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In this paper, we present an analytical framework to evaluate the effects of multiple spectrum handoffs on channel utilization and latency performances in cognitive radio (CR) networks. During the transmission period of a secondary connection, multiple interruptions from the primary users result in multiple spectrum handoffs. In order to decide the target channel for each spectrum handoff and resume the unfinished transmission, wideband sensing is performed in an on-demand reactive manner. Although spectrum handoff procedure can enhance channel utilization, transmission latency of the secondary users is prolonged due to multiple handoffs. Thus, two fundamental issues in CR networks with multiple spectrum handoffs arise: (1) to what extent the channel utilization can be improved; and (2) how long the transmission latency will be extended for the secondary users. To solve the first problem, we introduce the preemptive resume priority (PRP) M/G/1 queueing network to characterize the channel usage behaviors of CR networks. Based on this queueing network, channel utilization under various traffic arrival rates and service time distributions can be evaluated. Furthermore, on top of the proposed queueing network, a state diagram is developed to characterize the effects of multiple handoff delay on the transmission latency of the secondary users. The analytical results can provide a helpful insight to study the effects of traffic arrival rates and service time on channel utilization and transmission latency and then facilitate the designs of admission control rules for the secondary users subject to their performance requirements.