Traffic flow models recently discussed in the literature are mostly centered on either cellular automata or the hydrodynamic analog. The present paper reconsiders the approach of Prigogine and Herman [Kinetic Theory of Vehicular Traffic (American Elsevier, New York, 1971)], which hinges on the distribution function $f(x, v, t)$. While the work of Prigogine and Herman is an ab initio treatment, this paper presents an empirical alternative analysis regarding the fundamental diagram as an input quantity. With a series ansatz, solutions for $f$ in both, the stationary and time-dependent case, can be obtained. A number of traffic phenomena are shown to be reproduced.

• Received 17 July 1996

DOI:https://doi.org/10.1103/PhysRevE.54.6058