In recent years, field experiments have been performed on ring roadways with human-driven vehicles or with a mix of human-driven and autonomous vehicles. While these experiments demonstrate the potential for controlling traffic flows by a small number of autonomous vehicles, the theoretical framework about such a possibility is to a large extent incomplete. Indeed, most work on mixed traffic focused on classical asymptotical stability notions, neglecting that human drivers are prone to the interconnected instability known in the literature as string instability. This work aims to enhance the existing theories to meet the questions raised by the field experiments. It starts from the observation that the standard notion of string stability on a ring roadway is too demanding for a mixed traffic scenario: therefore, a new interconnected stability definition, named weak ring stability, is proposed. This new interconnected stability notion, in combination with classical stability, is able to explain phenomena observed in field experiments and to highlight possibilities and limitations of traffic control via sparse autonomous vehicle. Furthermore, it allows designing AV controllers with improved string stability specifications, at the price of reducing the sparsity of the autonomous vehicles.

This article considers criteria to determine when stop-and-go waves form in platoons of human-driven vehicles, and when they can be dissipated by the presence of an autonomous vehicle. Our analysis takes the start from the observation that the standard notion of string/ring stability definition, which requires uniformity with respect to the number of vehicles in the platoon, is too demanding for a mixed traffic scenario. The setting under consideration is the following: the vehicles run along a ring road and the human-driven vehicles obey a combined follow-the-leader and optimal velocity model, while the autonomous vehicle obeys an appropriately designed model. The criteria are tested on a linearized version of the resulting platoon dynamics and simulation tests using nonlinear model are carried out.