This article outlines the fundamental modeling issues of opportunistic spectrum access in cognitive radio networks. In particular, we identify the effects of connection-based channel usage on the QoS performance of spectrum management techniques. During the transmission period of a secondary users connection, the phenomenon of multiple spectrum handoffs due to interruptions of primary users arises quite often. In addition to multiple interruptions, the connection-based channel usage behaviors are also affected by spectrum sensing time, switching between different channels, generally distributed service time, and channel contention between multiple secondary users. An analytical framework based on the preemptive resumption priority M/G/1 queueing theory is introduced to characterize the effects of the above factors simultaneously. The proposed generalized analytical framework can incorporate various system parameters into the design of very broad spectrum management techniques, including spectrum sensing, spectrum decision, spectrum sharing, and spectrum mobility. The applications of this analytical framework on spectrum decision as well as spectrum mobility are discussed, and some open issues using this framework are suggested in this article.