A Stochastic Theory of the Diffusion of Traffic Flow

Abstract

This paper presents a study of the diffusion of traffic flow and an observation by a moving observer, that is, a Doppler's effect. First we introduce a time process and a space process, and we show they are composed Poisson processes under the suitable assumptions. Secondly, we derive transformation formulae between these processes, interpreting velocity as the measure preserving transformation. Moreover, we analyze a Doppler's effect occurring in an observation by a moving observer, and finally we demonstrate, in a simple case that the time process is a homogeneous Poisson process.