Macroscopic models for traffic and traffic safety

This paper describes models for traffic volumes and traffic safety. These models have a very simple mathematical form and consist of time parameters only. The first model assumes that fatality rates follow a negative exponential function. The second model assumes a logistic type of saturation model for traffic volumes. The models are applied to traffic volumes and fatality rates in the Netherlands, the United States, West Germany, and Great Britain. These applications show fairly good results. The agreement between the models and the data shows that linearity of the log-fatality rates and the log-volume rates turn out to be reasonable assumptions. Furthermore, a relation between the two models is suggested from the data that links safety outcomes to developments in traffic volume. From the models, predictions are made for traffic volume, fatality rates, and fatalities in the future on the basis of time parameters only.