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In this paper, we study utility-based maximization for resource allocation in the downlink direction of centralized wireless networks. We consider two types of traffic, i.e., best effort and hard QoS, and develop some essential theorems for optimal wireless resource allocation. We then propose three allocation schemes. The performance of the proposed schemes is evaluated via simulations. The results show that optimal wireless resource allocation is dependent on traffic types, total available resource, and channel quality, rather than solely dependent on the channel quality or traffic types as assumed in most existing work.