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QoS control and resource management in 802.11e WLANs to support real time and multimedia services remains an open problem. All the solutions that only aim to enhance the performance of the enhanced distributed channel access (EDCA) mechanism cannot resolve the performance degradation problem once the channel becomes saturated. Hence, an efficient admission control scheme in EDCA is a key to guarantee the QoS required by real-time and multimedia services. In this paper, we propose a model-based admission control algorithm that is located within the QoS access point (QAP). An accurate analytical model is used to predict the QoS metrics that can be achieved once a new flow is introduced in the WLAN. Based on this prediction and on the QoS constraints of already active flows as well as the new flow, the QAP takes its decision of admitting or rejecting the new flow. The proposed admission control scheme is completely compatible with the legacy 802.11e EDCA MAC protocol. It is validated numerically and through simulations using several realistic evaluation scenarios.