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The authors consider network utility maximisation problem in orthogonal frequency division multiple access (OFDMA) networks to study cross-layer, fair and efficient resource allocation. Assuming knowledge of the instantaneous channel gains, this problem is decomposed into rate control and scheduling problems at the transport and medium access control/physical layers, respectively. In contrast to the rate control problem that is solved using subgradient method, the scheduling problem has high computational complexity owing to optimising integer and continuous variables simultaneously. Based on the results from analysing the integer relaxed scheduling problem, computationally efficient adaptive scheduling (CEAS) and opportunistic time division multiple access (Opp-TDMA) scheduling schemes are proposed to joint subcarrier assignment and power allocation. Simulation results demonstrate that aggregate utility achieved in the network with the cooperation between rate control and proposed scheduling schemes outperforms those of previously proposed joint channel-aware and queue-aware scheduling schemes. Also, through comparison with the optimal solution, the authors conclude that CEAS is applicable for OFDMA real-time scheduling due to low computational complexity and high performance.