Performance analysis and optimization for cognitive radio networks with a finite primary user buffer and a probability returning scheme

Yuan Zhao; Wuyi Yue

doi:10.3934/jimo.2018195

Article Contents

2020, Volume 16, Issue 3: 1119-1134. Doi: 10.3934/jimo.2018195

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Performance analysis and optimization for cognitive radio networks with a finite primary user buffer and a probability returning scheme

Yuan Zhao^1, , and
Wuyi Yue^2,

1.
School of Computer and Communication Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
2.
Department of Intelligence and Informatics, Konan University, Kobe 658-8501, Japan

* Corresponding author: Yuan Zhao
* Corresponding author: Yuan Zhao

Received: October 2017

Revised: January 2018

Early access: December 2018

Published: March 2020

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Abstract

In this paper, in order to reduce possible packet loss of the primary users (PUs) in cognitive radio networks, we assume there is a buffer with a finite capacity for the PU packets. At the same time, focusing on the packet interruptions of the secondary users (SUs), we introduce a probability returning scheme for the interrupted SU packets. In order to evaluate the influence of the finite buffer setting and the probability returning scheme to the system performance, we construct and analyze a discrete-time Markov chain model. Accordingly, we determine the expressions of some important performance measures of the PU packets and the SU packets. Then, we show numerical results to evaluate how the buffer setting of the PU packets and the returning probability influence the system performance. Moreover, we optimize the system access actions of the SU packets. We determine their individually and the socially optimal strategies by considering different buffer settings for PU packets and different returning probabilities for SU packets. Finally, a pricing policy by introducing an admission fee is also provided to coincide the two optimal strategies.

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Mathematics Subject Classification: Primary: 68M10, 68M20; Secondary: 60J10.

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Figure 1. System actions of PU packets and SU packets

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Figure 2. Average queue length $ E_{PU} $ of PU packets

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Figure 3. Throughput $ \theta_{PU} $ of PU packets

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Figure 4. Blocking rate $ \beta_{SU} $ of SU packets

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Figure 5. Average delay $ \delta_{SU} $ of SU packets

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Figure 6. Function $ F_I(\lambda_2) $ of the individual net benefit

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Figure 7. Function $ F_S(\lambda_2) $ of the social net benefit

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Table 1. Notations for the system model

Symbol	Explanation
$ \lambda_1 $	Arrival rate of the PU packets
$ \lambda_2 $	Arrival rate of the SU packets
$ \mu_1 $	Transmission rate of the PU packets
$ \mu_2 $	Transmission rate of the SU packets
$ K_1 $	Capacity of the PU buffer
$ K_2 $	Capacity of the SU buffer
$ q $	Returning probability for the interrupted SU packets
$ P_n $	Number of PU packets in the system at the instant $ t=n^+ $
$ S_n $	Number of SU packets in the system at the instant $ t=n^+ $

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Table 2. Numerical results for the individually and socially optimal strategies

$ K_1 $	$ K_2 $	$ q $	$ \lambda_i $		$ r_i $		$ \lambda_s $	$ r_s $
$ K_1 $	$ K_2 $	$ q $	min	max	min	max	$ \lambda_s $	$ r_s $
0	5	0.4	0.26	0.27	0.52	0.54	0.18	0.36
2	5	0.4	0.15	0.16	0.30	0.32	0.10	0.20
0	5	0.8	0.30	0.31	0.60	0.62	0.19	0.38
2	5	0.8	0.20	0.21	0.40	0.42	0.12	0.24
0	8	0.8	0.32	0.33	0.64	0.66	0.22	0.44
2	8	0.8	0.23	0.24	0.46	0.48	0.15	0.30

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Table 3. Numerical results for the admission fee

$ K_1 $	$ K_2 $	$ q $	$ \lambda_s $	$ f $
0	5	0.4	0.18	1.9650
2	5	0.4	0.10	1.7917
0	5	0.8	0.19	5.8778
2	5	0.8	0.12	5.4328
0	8	0.8	0.22	6.3116
2	8	0.8	0.15	5.9168

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