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A new scheduling algorithm that achieves very low delay is presented in this paper and applied to Orthogonal Frequency Division Multiplexing (OFDM) broadcast channels (BC). The general approach consists of two parts: First, weight factors are found for the delay minimization problem with respect to the ergodic capacity region. An efficient, so called Idle State Prediction Algorithm is provided. In the second step resources are allocated by maximizing the weighted sum of rates according to the instantaneous capacity region. This technique largely simplifies the combinatorial structure of the cross-layer optimization problem. Simulation results confirm the superior performance of the presented scheme.