The development of traffic and traffic safety in six developed countries.

Two models are presented, describing the development of traffic and traffic safety. Traffic volumes, measured by the total amount of vehicle kilometres per year, are expected to follow a sigmoid saturation curve over time. The logistic function is used to model this development. The fatality rate, the number of fatalities per vehicle kilometre, is chosen to measure safety. The (negative) exponential function is selected to model the fatality rates over time. It is argued that these two aspects of the traffic system are fundamental and that the development of the number of fatalities results by multiplication. Given this assumption, the fall in the number of fatalities, noticed in almost all developed countries after a steady increase until 1970, does not need a special explanation. It follows from the combination of the monotonically increasing traffic volumes and the monotonically decreasing fatality rates. The two parsimonious models fit the data fairly well for six developed countries. The parameters differ substantially between countries, but also show common features. It is found from the parameters of the logistic function, that for all countries the points of maximum increase in traffic volume coincide just after 1970, the moment of the energy crisis. It is concluded from this finding that the energy crisis was caused by the cumulating demands of the oil-consuming countries, resulting in a reaction of the oil-producing countries. From the parameters of the exponential function, it is found that there also is a common point of intersection for fatality rates around 1980. It is shown that the development of safety is directly related to the development of traffic. The ten-year delay is interpreted as the time necessary for planning and implementation of safety measures. Finally, a striking relation is found between the volume parameters and the fatality-rate parameters, suggesting that the number of fatalities is a function of the derivative of the amount of traffic in the mathematical sense. (A) This paper was published in a special issue of Accident Analysis and Prevention entitled 'Theoretical models for traffic safety'