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The IEEE 802.11e protocol is designed to enhance the QoS capability of wireless local area networks (WLAN). In this paper, we propose a three dimensional Markov chain model for the 802.11e enhanced distributed coordination function (EDCF) mode and compute the maximum sustainable throughput and service delay distribution for each priority class when under heavy load. This provides an analytical approach to pick the parameter values associated with EDCF to meet the QoS requirements of each priority. This is accomplished by modeling the performance impact of all the major QoS-specific features (i.e. CWMin, CWMax, AIFS, internal collision resolution) of the 802.11e EDCF mode.