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In this paper, we study voice and data service provisioning in an integrated system of cellular and wireless local area networks (WLANs). With the ubiquitous coverage of the cellular network and the disjoint deployment of WLANs in hot-spot areas, the integrated system has a two-tier overlaying structure. As an essential resource allocation aspect, admission control can be used to properly admit voice and data calls to the overlaying cells and WLANs. A simple admission scheme is proposed in this study to analyze the dependence of resource utilization and the impact of user mobility and traffic characteristics on admission parameters. Both admission control and rate control are considered to limit the input traffic to the WLAN, so that the WLAN operates in its most efficient states and effectively complements the cellular network. The call blocking/dropping probabilities and data call throughput are evaluated for effective and accurate derivation of the admission parameters. It is observed that the utilization varies with the configuration of admission parameters, which properly distributes the voice and data traffic load to the cells and WLANs. Mobility and traffic variability have a significant impact on the selection of the admission parameters.