Citation

Gazis DC, Herman R, Weiss GH. Oper. Res. 1962; 10(5): 658-667.

Copyright

(Copyright © 1962, Operations Research Society of America, Publisher Institute for Operations Research and the Management Sciences)

DOI

10.1287/opre.10.5.658

PMID

unavailable

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.


Keywords: Driver distraction;