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Efficient uplink access control schemes am very important for supporting a large number of mobile users with various levels of quality of service (QoS). In our proposed scheme, high priority users request the uplink resources by a 1-phase access mechanism while low priority users request the uplink resources by a 2-phase access mechanism using RFR packet. Moreover, we propose a novel scheme for qualifying low priority users with physically colliding RFR packets as well as low priority users with physically non-colliding RFR packets. This scheme can solve the problem that low priority users cannot inform the BS of their request of qualification for transmission of request packets due to the collision of RFR packets, though the BS has resources to qualify more low priority users. We mathematically analyze success probability and throughput of each class as well as the total system of our novel access priority scheme.