A theorem on geometric probability and applications

the long version

Renyi has considered an interesting model of traffic flow on a divided highway which extends to infinity in one direction without traffic lights or other inhomogeneities. It is assumed that each car travels at a constant speed which is a random variable and passing is always possible without delays. Among others, Renyi has obtained some results regarding mainly the spatial distribution of cars along the highway when the temporal distribution of cars is assumed to be described by a Poisson process. The purpose of the paper is to discuss a number of results that can be related to low density traffic flow models on an infinite highway. (Author)