The support of multimedia traffic over IEEE 802.11 wireless local area networks (WLANs) has recently received considerable attention. This dissertation has proposed a new framework that provides efficient channel access, service differentiation and statistical QoS guarantees in the enhanced distributed channel access (EDCA) protocol of IEEE 802.11e. In the first part of the dissertation, the new framework to provide QoS support in IEEE 802.11e is presented. The framework uses three independent components, namely, a core MAC layer, a scheduler, and an admission control. The core MAC layer concentrates on the channel access mechanism to improve the overall system efficiency. The scheduler provides service differentiation according to the weights assigned to each Access Category (AC). The admission control provides statistical QoS guarantees. The core MAC layer developed in this dissertation employs a P-Persistent based MAC protocol. A weight-based fair scheduler to obtain throughput service differentiation at each node has been used. In wireless LANs (WLANs), the MAC protocol is the main element that determines the efficiency of sharing the limited communication bandwidth of the wireless channel. In the second part of the dissertation, analytical Markov chain models for the P-Persistent 802.11 MAC protocol under unsaturated load conditions with heterogeneous loads are developed. The Markov models provide closed-form formulas for calculating the packet service time, the packet end-to-end delay, and the channel capacity in the unsaturated load conditions. The accuracy of the models has been validated by extensive NS2 simulation tests and the models are shown to give accurate results. In the final part of the dissertation, the admission control mechanism is developed and evaluated. The analytical model for P-Persistent 802.11 is used to develop a measurement-assisted model-based admission control. The proposed admission control mechanism uses delay as an admission criterion. Both distributed and centralized admission control schemes are developed and the performance results show that both schemes perform very efficiently in providing the QoS guarantees. Since the distributed admission scheme control does not have a complete state information of the WLAN, its performance is generally inferior to the centralized admission control scheme. The detailed performance results using the NS2 simulator have demonstrated the effectiveness of the proposed framework. Compared to 802.11e EDCA, the scheduler consistently achieved the desired throughput differentiation and easy tuning. The core MAC layer achieved better delays in terms of channel access, average packet service time and end-to-end delay. It also achieved higher system throughput than EDCA for any given service differentiation ratio. The admission control provided the desired statistical QoS guarantees.