Citation

Mochon S. Math. Model. 1987; 9(1): 1-11.

Copyright

(Copyright © 1987, Elsevier Publishing)

DOI

10.1016/0270-0255(87)90068-6

PMID

unavailable

Abstract

In this paper we present an application of the theory of traffic flow formulated by Lighthill and Whitham to problems where a section of a road imposes different conditions on the flow of cars. To represent these situations mathematically, we use a different flow-density relationship which contains implicitly the changes in the properties of this special section of road. With this approach we analyze first some simplified problems of this type, the solutions of which are of use in more complicated problems. Also, we obtain the corresponding steady-state solutions and discuss their stability. Finally, to illustrate these ideas on more realistic situations, we obtain the solutions of the flow produced by heavy rain on a section of a highway and by the slowing down of a convoy of trucks moving on one lane of a three-lane highway.