A Highway Traffic Model

The trajectory of a car traveling at a constant speed on an idealized infinite highway can be viewed as a straight line in the time-space plane. Entry times are governed by a Poisson process with intensity parameter A leading to all trajectories as random lines in a plane. The Poisson distribution of number of encounters of cars on the highway is developed through random line models and non-homogeneous Poisson fields, and its parameter, which depends on the specific random measure employed, is obtained explicitly.