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Cognitive radio networks deal with opportunistic spectrum access leading to greater utilization of the spectrum. The extent of utilization depends on the primary user's traffic and also on the way the spectrum is accessed by the primary and secondary users. In this paper Continuous-time Markov chains are used to model the spectrum access. The proposed three- dimensional model represents a more accurate cognitive system than the existing models with increased spectrum utilization and than the random and reservation based spectrum access. A non- random access method is proposed to remove the forced termination states. In addition, call dropping and blocking probabilities are reduced. It is further shown that channel utilization is higher than random access and reservation based access.