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Adaptive resource allocation including the allocation of subcarrier, bit and power in orthogonal frequency division multiple access (OFDMA) system, can significantly improve spectral efficiency, increase capacity, and reduce power consumption. The resource allocation in an OFDMA system is normally modeled as a combinatorial optimization problem involving a nonlinear objective with nonlinear constraints. This leads to high computation complexity that is only solvable online. In this paper we first develop a nonlinear optimization model of OFDMA resource allocation that incorporates not only the throughput constraint but also the delay constraint. We then find an equivalent linear formulation to this optimization problem to facilitate analysis. Moreover, we develop a heuristic approximation algorithm to provide a close solution to the equivalent linear programming problem. The heuristic algorithm is efficient enough for on-line adaptive resource allocation. Simulation results show that the heuristic solution can achieve almost same capacity but with less computation complexity.