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To support the transmission of (high-rate and oftenbursty) multimedia data with performance guarantees in an IEEE 802.11e wireless local area network (LAN), it is crucial to design judicious algorithms for admission control and resource allocation. The traffic specification element (TSPEC) of the new IEEE 802.11e standard is used to facilitate the design of the admission control. Based on the traffic profile given in the TSPEC and the dual-token bucket regulation, a guaranteed rate is derived for our airtime-based admission control. The admission control is integrated with the contention-based enhanced distributed channel access (EDCA), which together can provide so-called "parameterized QoS" - as in the polling-based HCF controlled channel access (HCCA) - via a new distributed, quantitative control of stations' airtime usage. We also extend the current QoS signaling of HCCA defined in IEEE 802.11e to perform admission control for this enhanced EDCA. Furthermore, we extend the integrated scheme for QoS provisioning in ad hoc wireless LANs and design appropriate signaling procedures. We evaluate via simulation the effectiveness of this parameterized QoS-capable EDCA scheme, and demonstrate its advantages over the centralized, polling-based HCCA scheme.