Derivation, Properties, and Simulation of a Gas-Kinetic-Based, Non-Local Traffic Model

TL;DR

This paper develops a gas-kinetic-based macroscopic traffic model with non-local interactions, enabling real-time simulation of extensive freeway networks and facilitating analysis of traffic dynamics under various conditions.

Contribution

It derives a novel non-local traffic model from gas-kinetic equations, improving simulation speed and calibration with empirical data.

Findings

Model allows real-time simulation of thousands of freeway kilometers.

Simulation results match observed non-linear traffic phenomena.

Parameters are directly related to driver behavior and adaptable to conditions.

Abstract

We derive macroscopic traffic equations from specific gas-kinetic equations, dropping some of the assumptions and approximations made in previous papers. The resulting partial differential equations for the vehicle density and average velocity contain a non-local interaction term which is very favorable for a fast and robust numerical integration, so that several thousand freeway kilometers can be simulated in real-time. The model parameters can be easily calibrated by means of empirical data. They are directly related to the quantities characterizing individual driver-vehicle behavior, and their optimal values have the expected order of magnitude. Therefore, they allow to investigate the influences of varying street and weather conditions or freeway control measures. Simulation results for realistic model parameters are in good agreement with the diverse non-linear dynamical phenomena observed in freeway traffic.