Distribution function properties and the fundamental diagram in kinetic traffic flow theory

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.