On the Integration of Car-following Equations

A common principle of obtaining speed-flow-density relationships and thus capacities is by integrating car-following equations. However, the method of integration which is usually found in traffic-theory literature, is incorrect from a mathematical point of view. The error is due to ignoring the statistical distribution of the spacings between consecutive vehicles. In the paper it is shown how this distribution can be incorporated into the integration procedure. The results obtained are analysed and interpreted.