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In this paper we study the performance of IEEE 802.11e enhanced distributed channel access (EDCA) priority schemes under finite load and error-prone channel. We introduce a multi-dimensional Markov Chain model that includes all the mandatory differentiation mechanisms of the standard: QoS parameters, CWMIN, CWMAX arbitration inter-frame space (AIFS), and the virtual collision handler. The model faithfully represents the functionality of the EDCA access mechanisms, including lesser known details of the standard such as the management of the backoff counter which is technically different from the one used in the legacy DCF. We study the priority schemes under both finite load and saturation conditions. Our analysis also takes into consideration channel conditions.