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To accommodate spectrum access in multichannel cognitive radio networks (CRNs), the channel-assembling technique, which combines several channels together as one channel, has been proposed in many medium access control (MAC) protocols. However, analytical models for CRNs enabled with this technique have not been thoroughly investigated. In this paper, two representative channel-assembling strategies that consider spectrum adaptation and heterogeneous traffic are proposed, and the performance of these strategies is evaluated based on the proposed continuous-time Markov chain (CTMC) models. Moreover, approximations of these models in the quasistationary regime are analyzed, and closed-form capacity expressions are derived in different conditions. The performance of different strategies, including the strategy without assembling, is compared with one another based on the numerical results obtained from these models and validated by extensive simulations. Furthermore, simulation studies are also performed for other types of traffic distributions to evaluate the validity and the preciseness of the mathematical models. Through both analyses and simulations, we demonstrate that channel assembling represented by the investigated strategies can improve the system performance if a proper strategy is selected with appropriate system parameter configurations.