Mathematical Models for Freely-Flowing Highway Traffic

An attempt is made to construct models for the motion of cars on a highway in a manner analogous to the way one treats the motion of molecules in a gas as described by the kinetic theory of gases. In particular the comparison is made between a traffic flow at very low volumes and the motion in a rarefied gas. From this, we are led to expect that even a very crude model of the interaction between individual cars will give a quite reasonable description of the collective behavior of large groups of cars. Some simple estimates of the dependence of average velocity on density and distribution of cars in various lanes of a multilane highway based upon very crude models seem to confirm this expectation.

Operations Research, ISSN 0030-364X, was published as Journal of the Operations Research Society of America from 1952 to 1955 under ISSN 0096-3984.