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This paper focuses on the problem of queue-aware resource allocation for OFDMA cellular systems supporting both real-time and non-real-time services. A set of practical algorithms is proposed to solve the problem of maximizing the system utility under the constraints of both system resources and the actual amounts of data to be transmitted in buffers. Moreover, an upper bound is devised to quantify the global maximum of the overall system utility, and to appraise the proposed practical algorithms. Numerical results verify the efficacy of the upper bound and demonstrate the excellent performance of the proposed algorithms in solving queue-aware resource allocation problems.