Estimating the Relationship Between Accident Frequency and Homogenous and Non-homogenous Traffic Flow
L Hiselius, Lund Institute of Technology, SE
Accident prediction models are central when discussing traffic safety analysis. Using these models, we try to allocate resources in the best way by identifying dangerous locations that we may need to take care of. When identifying these locations we have to control for the exposure, i.e. the traffic flow, giving cause the accidents. Research indicates that the relationship between the number of accidents and traffic flow is non-liner, i.e. the ratio is not constant. For instance, an early report from Vickrey (1968) suggests that the marginal accident rate is 1.5 times the average accident rate and according to Hauer and Bamfo (1997) and a majority of the results reviewed in Ardekani et al (1997), the accident rate even decreases with an increasing number of vehicles.
These results among others indicate that the accident rate is not proper to use in order to compare the safety of sites with different traffic flow. There is then an interest in studying the relationship between the accident frequency and the traffic flow more thoroughly. This is not an easy task, though, since necessary data can be hard to find.
Studies estimating accident prediction models sometimes use observations from similar locations with different average daily traffic volume in order to estimate the relationship between the accident frequency, the accident rate and the traffic flow. However, in these cases there will always be an uncertainty regarding how similar the locations in fact are. Site-specific factors, that are not considered, may then influence the result.
Another factor complicating the task of estimating accident prediction models is whether the number of different road user groups should be taken into consideration. The vehicles on the road are very much inhomogeneous with respect to weight, average driving speed, etc, which indicates that they may affect the traffic safety differently.
There is then an interest in estimating the relationship between the number of accidents and the traffic flow separated for different vehicle types. However, since there are even more difficulties finding data separated on the flow of different traffic groups than when studying a homogeneous flow, there are only a few empirical studies made analysing this matter.
The study presented here has the advantage of studying the same locations at different hourly traffic flows and having data on hourly traffic flow separated on the number of cars and lorries. The aim of the study is to estimate the relationship between the accident frequency and the traffic flow, treating the traffic flow in two different ways. In the first model the traffic flow is defined as the number of vehicles per hour treating the traffic flow as if consisting of homogenous vehicles. In the second model the traffic flow is defined as the number of cars and the number of lorries per hour in order to take into consideration that different road user groups may affect the traffic safety differently.
Data is collected from 83 road sections in rural areas of Sweden, where the Swedish National Road Administration continuously counts the number of passing vehicles. The assumption is made that the counted traffic flow at a stationary place is valid along the section. Information on police reported accidents with personal casualties, which have occurred on the studied road sections, is collected from 1989 to the middle of 1995.
Given the time and date of the accidents that have occurred on the road sections, the hourly traffic flow that prevailed at the time of each accident is obtained. Furthermore, in order to calculate traffic flow frequencies, information on the number of hours that each traffic flow has been observed during 1990 is also collected on the assumption that this is a representative year.
Only accidents occurring on sections without intersections are included. Accidents involving animals are excluded together with accidents that may be considered specific for each road section. Since it is not possible to obtain information on driving speed, the analysis will be made bearing in mind that the estimated effect of the traffic flow may also be an effect of speed adjustment. Moreover, there are several other factors likely to influence the occurrence of accidents, e.g. weather, road conditions, and drivers' characteristics. In order to take some of these factors into account, daylight accidents are studied separately as well as single and multivehicle accidents.
We distinguish between four road types, road type I with speed limit 70 km/h and road width 6-9,7 m, road type II with speed limit 90 km/h and road width 6-7,9 m, road type III with speed limit 90 or 110 km/h and road width 8-13 m without separated road lanes and road type IV, motorways, with speed limit 90 or 110 km/h. The number of accidents that occurred on the studied sections of road type I, II, III and IV is 59, 83, 179 and 186 respectively.
The relationship between the accident frequency and the traffic flow is estimated empirically using regression analysis. Both the Poisson and the Negative Binomial distribution are applied. In order to adopt the result on time periods and road systems of different length the accident frequency is defined as the expected number of accidents per hour and kilometre taking into consideration the number of hours and kilometres that each road type has been studied. An exponential function is estimated, since this function ensures that the expected number of accidents is a positive number and the use of this model function is being supported by studying the data visually and by analysing the residuals.
The result generally suggests a good fit for both the Poisson and the Negative Binominal regression model. All estimated parameter values are significantly different from zero.
Furthermore, for all road types, except for road type I, the estimated exponent is significantly different from one when treating the traffic flow as homogenous. Thus we may reject the hypothesis that the expected accident frequency increases in proportion with the traffic flow for these road types, i.e. that the accident rate is constant. Instead, an additional vehicle lowers the accident rate and increases the traffic safety.
Accidents that occur at daylight are also studied. For the majority of road types, the estimated parameters are lower than when studying accidents that have occurred throughout the day. The difference is, however, not significant. When studying different accident types the result indicates that the accident rate for single vehicle accidents decreases with increasing number of vehicles, whereas the accident rate for multivehicle accidents is constant or increasing. The result, when separating on type of accident, seems logical since the risk for a single vehicle accident ought to be lower at hours with heavy traffic than at hours with few vehicles on the road. Consequently, the risk for a multivehicle accident ought to increase with an increasing number of vehicles.
When studying the traffic flow for cars and lorries separately, a rather different result is received. For road type I and IV, the expected number of accidents increases more than proportionally with the number of cars per hour, i.e. that the accident rate increases. For road type II and III, the exponent is not significantly different from one, however. The estimated exponent for the flow of lorries is generally negative and different from zero.
The result suggests that the number of lorries per hour lower the expected number of accidents independently of the flow of cars.
The estimates when studying accidents occurring at daylight are not significantly different from those when studying all accidents together. The results for single and multivehicle accidents are similar to that of homogenous traffic flow when studying the flow of cars. The flow of lorries is again affecting the traffic safety positively, lowering the accident rate for both single and multivehicle accidents.
The result of this study indicates that there is important information lost if no consideration is taken to differences between vehicle types when estimating the marginal effect of the traffic flow. The accident rate decreases when the traffic flow is treated as if homogeneous. Since cars constitute the main part of the traffic flow, one may expect the same result when studying the flow of cars. However, when cars are studied the result suggests that the accident rate is constant or increases. The result with respect to the flow of lorries may be described as an effect of people?s unease when sharing the road-space with a lorry. The presence of a lorry may cause other road users attention to increase, which in its turn lowers the number of accidents occurring.
Ardekani, S., Hauer, E. and Jamei, B. (1997) Traffic Impact Models in Traffic Flow Theory - A State-of-the-Art Report, Gartner, N. et al (ed). Project Report, Oak Ridge National Laboratory.
Hauer, E., Bamfo, J., 1997. Two tools for finding what function links the dependent variable to the explanatory variables. Paper presented 5-7 November 1997 at the ICTCT Conference, Lund.
Vickery, W. S. (1968) Automobile Accidents, Tort Law, Externalities and Insurance. Journal of Law and Contemporary problems, vol. 33, pp: 464-484.
Association for European Transport