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A cross-layer scheduling algorithm that combines packet scheduling and an efficient bandwidth allocation for orthogonal frequency division multiple access (OFDMA) systems with heterogeneous user's delay requirements are proposed. The proposed work employs channel fluctuation and queue states in their decision rules for packet scheduling, which determines the optimum subcarrier allocation policy to maximise the system throughput subject to individual user's delay constraints. The delay sensitive subcarrier allocation strategy has linear complexity with respect to the number of users and number of subcarriers. The cross-layer scheduling algorithm also use an adaptive modulation and coding (AMC) scheme, which adapt according to the channel condition and queue states in terms of signal-to-noise ratio (SNR) constraints to improve the bandwidth usage in an efficient manner. The simulation results show that substantial throughput gain and spectral efficiency improvement are obtained while satisfying the delay constraint when the delay sensitive jointly optimum rate and subcarrier allocation policy with AMC is adopted.