The topic of subcarrier and power allocation in the downlink of an orthogonal frequency division multiple access decode-and-forward relaying system is presented with the objective of encompassing system stability and interference limitations in one inclusive problem. The introduced model is designed to maximize the overall throughput of the cell-edge users that are served by relay stations. We analyze the stability requirement of buffers in the base station and the corresponding relay stations, and define the rate constraints in order to guarantee queue stability without requiring a priori knowledge of arrival traffic’s statistics. The explained model results in a nonconvex optimization problem, and therefore, we employ a time-shared technique to achieve the closed form solution, which is only applicable when subcarriers can be shared by the users during one time-slot. In the case where the subcarriers are not allowed to be time-shared, we introduce a computationally efficient optimal binary subcarrier and power allocation method, in addition to a power conservative allocation mechanism. Using geometric-programming and monomial approximation techniques, we show that the proposed conservative approach, although nonconvex, can be solved in polynomial time. We also study the impact of adjustable time-slot division and interference-tolerance parameters on improving system performance. The extensive simulation results demonstrate the success of the proposed methods in terms of stabilizing the queues, improving the throughput by 30% and energy efficiency gain by 90%, in comparison with the existing similar models in the literature.