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In this paper, we study utility-based optimal resource allocation in wireless networks. Utility here refers to a function which describes the degree of user satisfaction with a certain amount of allocated resource. We introduce utility function maximization in a centralized wireless environment and consider two types of traffic, i.e., best effort and QoS, the characteristics of which can be described by two existing utility functions. An allocation for the mixture of QoS and best effort traffics is proposed and its performance is evaluated via simulations. From this study, we show that optimal wireless resource allocation depends on the traffic types, the total available resource, and the channel quality, rather than solely dependent on the channel quality or traffic types as assumed in most existing work.