Nonlinear Stability Analysis of a Macroscopic Traffic Flow Model for Adaptive Cruise Control Systems

The occurrence of perturbations in traffic flow may lead to the formation of stop-and-go waves traveling upstream, or to traffic jams. Therefore, traffic flow stability analysis is considered to be one of the fundamental problems in traffic flow theory, and a lot of effort has been spent to analyze the formation and evolution of such traffic flow instabilities. Recent advances in the field of Vehicle Automation and Communication Systems (VACS), including the most widespread Adaptive Cruise Control (ACC) systems, may consist a possible solution in reducing the magnitude or even eradicating the development of such traffic flow instabilities. This paper aims to perform a nonlinear stability analysis of a second-order macroscopic traffic flow model, which was recently developed by the authors for the simulation of the traffic flow of ACC-equipped vehicles, and identify the ways that ACC systems affect the stability of the flow, in relation with large traffic disturbances around the equilibrium state. Numerical simulations are additionally conducted, to validate the derived stability conditions.