Car-following Models and Congestion Control with Followerstopper on a Ring-Road under Known Delay -- Examining Limit Cycle

This paper examines the IDM microscopic car-following model from a dynamical systems perspective, analyzing the effects of delay on congestion formation. Further, a case of mixed-autonomy is considered by controlling one car with Followerstopper in a ring road setting containing IDM vehicles as human drivers. Specifically, the stop-and-go waves phenomenon in idealized traffic from a dynamical systems perspective is examined. We show that Followerstopper-controlled vehicle is effective at eliminating emergent stop-and-go waves in the IDM traffic simulation. We show through simulation that the uniform flow manifold is unstable for the ring road simulation with IDM vehicles, and that replacing a single car with Followerstopper induces stability, allowing the cars to drive safely at a uniform speed. Additionally, the case of known delay is considered in a mixed-autonomy scenario. Our simulation result shows that while considering a known time delay, traffic waves emerge earlier than in the no-delay case. At the same time, a single-vehicle controlled using Followerstopper controller is able to prevent the emergence of traffic waves even in the presence of delay.