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In this paper, we propose an analytical model to evaluate the maximum stable throughput of a cognitive IEEE 802.11-based WLAN sharing the downlink band of a cellular network. Our model has been found on an open queueing network which includes both asymmetric and non-saturated aspects of secondary nodes as well as the time-varying nature of the channel due to intermittent primary nodes. By mapping the details of MAC scheme of the cognitive WLAN, regarding the dynamic nature of spectrum opportunities, onto suitable parameters of the proposed queueing network and writing the corresponding traffic equations, we are able to find the maximum stable throughput, i.e., the maximum rate of packet generation at the cognitive nodes guaranteeing the stability of all nodes. Simulation results show the validity of our analytical approach.