Stability Analysis of Nonlinear Inviscid Microscopic and Macroscopic Traffic Flow Models of Bidirectional Cruise-Controlled Vehicles

TL;DR

This paper develops and analyzes a new bidirectional microscopic and macroscopic inviscid traffic flow model for vehicles with adaptive cruise control, providing stability guarantees and demonstrating exponential convergence under certain conditions.

Contribution

It introduces a novel bidirectional microscopic ACC model and derives a corresponding macroscopic model with stability analysis and convergence properties.

Findings

The microscopic model guarantees uniform convergence to equilibrium.

The macroscopic model exhibits exponential convergence of speed and density.

Numerical simulations validate the theoretical stability results.

Abstract

The paper introduces a new bidirectional microscopic inviscid Adaptive Cruise Control (ACC) model that uses only spacing information from the preceding and following vehicles in order to select the proper control action to avoid collisions and maintain a desired speed. KL estimates that guarantee uniform convergence of the ACC model to the set of equilibria are provided. Moreover, the corresponding macroscopic model is derived, consisting of a conservation equation and a momentum equation that contains a nonlinear relaxation term. It is shown that, if the density is sufficiently small, then the macroscopic model has a solution that approaches exponentially the equilibrium speed (in the sup norm) while the density converges exponentially to a traveling wave. Numerical simulations are also provided, illustrating the properties of the microscopic and macroscopic inviscid ACC models.