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In this paper, a queuing model is introduced to analyze the HCF controlled channel access (HCCA/IEEE802.11e) used in multi-rate wireless local area networks using adaptive modulation and coding, which is a key to wireless networks to increase effective transmission rate. The proposed model which is based on a MAP/PH/1 queue with vacation and time-limited service is useful in optimizing the parameters in cross layer designs and improving spectrum efficiency. Using Markovian arrival process (MAP) for traffic arrival process and phase type (PH) distribution for service process, vacation and non-transmission period make the mode more comprehensive to support practical traffic streams. To formulate the model, powerful matrix-geometric method is employed, and the mutual impacts of some parameters in the MAC and PHY layers are then evaluated and optimized to improve system performance.