A DISTRIBUTIONAL MODEL OF HIGHWAY TRAFFIC FLOW WITH APPLICATION TO HIGHWAY PRICING

A kinetic theory theory of highway traffic due to I. Prigogine, et al., is compared with observed highway speed distributions. An argument is made that in the absence of congestion or speed limits, highway speeds are lognormally distributed. The lognormal speed distribution is adjusted for speed limits and applied to the kinetic model. It is shown that regardless of the values of the parameters in the kinetic model, a satisfactory fit to both mean speed and variance of observed traffic cannot be obtained.;A distinction is made between space mean speed and time mean speed for highway traffic. This leads to the necessary inclusion of the variance of f(v) in the classic highway pricing problem in economics. Optimum congestion tolls on a highway are calculated with and without considering variance. It is found that, at least in some circumstances, the inclusion of variance in the problem significantly changes the solutions obtained.;An analysis of the ratios of frequencies of speeds with and without congestion leads to the conclusion that f(,1)(v)/f(v), where f(v) is the probability density function of the speed distribution under congestion and f(,1)(v) is the probability density function without congestion, is approximately proportional to a power of v. Further analysis leads to the conclusion that f(v) = kf(,1)(v)/(1 + (gamma)v((v/v)('p) - 1)) where k is a normality constant, v is the mean speed, (gamma) is a specified increasing function of highway density, and p is a parameter, possibly independent of density, to be determined. The model is tested against observed traffic and is found to give a fairly good fit for p (DBLTURN) 30.