Contributions to the kinetic theory of traffic flow with queuing

Citation

Molloy, Charles T. (1985) Contributions to the kinetic theory of traffic flow with queuing. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/d1e4-5g29. https://resolver.caltech.edu/CaltechETD:etd-03262008-101545

Abstract

This thesis contains investigations of the effects of a probability distribution of the desired speeds of the drivers and of the effects of overtaking waiting time. It deals only with traffic for which the density is less than the critical density. Part I concerns simple approaches for assessing the effects for steady-state flow. Part II is a detailed formulation of integro-differential equations for the velocity distribution functions. We prove that solutions to these equations exist, are unique, are nonnegative, and are continuous along characteristics. We make use of the simplifying assumption that, in lighter traffic, a car that has been slowed by one car is unlikely to be slowed still further before passing. We examine the possibility of constant speed, constant shape solutions, and we investigate some special solutions as time approaches infinity. Delta function solutions are found. For one case, we look at the difference between the velocity distribution functions for models with continuous vs. discrete spatial distributions. We compare the steady-state case for the model of Part II with that of Part I. Preliminary comparison with observations is good.

Thesis Files