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

## TL;DR

This paper generalizes the Prigogine-Herman traffic equation to include vehicle length, resulting in fundamental diagrams that align well with empirical data, enhancing understanding of traffic flow dynamics.

## Contribution

It introduces a novel extension of the Prigogine-Herman equation accounting for vehicle length, improving the modeling of traffic flow relations.

## Key findings

- Fundamental diagrams match empirical traffic data.
- Vehicle length significantly affects flow-density relations.
- The model accurately predicts traffic behavior for aggressive drivers.

## Abstract

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.