Some models for traffic congestion.

This paper is concerned with two simple congestion models for traffic. First a stochastic model for vehicles travelling in a one-lane road of maximum capacity is considered; probabilities for the number of vehicles on the road at a certain time are derived, and a measure of traffic congestion defined in terms of them. Two-lane road models are then discussed; deterministic solutions are found for several of these with lanes of certain maximum capacities. Analogous stochastic models, though not easily solvable in an explicit form, readily yield stationary probabilities of the number of vehicles in the two lanes.