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This article discusses downlink resource allocation and scheduling for OFDM-based broadband wireless networks. We present a cross-layer resource management framework leveraged by utility optimization. It includes utility-based resource management and QoS architecture, resource allocation algorithms, rate-based and delay-based multichannel scheduling that exploits wireless channel and queue information, and theoretical exploration of the fundamental mechanisms in wireless resource management, such as capacity, fairness, and stability. We also provide a solution that can efficiently allocate resources for heterogeneous traffic with diverse QoS requirements.