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With the extensive deployment of 802.11 wireless local area networks (WLANs) and the need for better quality of service (QoS), the 802.11e MAC with service differentiation was developed. Analysing the effect of fading, shadowing and near-far effect on the performance of 802.11 is a fundamental consideration in practical situations since the wireless channels are error-prone. This paper develops a p-persistent CSMA protocol, which allows for service differentiation by using multiple traffic types, into an accurate and practical model that takes into account the capture effect in a Rayleigh multipath fading environment. A new analytical approach is developed to calculate the throughput and packet delay for multiple traffic types. Results provided for this new model show that the capture effect increases the throughput by 32% in a highly loaded system thereby demonstrating the importance of including the capture effect in wireless protocols.