A Contribution to Theory of Traffic Flow

This paper presents an analysis of a car following model of general form: ẍ_{n + 1} = A (ẋ_n -ẋ_{n + 1})/(x_n - x_{n + 1})^m, where A and m are constants, x_{n + 1} is the position of the following car, x_n the position of the followed car, ẋ_{n + 1} and ẋ_n the corresponding velocities, and ẍ_{n + 1} the acceleration of the following car. Several specific values of m are considered and their correlation with various traffic flow diagrams is established. Traffic flow in which all drivers, in line of vehicles, maintain a certain minimum safe distance is represented by the case, m = 0. The case, m = l, is shown to lead to a velocity-concentration curve due to Greenberg. The case, m = 2, is correlated with the rate of change of the visual perceptual angle of the follower and is shown to lead to Greenshields' velocity-concentration curve. Finally, the implications of the case when → ∞ are explored.