Phase-Space Analysis of Fluid-Dynamical Models of Traffic Flow

TL;DR

This paper analyzes two fluid-dynamical traffic flow models using phase space methods to understand their steady states and trajectories, providing insights into their dynamic behavior.

Contribution

It offers a novel phase space analysis of Borsche-Kimathi-Klar and Helbing traffic models, highlighting their steady states and trajectories.

Findings

Explicit phase space trajectories constructed

Steady states of models identified and discussed

Dynamic behaviors analyzed through phase space paths

Abstract

The present research article is devoted to the study of two fluid-dynamical traffic models and their steady states by first analyzing the kinetic-type Borsche-Kimathi-Klar model and the Navier-Stokes-type Helbing model. To fulfill this purpose, the study is made by means of a general analysis in the phase space. Phase space paths are constructed in several cases for both models, evaluating explicitly some phase space trajectories. Ultimately, the results of these analyses are discussed.