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

Since the early days of traffic engineering, traffic flow stability has attracted a lot of attention, as the frequent occurrence of traffic jams, caused by small perturbations in traffic flow such as a sudden deceleration of a vehicle, deteriorate the performance of traffic flow and the utilization of the available infrastructure. Such traffic jams are usually related to instabilities in traffic flow, resulting in the formation of stop-and-go waves, propagating upstream the traffic flow. Emerging technologies in the field of Vehicle Automation and Communication Systems (VACS), such as Adaptive Cruise Control (ACC) systems, appear to be a remedy to reduce the amplitude or to eliminate the formation of such traffic instabilities. To this end, this work aims to derive a stability threshold of a novel macroscopic model, developed to simulate the flow of ACC-equipped vehicles, and study the impact of such vehicles on the stabilization of the traffic flow, with respect to small perturbations. The adopted macroscopic approach reflecting ACC traffic dynamics is based on the gas-kinetic (GKT) traffic flow model. The analytic results show that ACC vehicles enhance the stabilization of the traffic flow; the instability region is very narrow and by reducing the ACC time-gap setting it moves to higher values of density.