The growing proliferation of wireless devices in contemporary wireless networks requires more spectrum usage. As a consequence, spectrum bands are pressingly getting congested. However, a number of frequency bands licensed to operators are under utilized for transmission. Cognitive Radio (CR), as a promising technique for improving spectrum utilization, can dynamically allocate spectrum. In this paper, we investigate the performance of a CR network composed of a primary/licensed user and a number of secondary/unlicensed users, which are subject to self-similar traffic flows and contend for a unique channel. An analytical model is developed to isolate the primary and secondary users from the original networks. Further, we address the queueing performance of individual secondary users by employing a decomposition approach. The comparison between analytical and simulation results validates the accuracy of the developed model.