Channel allocation protocol plays a crucial role in ensuring that cognitive radio technology achieves more efficient radio resource utilization. To evaluate and compare the performance of different channel allocation protocols accurately, we need to model the cognitive radio system using various channel allocation protocols under one identical framework. Building such a framework is challenging. In this paper, we propose a method named distribution probability matrix (DPM) to describe the allocation results under different allocation protocols and a queueing analysis framework that uses DPM method. A framework that is capable of analyzing every individual secondary user (SU) in the system is developed. We also propose a maximum throughput (MT) channel allocation protocol aimed at achieving optimal throughput. Then we compare the MT protocol and existing protocols with the same objective using our proposed framework. The numerical results show that the MT protocol outperforms the existing protocols. Performance comparisons of different SUs are carried out to compare the protocols comprehensively. The convenience using our analytical framework of modeling different allocation protocols and evaluating the overall performances of the protocols is revealed throughout the analysis.