A Theory of the Diffusion of Traffic Platoons

A theoretical investigation is made of the diffusion of a traffic platoon as it moves down a road. The basic assumption of the mathematical model is a kinematical one—that the speeds of the cars in the platoon are distributed normally. The parameters of this distribution are related to a diffusion constant that measures the spreading of the platoon. For certain assumed initial conditions, analytical and numerical solutions of the model are presented and applied to the problem of the coordination of two successive traffic lights.