Low density traffic streams

Abstract

Low density traffic refers to the study of macroscopic properties of a traffic stream when vehicles travel independently of one another. It is usually assumed that each vehicle travels at a constant velocity, the velocity varying from vehicle to vehicle. We allow very general vehicular motions and study various aspects of the traffic streams. For example, it is shown that if π [a,b] is the expected time for a vehicle to travel fromatobunder the stochastic process governing the motion of vehicles, then a non-homogeneous Poisson spatial process with mean measure π is invariant.