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This paper presents a time-aware admission control and resource allocation scheme in wireless networks in the context of a future generation cellular network. The quality levels (and their respective utility) of different connections are specified using discrete resource-utility (R-U) functions. The scheme uses these R-U functions for allocating and reallocating bandwidth to connections, aiming to maximize the accumulated utility of the system. However, different applications react differently to resource reallocations. Therefore, at each allocation time point, the following factors are taken into account: the age of the connection, a disconnection (drop) penalty, and the sensitiveness to reallocation frequency. The evaluation of our approach shows a superior performance compared to a recent adaptive bandwidth allocation scheme (RBBS). In addition, we have studied the overhead that performing a reallocation imposes on the infrastructure. To minimize this overhead, we present an algorithm that efficiently reduces the number of reallocations while remaining within a given utility bound.