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This paper focuses on the study of queueing theoretic problem of OFDMA-based WiMAX with three classes of connections, connections with High Priority (HP), conections with Medium Priority (MP) and connections with Low Priority (LP). The key idea to solve the problem of the mixed priority strategy is the technique of the Shadow server approximation. Specifically, we present a single-cell WiMAX environment in which the base station allocates subchannels to the subscriber stations in its coverage area. The subchannels allocated to a subscriber station are shared by multiple connections at that subscriber station. To ensure the Quality of Service (QoS) performances, two Connection Admission Control (CAC) mechanisms, namely, threshold-based (tb) and queue-aware (qa) CAC schemes are considered at a subscriber station. Then, based on the queueing model, both the connection-level and the packet-level performances are studied and compared with their analogues in the case without CAC. The connection arrival is modeled by a Poisson process and the packet arrival for a connection by a Markov Modulated Poisson Process (MMPP). Several performance measures are derived.