Application of the Theory of a Single First Order Equation to Traffic Flow

Abstract

Few years ago, Lighthill and Whitham (1955) published a lengthy paper dealing with the theory of highway traffic flow .The basic idea in their approach to the problem is that the flow of traffic along a highway is analogous to the flow of a fluid in an open channel or pipe. This point of view replaces a long column of closely spaced discrete moving vehicles with an equivalent continuous moving stream of liquid (e.g. water) or gas (e.g. air). In other words, Lighthill and Whitham analyzed the phenomenon of traffic flow as though it were a problem in fluid mechanics. This approach allows some, though certainly not all, of the physical and mathematical relationships of hydrodynamics and aerodynamics to be utilized in the traffic flow problem. (Bank, p. 272)

DOI: http://dx.doi.org/10.3126/jie.v9i1.10681

Journal of the Institute of Engineering, Vol. 9, No. 1, pp. 175–181