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Opportunistic Spectrum Sharing (OSS) has recently attracted increasing interest. We analytically model a wireless network that allows opportunistic spectrum sharing and analyze its performance through a queueing theoretic framework. The OSS system consists of the secondary users opportunistically sharing a set of spectrum resources with the primary users over a coverage area. The secondary users equipped with cognitive radios sense channels that are unused by the primary users and then make use of the idle channels. An ongoing secondary user also detects when a primary user accesses its channel and then either moves to another idle channel or moves to a waiting pool. Unreliable spectrum sensing is possible which are modeled by false alarm and misdetection events. We solve the steady-state probability of the system and derive several performance metrics of interest. Numerical and simulation results are presented. The proposed modeling method can be used to evaluate the performance of future opportunistic spectrum sharing networks.