# American Institute of Mathematical Sciences

July  2017, 13(3): 1255-1271. doi: 10.3934/jimo.2016071

## Equilibrium analysis of an opportunistic spectrum access mechanism with imperfect sensing results

 1 School of Information Science and Engineering, Key Laboratory for Computer Virtual Technology, and System Integration of Hebei Province, Yanshan University, Qinhuangdao 066004, China 2 Department of Intelligence and Informatics, Konan University, Kobe 658-8501, Japan 3 School of Information Science and Engineering, Key Laboratory for Computer Virtual Technology, and System Integration of Hebei Province, Yanshan University, Qinhuangdao 066004, China

The reviewing process of the paper was handled by Yutaka Takahashi as Guest Editor.

Received  October 2015 Published  October 2016

In order to reduce the average delay of secondary user (SU) packets and adapt to various levels of tolerance for transmission interruption, we propose a novel opportunistic channel access mechanism with admission threshold and probabilistic feedback in cognitive radio networks (CRNs). Considering the preemptive priority of primary user (PU) packets, as well as the sensing errors of missed detection and false alarm caused by SUs, we establish a type of priority queueing model in which two classes of customers may interfere with each other. Based on this queueing model, we evaluate numerically the proposed mechanism and then present the system performance optimization. By employing a matrix-geometric solution, we derive the expressions for some important performance measures. Then, by building a reward function, we investigate the strategies for both the Nash equilibrium and the social optimization. Finally, we provide a pricing policy for SU packets to coordinate these two strategies. With numerical experiments, we verify the effectiveness of the proposed opportunistic channel access mechanism and the rationality of the proposed pricing policy.

Citation: Shunfu Jin, Wuyi Yue, Shiying Ge. Equilibrium analysis of an opportunistic spectrum access mechanism with imperfect sensing results. Journal of Industrial & Management Optimization, 2017, 13 (3) : 1255-1271. doi: 10.3934/jimo.2016071
##### References:

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##### References:
Transmission process of a PU packet
Transmission process of an SU packet
Throughput $\phi$ of SU packets
Block rate $\beta$ of SU packets
Average delay $W(\lambda_{su})$ of SU packets
Change trend for the net benefit of an SU packet
Change trend for the social welfare
Parameter settings in numerical experiments
 Parameters Values slot 1 ms transmission rate in physical layer 11 Mbps arrival rate of SU packets 0.3 mean size of an SU packet 1760 Byte arrival rate of PU packets 0.05 mean size of a PU packet 2010 Byte feedback probability 0.0-1.0 energy threshold 1.0-7.0 simulation scale 3 million slots sensing time 0.1 ms sensing frequency 10 times/ms
 Parameters Values slot 1 ms transmission rate in physical layer 11 Mbps arrival rate of SU packets 0.3 mean size of an SU packet 1760 Byte arrival rate of PU packets 0.05 mean size of a PU packet 2010 Byte feedback probability 0.0-1.0 energy threshold 1.0-7.0 simulation scale 3 million slots sensing time 0.1 ms sensing frequency 10 times/ms
Numerical results for the admission price $F$
 Admission threshold $H$ Admission probability $r$ Feedback probability $q$ Admission price $F$ 4 0.4 0.4 1.0873 3 0.4 0.4 1.0687 2 0.4 0.4 1.0272 2 0.4 0.0 1.0341 2 0.4 0.7 1.0163 2 0.8 0.7 1.0640 2 0.1 0.7 0.9938
 Admission threshold $H$ Admission probability $r$ Feedback probability $q$ Admission price $F$ 4 0.4 0.4 1.0873 3 0.4 0.4 1.0687 2 0.4 0.4 1.0272 2 0.4 0.0 1.0341 2 0.4 0.7 1.0163 2 0.8 0.7 1.0640 2 0.1 0.7 0.9938
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