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The recently ratified IEEE 802.11e standard defines the enhanced distributed channel access (EDCA) function for quality-of-service (QoS) provisioning in the wireless local area networks (WLANs). The EDCA uses carrier sense multiple access with collision avoidance (CSMA/CA) and slotted binary exponential backoff (BEB) mechanism. We present a simple mathematical analysis framework for the EDCA function. Our analysis considers the fact that the distributed random access systems exhibit cyclic behavior where each station successfully transmits a packet in a cycle. Our analysis shows that an AC-specific cycle time exists for the EDCA function. Validating the theoretical results via simulations, we show that the proposed analysis accurately captures EDCA saturation performance in terms of average throughput, medium access delay, and packet loss ratio. The cycle time analysis is a simple and insightful substitute for previously proposed more complex EDCA models.