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As vehicles become autonomous and connected, intelligent management techniques can be utilized to operate an intersection without a traffic light. When a Connected Autonomous Vehicle (CAV) approaches an intersection, it shares its status and intended direction with the Intersection Manager (IM), and the IM checks the status of other CAVs and assigns a target velocity/reference trajectory for it to maintain. In practice, however, there is an unknown delay between the time a CAV sends a request to the IM and the moment it receives back the response, namely, the Round-Trip Delay (RTD). As a result, the CAV will start tracking the target velocity/reference trajectory later than when the IM expects, which may lead to accidents. In this article, we present a time-aware approach, Crossroads+, that makes CAVs’ behaviors deterministic despite the existence of the unknown RTD. In Crossroads+, we use timestamping and synchronization to ensure that both the IM and the CAVs have the same notion of time. The IM will also set a fixed start time to track the target velocity/reference trajectory for each CAV. The effectiveness of the proposed Crossroads+ technique is illustrated by experiments on a 1/10 scale model of an intersection with CAVs. We also built a simulator to demonstrate the scalability of Crossroads+ for multi-lane intersections. Results from our experiments indicate that our approach can reduce the position uncertainty by 15% in comparison with conventional techniques and achieve up to 36% better throughputs.