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In a cognitive radio network (CRN), instead of direct leaving, an interrupted secondary user is suspended to wait for accessing another channel in a call level queue. The policy for handling the packets generated by the secondary user during the suspending period can be either delaying or discarding. According to these two packet level policies, the queue is separated into two parts, delay queue and discard queue. The paper mainly analyzes the performance of a CRN with such a two-part call level queue. Here, a Markov model is proposed to derive the formulas for packet loss ratio, packet delay, spectrum utilization and throughput. Numerical results show that theoretical models are consistent with simulation results. The major observations are summarized below, (i) Both packet loss ratio and throughput increase while the packet delay decreases with the increase of the delay queue length, (ii) Adopting different delay queue length does not cause much difference in CRN's spectrum utilization, but has a large effect on throughput. (iii) The performance is bounded when the arrival rate goes into infinitely high.