Derivation of Non-Local Macroscopic Traffic Equations and Consistent Traffic Pressures from Microscopic Car-Following Models

TL;DR

This paper compares methods for deriving macroscopic traffic equations from microscopic models, proposing a smooth particle hydrodynamic approach that avoids approximations and provides consistent traffic pressure expressions.

Contribution

It introduces a novel derivation method using smooth particle hydrodynamics, avoiding gradient expansions and theoretical inconsistencies in macroscopic traffic models.

Findings

The new approach avoids gradient expansions and approximations.

It provides a generalized expression for traffic pressure.

The method demonstrates broad validity of macroscopic traffic equations.

Abstract

This contribution compares several different approaches allowing one to derive macroscopic traffic equation directly from microscopic car-following models. While it is shown that some conventional approaches lead to theoretical problems, it is proposed to use a smooth particle hydrodynamic approach and to avoid gradient expansions. The derivation circumvents approximations and, therefore, demonstrates the large range of validity of macroscopic traffic equations, without the need of averaging over many vehicles. It also gives an expression for the ``traffic pressure'', which generalizes previously used formulas. Furthermore, the method avoids theoretical inconsistencies of macroscopic traffic models, which have been criticized in the past by Daganzo and others.