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With the rapid development of connected and automated vehicles (CAVs) and intelligent transportation infrastructure, CAVs, connected human-driven vehicles (CHVs), and un-connected human-driven vehicles (HVs) will coexist on the roads in the future for a long time. This paper comprehensively considers the different traffic characteristics of CHVs, CAVs, and HVs, and systemically investigates the unsignalized intersection management strategy from the upper decision-making level to the lower execution level. The unsignalized intersection management strategy consists of two parts: the heuristic priority queues based right of way allocation (HPQ) algorithm and the vehicle planning and control algorithm. In the HPQ algorithm, a vehicle priority management model considering the difference between CAVs, CHVs, and HVs, is built to design the right of way management for different types of vehicles. In the lower level for vehicle planning and control algorithm, different control modes of CAVs are designed according to the upper-level decision made by the HPQ algorithm. Moreover, the vehicle control execution is realized by the model predictive controller combined with the geographical environment constraints and the unsignalized intersection management strategy. The proposed strategy is evaluated by simulations, which show that the proposed intersection management strategy can effectively reduce travel time and improve traffic efficiency. Results show that the proposed method can decrease the average travel time by 5% to 65% for different traffic flows compared with the comparative methods. The intersection management strategy captures the real-world balance between efficiency and safety for future intelligent traffic systems.