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In this paper, we propose a joint admission control and bandwidth allocation scheme for packet-switched multiservices cellular networks. The main idea of the scheme is to adjust the acceptance ratios and the bandwidth allocated for different types of services in order to maintain maximum bandwidth utilization while guaranteeing quality of service (QoS) requirements for users. First, we define a total user utility function as the measure of how efficiently the bandwidth resource is used. Then, by using a Markovian queueing model, we obtain the optimal connection acceptance ratios and bandwidth allocation strategy that maximize total user utility. Simulation results demonstrate that using our scheme, bandwidth resource is most efficiently utilized and at the same time, the call-level and packet-level QoS requirements for both voice and data users are guaranteed.