As the demand for wireless communication services increases, most of usable radio spectrum has already been allocated. Fortunately, a recent study found out that a large part of allocated spectrum is not occupied for most of time. To improve the utilization of radio spectrum, the concept of the cognitive radio (CR) network has been introduced. In this thesis, we consider a time slotted CR network with one PU and one SU. Our main goal is to analyze the queueing performance of the SU focusing on the impact of the PU`s activity. The distributions of the lengths of the busy and idle periods of the PU follow heavy-tailed or light-tailed. In the simulation result, we obtain the tail distribution of the queue size of the SU according to the PU`s activity.