# Cooperative Roundabout Control Strategy for Connected and Autonomous Vehicles
## 1 Introduction  
Traffic smoothness is a description of the consistency and invariance of traffic flow. A common symptom of unsmooth traffic is traffic oscillations, which is the \"stop-and-go\" or \"slow-and-fast\" flow pattern [1]. Traffic oscillations can result in traffic congestion, thus affecting traffic capacity, reducing traffic safety, and increasing energy consumption. Compared to traffic flow on freeways, urban network traffic has lesser smoothness due to the presence of intersections. The intersection is an essential component of urban road networks. Compared to other road facilities, traffic flow conflicts are more complex at intersections due to the number of different flow directions [2]. Therefore, the efficiency and capacity of an intersection are critical factors for measuring urban transportation system performance. In general, intersections are stop-controlled or signal-controlled. Stop-controlled intersections do not allow multiple vehicles to use the intersection at the same time to ensure safety, which can be inefficient in high-demand cases. Traffic signals separate conflicting traffic flows into different signal phases to enhance the intersection safety. However, the variance and uncertainty in demand decrease the efficiency of signalized intersections. Intersection signal optimization methods, such as [3; 4; 5], focus on optimizing the phase lengths to the incoming demands adaptively to reduce inefficient phase time and enhance the overall throughput of the intersection. However, due to the existence of the red phase, traffic has to stop at intersections, leading to limited smoothness. Compared to signalized intersections, a roundabout has smoother traffic flow characteristics. Roundabouts are circular intersections where road traffic only flows in one direction around a central island. Vehicles only yield to the traffic rather than stop entirely at entry points of the roundabout. Therefore, roundabouts can enhance the smoothnessof the intersection. Ref. [6] showed that there is an 89 percent reduction in delays and a 56 percent reduction in vehicle stops after the conversion from signalized intersections to roundabouts. Additionally, roundabouts can improve traffic safety. On the one hand, vehicles will not speed up to try to beat a traffic light because there is no incentive that vehicles can skip a long red phase if they do so. On the other hand, the one-way traffic in the roundabout reduces the possibility of severe T-bone and head-on collisions. Ref. [6] found a 72-80 percent reduction in injury crashes and a 35-47 percent reduction in all crashes in studies of intersections converted from traffic signals to roundabouts. This is because there are only eight conflicting points in a typical four-approach roundabout (without any crossing conflicting points), while a four-approach signalized intersection has 32 conflicting points (16 of them are crossing conflicting points). Compared to merging and diverging conflicting points, crossing conflicting points can entail a higher likelihood of severe accidents because vehicles have higher relative speeds. However, since traffic flows from different directions are not as clearly separated as in signalized intersections, there are more merging and diverging behaviors in roundabouts, which can be challenging for human drivers. To ensure safety, drivers are required to operate vehicles at low speeds when passing through a roundabout. The major causes of collisions in roundabouts are speeding, failing to yield, and improper stopping when proceeding in roundabouts [6]. Further, signalized intersections can adjust the phase lengths of flows from different directions to achieve better system performance, while roundabouts follow the first-come-first-serve rule more strictly as they lack holistic control schemes.