# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020144

## Performance analysis and optimization research of multi-channel cognitive radio networks with a dynamic channel vacation scheme

 1 School of Science, Yanshan University, Qinhuangdao 066004, China 2 First Experimental Primary School of Tongzhou District, Beijing Academy of Educational Sciences, Beijing 101100, China 3 Department of Intelligence and Informatics, Konan University, Kobe 658-8501, Japan 4 The Kyoto College of Graduate Studies for Informatics, Kyoto 600-8216, Japan

*Corresponding author: Zhanyou Ma

Received  October 2018 Revised  July 2020 Published  September 2020

In order to resolve the issues of channel scarcity and low channel utilization rates in cognitive radio networks (CRNs), some researchers have proposed the idea of "secondary utilization" for licensed channels. In "secondary utilization", secondary users (SUs) opportunistically take advantage of unused licensed channels, thus guaranteeing the transmission performance and quality of service (QoS) of the system. Based on the channel vacation scheme, we analyze a preemptive priority queueing system with multiple synchronization working vacations. Under this discipline, we build a three-dimensional Markov process for this queueing model. Through the analysis of performance measures, we obtain the average queueing length for the two types of users, the mean busy period and the channel utility. By analyzing several numerical experiments, we demonstrate the effect of the parameters on the performance measures. Finally, in order to optimize the system individually and socially, we establish utility functions and provide some optimization results for PUs and SUs.

Citation: Zhanyou Ma, Wenbo Wang, Wuyi Yue, Yutaka Takahashi. Performance analysis and optimization research of multi-channel cognitive radio networks with a dynamic channel vacation scheme. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020144
##### References:

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##### References:
The dynamic channel vacation scheme proposed in this paper
The running mode of the system
The relation of $E({L_1})$ to ${\mu _2}$ and $c$
The relation of $E({L_2})$ to ${\mu _2}$ and $\theta$
The relation of ${P_d}$ to ${\lambda _2}$ and $c$
The relation of ${P_b}$ to ${\lambda _2}$ and $c$
The relation of ${P_{wv}}$ to ${\lambda _2}$ and $c$
The relation of ${P_u}$ to ${\mu _2}$ and $c$
The relation of ${U_{I1}}$ to $\mu_2$ and $\theta$
The relation of ${U_{I2}}$ to $\mu_2$ and $\theta$
The relation of ${U_{s}}$ to ${\lambda _2}$ and $c$
The relation of ${U_{s}}$ to ${\mu_2}$ and $\theta$
The Relation of $E(B)$ to ${\lambda _2}$ and $c$
 $c$ $\lambda _2 =6$ $\lambda _2 =7$ $\lambda _2=8$ $\lambda _2=9$ $\lambda _2=10$ 3 0.4900 0.4983 0.5052 0.5109 0.5156 4 0.4678 0.4793 0.4891 0.4975 0.5046 5 0.4594 0.4731 0.4852 0.4957 0.5049
 $c$ $\lambda _2 =6$ $\lambda _2 =7$ $\lambda _2=8$ $\lambda _2=9$ $\lambda _2=10$ 3 0.4900 0.4983 0.5052 0.5109 0.5156 4 0.4678 0.4793 0.4891 0.4975 0.5046 5 0.4594 0.4731 0.4852 0.4957 0.5049
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