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We consider resource allocation for elastic wireless applications that measure utility by target connection average throughput and achieved throughput. We construct a framework for connection access control and rate scheduling that supports this class of applications by maximizing long term average utility. We present a decomposition of the problem into connection access control and rate scheduling layers. The connection access control layer considers current commitments and decides whether to admit new sessions. For admitted users, the layer sets a target throughput to be achieved of the lifetime of the session. The rate scheduling layer adjusts the instantaneous rates of each connection on the basis of how well it is achieving each performance goal and on the relative strength of each connectionpsilas current channel. We illustrate how commonly used connection access control and rate scheduling techniques can be applied to design these two layers using an exchange of information regarding future target throughputs and achieved throughputs. Through numerical analysis, we show how wireless channel time diversity and multi-user diversity can be exploited to construct a rate scheduling algorithm that is superior to proportional fairness. Finally, this utility-based framework is compared to a method that does not use utility.