On the Statistical Distribution Function Theory of Traffic Flow

The homogeneous time-independent solution for a one-car speed distribution function is derived for a Boltzmann-like approach to the statistical theory of traffic flow. Numerical results are discussed for a number of different desired speed-distribution functions. Among these distribution functions, chosen for mathematical simplicity are, for example, the exponential, linear, and parabolic. Flow versus concentration curves and distribution function versus speed curves are given for several of the models.