Steady state solutions of hydrodynamic traffic models

TL;DR

This paper analyzes steady state solutions in hydrodynamic traffic models, revealing seven types of inhomogeneous solutions and their universal properties, which are relevant for understanding traffic jams and model universality.

Contribution

It identifies seven inhomogeneous steady state solutions in hydrodynamic traffic models and discusses their universal characteristics and implications for traffic flow modeling.

Findings

Seven types of steady state solutions identified

Wide jam properties are uniquely determined

Universal behavior across different traffic models

Abstract

We investigate steady state solutions of hydrodynamic traffic models in the absence of any intrinsic inhomogeneity on roads such as on-ramps. It is shown that typical hydrodynamic models possess seven different types of inhomogeneous steady state solutions. The seven solutions include those that have been reported previously only for microscopic models. The characteristic properties of wide jam such as moving velocity of its spatiotemporal pattern and/or out-flux from wide jam are shown to be uniquely determined and thus independent of initial conditions of dynamic evolution. Topological considerations suggest that all of the solutions should be common to a wide class of traffic models. The results are discussed in connection with the universality conjecture for traffic models. Also the prevalence of the limit-cycle solution in a recent study of a microscopic model is explained in this approach.