Finite-size effects in the Nagel-Schreckenberg traffic model

Abstract

We examine the Nagel-Schreckenberg traffic model for a variety of maximum speeds. We show that the low-density limit can be described as a dilute gas of vehicles with a repulsive core. At the transition to jamming, we observe finite-size effects in a variety of quantities describing the flow and the density correlations, but only if the maximum speed V_{max} is larger than a certain value. A finite-size scaling analysis of several order parameters shows universal behavior, with scaling exponents that depend on V_{max}. The jamming transition at large V_{max} can be viewed as the nucleation of jams in a background of freely flowing vehicles. For small V_{max} no such clean separation into jammed and free vehicles is possible.