from an external viewpoint, like that of a motorway operator. This means that we are modeling the probability of observing a crash in a given set of traffic conditions. To reason as a vehicle occupant, the result shown in Fig. 5 is the most pertinent, i.e. for a given flow, the probability of being the victim of a crash is higher when traffic is light, and more likely on a 3-lane motorway. After moving through the minimum for hourly traffic of 1000 vehicles/h for 2-lane and 1500 for 3-lane motorways, it increases regularly at the same rate as the traffic, as does the probability of being in a crash involving several vehicles.

6. Conclusion

The estimate of the average number of vehicles exposed to the risk of crashes and knowledge about damage-only crashes made it possible to determine the probability of observing a crash involving several vehicles per kilometer and per time period and also the probability of injury in the event of a crash. The results obtained show that crash rates are highest, both for damage-only and injury-crashes, in light traffic, the lowest between 1000 and 1500 vehicles/h, and that both increase proportionally to the average number of vehicles involved per crash. In light traffic, the number of crashes is higher on 3-lane than on 2-lane motorways, and higher at weekends (or when truck traffic is restricted). When traffic is heavy, the number of crashes is higher on weekdays. On the other hand, there is no significant difference between daytime and night-time whatever the traffic.

Concerning crash severity, no difference was observed for the number of lanes or the period of the week for a given set of traffic. Conversely, severity is 17% worse at night, 14% worse in hourly traffic of under 400 vehicles/h and more particularly when traffic is light, for crashes involving several vehicles.

In comparison with the vehicles passing through, light traffic is a safety problem for crash frequency and severity. Although traffic flows of under 400 vehicles/h only account for 15% of all traffic, this problem is nevertheless worrying when, particularly in France, motorways with relatively light forecast traffic are starting to be built. This is why we believe it is important to introduce road safety campaigns targeting motorway users to influence their behavior in these driving conditions, in which average speeds measured are high and distances between vehicles often surprisingly small (Aron et al., 1999). The increased relaxation felt by the road user when traffic volume is light on motorways, probably leads to overcompensation in speed, to the detriment of his safety. This is probably similar on rural roads, although driving distances are generally longer, and driving while intoxicated less frequent.

In a subsequent research program, we will try to include those dimensions unavailable for this study, such as the percentage of trucks in hourly traffic and flow speed estimates.

Acknowledgements

We would like to thank the ASF (Southern France Motorways Operator) with whom we work for crash data base maintenance and more specifically Jean-Marie Be´rier and Nicolas Schwab who made the traffic data available. Our thanks also go to LICIT/INRETS researcher Christine Buisson for his expert advice, the members of UMRETTE, my laboratory, Mireille Chiron, Sylviane Lafont and Robert Quincy for their pertinent comments and Pierre Bloch and Yves Derrien for updating the database.

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