STATISTICAL PROPERTIES OF LOW-DENSITY TRAFFIC
Abstract : An infinitely long line of traffic moving on a highway without traffic lights or other inhomogeneities is studied. It is assumed that each car travels at a constant speed which is a random variable. A further assumption is that when one car overtakes another, passing is always possible and occurs without change of speed. It is shown that any initial headway distribution must relax to a negative exponential distribution in the limit of t becoming infinite. The statistics of passing events are examined, and it is shown that the probability of passing or being passed by n cars in time t is described by a Poisson distribution. (Author)