Scheduling driverless vehicles with different priorities to pass through intersections efficiently and safely has been becoming an important passing-through intersection (PTI) problem in the field of novel intelligent traffic systems (ITS), which is increasingly becoming cyber-physical-fused and social-serviceoriented. Considering new emerging features with possible priorities, a novel centralized priority scheduling mechanism is mainly explored in this paper. First, related pivotal aspects of environment and driverless vehicles are modeled by fusing their physical and kinematic characters. Based on these models, PTI-related motions are further abstracted as several reservation-oriented standard states and actions. Then, an event-triggered and state-driven autonomous control procedure is designed. By mapping vehicular relations in spatiotemporal domain into time-distance windows, a universal passing-through principle, rules, and priority-based scheduling mechanisms are proposed and described in detail. Finally, a priority scheduling algorithm sPriorFIFO is proposed and designed. These models and mechanisms are then implemented within an algorithm simulator, through which scheduling performances are verified and evaluated.