Performance Analysis of a Communication Failure and Repair Mechanism with Classified Primary Users in CRNs  
[PERSON]  
1 School of Computer and Communication Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China; [EMAIL_ADDRESS] (Q.L. ); [EMAIL_ADDRESS] (S.Y. ); zhishengye1199163.com (Z.Y. )1  
[PERSON]  
1 School of Computer and Communication Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China; [EMAIL_ADDRESS] (Q.L. ); [EMAIL_ADDRESS] (S.Y. ); zhishengye1199163.com (Z.Y. )1  
[PERSON]  
1 School of Computer and Communication Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China; [EMAIL_ADDRESS] (Q.L. ); [EMAIL_ADDRESS] (S.Y. ); zhishengye1199163.com (Z.Y. )1  
[PERSON]  
1 School of Computer and Communication Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China; [EMAIL_ADDRESS] (Q.L. ); [EMAIL_ADDRESS] (S.Y. ); zhishengye1199163.com (Z.Y. )1  
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occurrence of communication failures has a momentous influence on CRNs, so we ought to conduct in-depth research on this area. Communication failure has an essential influence on the CRN system performance. In [13], a continuous-time Markov chain (CTMC) model was designed, and all the performance metrics under different PUs' and SUs' arrival and channel failure rates were estimated. In [14], under multi-channel malfunction and PUs' arrival rates, a model was formulated to evaluate the network performance. In [15], the authors described the most common failure sources and offered a failure classification program for wireless networks using CRs, and again emphasized that the dominating requirement for an SU is to respect the priority of PUs. From [13; 14; 15], we can find that failure rate is an essential variable in the performance evaluation of CRN models, and most studies on CRNs have focused on the priority between PUs and SUs, but priorities within users of the same category are not considered. The same type of users also have different transmission needs [16], such as different requirements for real-time performance. Therefore, to reduce the impact of communication failure on users with higher priorities, it is worth considering the classification of users and arranging a reasonable preemption principle. Moreover, spectrum sensing and spectrum allocation are hot topics in CRNs. CRNs require reliable cognitive algorithms to detect signals from licensed primary radios and find unexploited spectrum holes to avoid harmful interference [17]. However, we note that the focus of this paper is not spectrum sensing, but spectrum allocation, that is, how to design a reasonable and efficient spectrum allocation strategy to effectively use spectrum resources under the background of communication failure and repair. Considering the digital characteristic of data transmission, we use a discrete-time queueing model to analyze the proposed mechanism. The main mathematical tool of discrete-time queueing analysis is Markov chain, which refers to a random process in the state space that goes through a transition from one state to another, in which the probability of state transition at a certain moment depends only on its previous state. Markov chain is conceptually very intuitive and easy to implement. In our paper, we apply the widely used Markov chain for model analysis since we are concerned with the state transition of the system. In summary, the purpose of this study is as follows:  
1. Explore the impact of communication failure and repair on the system. 2. Considering the transmission needs of different PUs, establish a reasonable channel allocation mechanism to improve the network performance of the system. 3.