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

by Denos C. Gazis,
Robert Herman,
Richard W. Rothery,

Serial Information: Journal of the Engineering Mechanics Division, 1963, Vol. 89, Issue 6, Pg. 29-46

Document Type: Journal Paper


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.

Subject Headings: Traffic analysis | Traffic flow | Transportation studies | Mathematics | Driver behavior | Traffic models | Equations of motion | Automobiles

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