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For protocol and system design in cognitive radio networks (CRNs), it is essential to identify which system settings or environmental conditions have great impacts on the quality-of-service (QoS) performance for secondary users (SUs) and how they influence it, which are still open issues. In this paper, an analytical framework to quantify the queue dynamics of a multi-SU multichannel CRN is developed. In the analytical framework, we consider the important lower-layer mechanisms and settings, including spectrum sensing errors, medium-access control (MAC) protocols, link adaptation technologies such as adaptive modulation and coding (AMC) and automatic repeat request (ARQ), and limited buffer size. By modeling the queue dynamics as a discrete-time finite-state Markov chain (FSMC), we derive the analytical expressions of the average queue length, packet-dropping rate, and packet-collision rate. Based on these expressions, the QoS metrics including average queueing delay, packet-loss rate, and effective throughput are obtained. Simulation and numerical results are presented to verify the accuracy of the proposed analytical framework and investigate the QoS performance of SUs.