Several authors have originated and developed models to describe the traffic flow on highways. There are at least two approaches to this problem. The microscopic approach, sometimes referred to as the car following theory, takes as its elements individual vehicular spacing and speed, while the macroscopic approach deals with traffic stream flows, densities, and average speeds. In recent years it has been shown that the two approaches are interrelated. This paper consists of four major parts. First, a brief background will be given of macroscopic and macroscopic theories of traffic flow, with special emphasis on their interrelationship. A comprehensive matrix is the developed results in a set of steady state flow equations, which includes the major macroscopic and microscopic theories. The third portion of this paper consists of analytical techniques for evaluating the various theories on the basis of experimental data. The last section deals with the investigation of a continuum of non-integer car-following models for the development of deterministic flow models, which describe interrelationships between flow characteristics.
Abstract