The paper introduces a high level speed control method for the coordination of multiple autonomous vehicles (AVs) in roundabout scenarios. The aim of the control method is to guarantee collision-free motion of the AVs, and similarly, to minimize their traveling time. In the method a priority-based ordering process of the AVs is used, which enforces the time-efficient motion of the AVs. The collision-free motion is guaranteed through an optimization-based method including control input constraints. The ordering process and the optimization form a low complexity solution, which requires low computation effort. The proposed control strategy is involved in the high level of a hierarchical control structure. The effectiveness of the proposed control strategy is illustrated by simulation examples and hardware-in-the-loop demonstration.