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July  2017, 13(3): 1449-1466. doi: 10.3934/jimo.2017001

Cognitive radio networks with multiple secondary users under two kinds of priority schemes: Performance comparison and optimization

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

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

Received  September 2015 Published  December 2016

In this paper, we consider a cognitive radio network with multiple Secondary Users (SUs). The SU packets generated from the SUs are divided into SU1 packets and SU2 packets, and the SU1 packets have higher priority than the SU2 packets. Different from the conventional preemptive priority scheme (called Scheme Ⅰ), we propose a non-preemptive priority scheme for the SU1 packets (called Scheme Ⅱ) to guarantee the transmission continuity of the SU2 packets. By constructing a three-dimensional Markov chain, we give the transition probability matrix of the Markov chain, and obtain the steady-state distribution of the system model. Accordingly, we derive some performance measures, such as the channel utilization, the blocking probability of the SU1 packets, the interruption probability of the SU1 packets and the SU2 packets, the normalized throughput of the SU1 packets, and the average latency of the SU2 packets. Moreover, we provide numerical experiments to compare different performance measures between the two priority schemes. Finally, we show and compare the Nash equilibrium strategy and the socially optimal strategy for the SU2 packets between Scheme Ⅰ and Scheme Ⅱ.

Citation: Yuan Zhao, Wuyi Yue. Cognitive radio networks with multiple secondary users under two kinds of priority schemes: Performance comparison and optimization. Journal of Industrial and Management Optimization, 2017, 13 (3) : 1449-1466. doi: 10.3934/jimo.2017001
References:
[1]

A. S. Alfa, Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System, Springer, New York, 2010. doi: 10.1007/978-1-4419-7314-6.

[2]

I. A. M. BalapuwadugeL. JiaoV. Pla and F. Y. Li, Channel assembling with priority-based queues in cognitive radio networks: Strategies and performance evaluation, IEEE Transactions on Wireless Communications, 13 (2014), 630-645.  doi: 10.1109/TWC.2013.120713.121948.

[3]

X. ChenH. Chen and W. Meng, Cooperative communications for cognitive radio networks--From theory to applications, IEEE Communications Surveys & Tutorials, 16 (2014), 1180-1192.  doi: 10.1109/SURV.2014.021414.00066.

[4]

J. ChuR. Ma and K. Feng, Stochastic spectrum handoff protocols for partially observable cognitive radio networks, Wireless Networks, 20 (2014), 1003-1022.  doi: 10.1007/s11276-013-0658-x.

[5]

C. T. DoN. H. TranM. V. NguyenC. S. Hong and S. Lee, Social optimization strategy in unobserved queueing systems in cognitive radio networks, IEEE Communications Letters, 16 (2012), 1944-1947.  doi: 10.1109/LCOMM.2012.111412.120830.

[6]

D. Hamza and S. Aïssa, Enhanced primary and secondary performance through cognitive relaying and leveraging primary feedback, IEEE Transactions on Vehicular Technology, 63 (2014), 2236-2247.  doi: 10.1109/TVT.2013.2292532.

[7]

R. Hassin and M. Haviv, To Queue or not to Queue: Equilibrium Behavior in Queueing Systems, Kluwer Academic Publishers, Boston, 2003. doi: 10.1007/978-1-4615-0359-0.

[8]

K. J. KimK. S. Kwak and B. D. Choi, Performance analysis of opportunistic spectrum access protocol for multi-channel cognitive radio networks, Journal of Communications and Networks, 15 (2013), 77-86.  doi: 10.1109/JCN.2013.000013.

[9]

Y. LeeC. G. Park and D. B. Sim, Cognitive radio spectrum access with prioritized secondary users, Applied Mathematics & Information Sciences, 6 (2012), 595S-601S. 

[10]

X. XuX. Chai and Z. Zhang, Self-organization approaches for optimization in cognitive radio networks, China Communications, 11 (2014), 121-129.  doi: 10.1109/CC.2014.6827574.

[11]

Y. ZhangT. JiangL. ZhangD. Qu and W. Peng, Analysis on the transmission delay of priority-based secondary users in cognitive radio networks, Proceedings of the International Conference on Wireless Communications & Signal Processing, (2013), 1-6. 

[12]

Z. ZhangK. Long and J. Wang, Self-organization paradigms and optimization approaches for cognitive radio technologies: A survey, IEEE Wireless Communications, 20 (2013), 36-42.  doi: 10.1109/MWC.2013.6507392.

[13]

Y. ZhaoS. Jin and W. Yue, Adjustable admission control with threshold in centralized CR networks: Analysis and optimization, Journal of Industrial and Management Optimization, 11 (2015), 1393-1408.  doi: 10.3934/jimo.2015.11.1393.

[14]

Y. Zhao and W. Yue, Performance comparison between two kinds of priority schemes in cognitive radio networks, in Queueing Theory and Network Applications (eds. T. V. Do, Y. Takahashi, W. Yue and V. Nguyen), Springer, Switzerland, 383 (2015), 73-80. doi: 10.1007/978-3-319-22267-7_7.

show all references

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

References:
[1]

A. S. Alfa, Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System, Springer, New York, 2010. doi: 10.1007/978-1-4419-7314-6.

[2]

I. A. M. BalapuwadugeL. JiaoV. Pla and F. Y. Li, Channel assembling with priority-based queues in cognitive radio networks: Strategies and performance evaluation, IEEE Transactions on Wireless Communications, 13 (2014), 630-645.  doi: 10.1109/TWC.2013.120713.121948.

[3]

X. ChenH. Chen and W. Meng, Cooperative communications for cognitive radio networks--From theory to applications, IEEE Communications Surveys & Tutorials, 16 (2014), 1180-1192.  doi: 10.1109/SURV.2014.021414.00066.

[4]

J. ChuR. Ma and K. Feng, Stochastic spectrum handoff protocols for partially observable cognitive radio networks, Wireless Networks, 20 (2014), 1003-1022.  doi: 10.1007/s11276-013-0658-x.

[5]

C. T. DoN. H. TranM. V. NguyenC. S. Hong and S. Lee, Social optimization strategy in unobserved queueing systems in cognitive radio networks, IEEE Communications Letters, 16 (2012), 1944-1947.  doi: 10.1109/LCOMM.2012.111412.120830.

[6]

D. Hamza and S. Aïssa, Enhanced primary and secondary performance through cognitive relaying and leveraging primary feedback, IEEE Transactions on Vehicular Technology, 63 (2014), 2236-2247.  doi: 10.1109/TVT.2013.2292532.

[7]

R. Hassin and M. Haviv, To Queue or not to Queue: Equilibrium Behavior in Queueing Systems, Kluwer Academic Publishers, Boston, 2003. doi: 10.1007/978-1-4615-0359-0.

[8]

K. J. KimK. S. Kwak and B. D. Choi, Performance analysis of opportunistic spectrum access protocol for multi-channel cognitive radio networks, Journal of Communications and Networks, 15 (2013), 77-86.  doi: 10.1109/JCN.2013.000013.

[9]

Y. LeeC. G. Park and D. B. Sim, Cognitive radio spectrum access with prioritized secondary users, Applied Mathematics & Information Sciences, 6 (2012), 595S-601S. 

[10]

X. XuX. Chai and Z. Zhang, Self-organization approaches for optimization in cognitive radio networks, China Communications, 11 (2014), 121-129.  doi: 10.1109/CC.2014.6827574.

[11]

Y. ZhangT. JiangL. ZhangD. Qu and W. Peng, Analysis on the transmission delay of priority-based secondary users in cognitive radio networks, Proceedings of the International Conference on Wireless Communications & Signal Processing, (2013), 1-6. 

[12]

Z. ZhangK. Long and J. Wang, Self-organization paradigms and optimization approaches for cognitive radio technologies: A survey, IEEE Wireless Communications, 20 (2013), 36-42.  doi: 10.1109/MWC.2013.6507392.

[13]

Y. ZhaoS. Jin and W. Yue, Adjustable admission control with threshold in centralized CR networks: Analysis and optimization, Journal of Industrial and Management Optimization, 11 (2015), 1393-1408.  doi: 10.3934/jimo.2015.11.1393.

[14]

Y. Zhao and W. Yue, Performance comparison between two kinds of priority schemes in cognitive radio networks, in Queueing Theory and Network Applications (eds. T. V. Do, Y. Takahashi, W. Yue and V. Nguyen), Springer, Switzerland, 383 (2015), 73-80. doi: 10.1007/978-3-319-22267-7_7.

Figure 1.  Flow diagram for the proposed non-preemptive priority scheme.
Figure 2.  Time diagram of the system model.
Figure 3.  State transition diagram for the number of SU2 packets in the system model.
Figure 4.  Change trend of the channel utilization $\xi$.
Figure 5.  Change trend of the interruption probability $\gamma_{21}$ of the SU1 packets.
Figure 6.  Change trend of the interruption probability $\gamma_{22}$ of the SU2 packets.
Figure 7.  Change trend of the normalized throughput $\theta_{21}$ of the SU1 packets.
Figure 8.  Change trend of the average latency $\delta_{22}$ of the SU2 packets.
Figure 9.  Individual net benefit $W_I(\lambda_{22})$ vs. arrival rate $\lambda_{22}$ of the SU2 packets.
Figure 10.  Social net benefit $W_S(\lambda_{22})$ vs. arrival rate $\lambda_{22}$ of the SU2 packets.
Table 1.  Numerical results with Nash equilibrium strategy
$\lambda_1$$\lambda_{21}$$\lambda_e$$q_e$
MinMaxMinMax
0.150.200.160.170.800.85
Scheme Ⅰ 0.200.200.130.140.650.70
0.200.250.110.120.550.60
0.150.200.200.201.001.00
Scheme Ⅱ0.200.200.170.180.850.90
0.200.250.150.160.750.80
$\lambda_1$$\lambda_{21}$$\lambda_e$$q_e$
MinMaxMinMax
0.150.200.160.170.800.85
Scheme Ⅰ 0.200.200.130.140.650.70
0.200.250.110.120.550.60
0.150.200.200.201.001.00
Scheme Ⅱ0.200.200.170.180.850.90
0.200.250.150.160.750.80
Table 2.  Numerical results with socially optimal strategy
$\lambda_1$$\lambda_{21}$$\lambda^*$$q^*$
0.150.200.100.50
Scheme Ⅰ 0.200.200.080.40
0.200.250.070.35
0.150.200.130.65
Scheme Ⅱ0.200.200.110.55
0.200.250.100.50
$\lambda_1$$\lambda_{21}$$\lambda^*$$q^*$
0.150.200.100.50
Scheme Ⅰ 0.200.200.080.40
0.200.250.070.35
0.150.200.130.65
Scheme Ⅱ0.200.200.110.55
0.200.250.100.50
Table 3.  Numerical results with admission fee
$\lambda_1$$\lambda_{21}$$\lambda^*$$f$
0.150.200.106.9918
Scheme Ⅰ 0.200.200.086.5472
0.200.250.075.4116
0.150.200.138.1169
Scheme Ⅱ0.200.200.117.1114
0.200.250.106.4127
$\lambda_1$$\lambda_{21}$$\lambda^*$$f$
0.150.200.106.9918
Scheme Ⅰ 0.200.200.086.5472
0.200.250.075.4116
0.150.200.138.1169
Scheme Ⅱ0.200.200.117.1114
0.200.250.106.4127
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