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The IEEE 802.11e medium access control (MAC) layer protocol is an emerging standard to support quality of service (QoS) in 802.11 wireless networks. Some recent work shows that the 802.11e hybrid coordination function (HCF) can improve significantly the QoS support in 802.11 networks. A simple HCF referenced scheduler has been proposed in the 802.11e which takes into account the QoS requirements of flows and allocates time to stations on the basis of the mean sending rate. As we show in this paper, this HCF referenced scheduling algorithm is only efficient and works well for flows with strict constant bit rate (CBR) characteristics. However, a lot of real-time applications, such as videoconferencing, have some variations in their packet sizes, sending rates or even have variable bit rate (VBR) characteristics. In this paper we propose FHCF, a simple and efficient scheduling algorithm for 802.11e that aims to be fair for both CBR and VBR flows. FHCF uses queue length estimations to tune its time allocation to mobile stations. We present analytical model evaluations and a set of simulations results, and provide performance comparisons with the 802.11e HCF referenced scheduler. Our performance study indicates that FHCF provides good fairness while supporting bandwidth and delay requirements for a large range of network loads.