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To support the differentiated Quality-of-Service (QoS) and improve the utilization of the scarce wireless bandwidth, the IEEE 802.11e standard specifies an efficient burst transmission scheme referred to as the transmission opportunity (TXOP). Recently, analytical models have been reported to evaluate the performance of the TXOP scheme. However, most of these models were developed under the assumptions of the ideal channels or uniform error channels which fail to capture the characteristics of bursty and correlated channel errors in the practical wireless environment. In this paper, we propose an analytical model for the TXOP scheme in WLANs in the presence of bursty error channels. To this end, the transmission queue of each station is modelled by a two-state continuous time Markov chain. This model can be adopted to obtain the performance metrics including the throughput and buffer overflow probability. The accuracy of the analytical model is validated via NS-2 simulation experiments. Utilizing the proposed model, we investigate the impact of traffic loads, TXOP limit, and the number of stations on the performance of the TXOP scheme under various channel conditions.