In this thesis, we analyze the queueing performance of a cognitive radio network with 1 primary user and 1 secondary user. The packet arrival processes of the primary user and the secondary user are according to independent and identically distributed Bernoulli process. We construct a quasi-birth-and-death process and use the matrix-geometric property to analyze the queueing system. We obtain tail distributions and packet delays of the primary user and the secondary user. Based on our analytic model, we formulate an optimization problem. We also investigate the effect of the estimation error.