Analytical Methods in Transportation: Mathematical Car-Following Theory of Traffic Flow

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Abstract
A mathematical theory that attempts to describe the detailed manner in which one vehicle follows another in a single lane is reviewed. According to this theory, the motion of a line of cars is described by a system of differential difference equations. The parameters entering these equations have been obtained by a series of car-following experiments. Stability criteria, as well as steady state flow relationships between density, speed, and volume of traffic, are presented. In order to test the validity of this car-following model in the case of single lane traffic flow, comparisons are made with a number of experiments and observations.

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