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We propose an analytical model for the performance analysis of the enhanced distributed channel access (EDCA) function of the IEEE 802.11e standard. The proposed discrete-time Markov chain (DTMC) model incorporates the main quality-of-service (QoS) features of 802.11e, namely, contention window (CW), arbitration interframe space (AIFS), and transmit opportunity (TXOP) differentiation. Due to its specific design, the proposed DTMC model jointly considers the state of the medium access control (MAC) layer buffer and the MAC differentiation mechanisms which facilitates a novel performance analysis framework at an arbitrary traffic load. Analytical and simulation results are compared to demonstrate the accuracy of the proposed approach for varying traffic load, EDCA parameters, and MAC layer buffer space.