With the rapid advancement of autonomous driving and vehicular communication technology, intelligent intersection management has shown great promise in improving transportation efficiency. In a typical intelligent intersection, an intersection manager communicates with autonomous vehicles wirelessly and schedules their crossing of the intersection. Previous system designs, however, do not address the possible communication delays due to network congestion or security attacks, and could lead to unsafe or deadlocked systems. In this work, we propose a delay-tolerant protocol for intelligent intersection management, and develop a modeling, simulation and verification framework for analyzing the protocol's safety, liveness and performance. Experiments demonstrate the advantages of our proposed protocol over traditional traffic light control, and more importantly, demonstrate the importance and effectiveness of using this framework to address timing (delay) in vehicular network applications. This work is the first step towards a comprehensive delay-aware design and verification framework for practical vehicular network applications.