Fundamental Diagram of Traffic Flow from Prigogine-Herman-Enskog Equation

Recent applications of a new methodology to measure fundamental traffic relations on freeways shows that many of the critical parameters of the flow-density and speed-spacing diagrams depend on vehicle length. In response to this fact, we present in this work a generalization of the Prigogine-Herman traffic equation for aggressive drivers which takes into account the fact that vehicles are not point-like objects but have an effective length. Our approach is similar to that introduced by Enskog for dense gases and provides the construction of fundamental diagrams which are in excellent agreement with empirical traffic data.