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Cognitive Radio Networks allow opportunistic spectrum usage by the cognitive users leading to better spectrum utilization. The spectrum utilization however depends on the channel access method adopted and the access of the channel by the primary and the cognitive users. In this paper, a non-random channel access method with dedicated channels for the primary users has been proposed which buffers the requesting cognitive users when all channels are busy. A four dimensional Continuous Time Markov Chain (CTMC) has been developed to analyze our proposed algorithm. The performance of the algorithm has been compared with the existing non-random channel access method and about 71% improvement has been achieved in the Call Blocking Probability while the Channel Utilization and Call Dropping Probability remains almost unchanged.