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In this paper, we focus on a cognitive network scenario, comprised of a multi-hop IEEE 802.11-based WLAN overlaid on a cellular network. In this scenario, the wireless nodes in a WLAN, i.e., cognitive nodes, use the downlink frequency channels of the cellular network opportunistically, such that at each packet transmission all idle channels have been exploited. In order to evaluate the capability of the considered cognitive network scenario, we propose an open queueing network model such that different packet transmission phases are mapped onto different queueing nodes. We also map different types of collisions, i.e., collision on control signals as well as collision on data transmission due to hidden terminals and the activation of primary users, onto suitable parameters of the queueing network. By writing the corresponding traffic equations and applying the stability conditions, we derive the maximum stable throughput, i.e., the maximum packet generation rate at cognitive nodes such that all queues are stable. Finally, we show the applicability of our analytical model in different situations and confirm our model by simulations.