Density Oscillations Between Lanes of a Multilane Highway

Denos C. Gazis, Robert Herman and George H. Weiss
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Denos C. Gazis: IBM Research Center, Yorktown Heights, New York
Robert Herman: General Motors Research Laboratories, Warren, Michigan
George H. Weiss: Institute for Fluid Dynamics and Applied Mathematics, University of Maryland

Operations Research, 1962, vol. 10, issue 5, 658-667

Abstract: The interchange of traffic density between lanes moving in the same direction is investigated on the basis of a simple mathematical model. Emphasis is placed on the question of stability, i.e., attenuation of disturbances from an “equilibrium density distribution.” A solution is obtained for a system of differential difference equations with a time lag corresponding to the interaction of two lanes. This solution is directly applicable to other problems described by similar equations, such as the follow-the-leader problem. The solution is generalized to n lanes, and it is found that the inherent instability is twice as great for n approaching infinity as it is for two lanes.

Date: 1962
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