# American Institute of Mathematical Sciences

• Previous Article
Performance analysis and optimization of a pseudo-fault Geo/Geo/1 repairable queueing system with N-policy, setup time and multiple working vacations
• JIMO Home
• This Issue
• Next Article
Rescheduling optimization of steelmaking-continuous casting process based on the Lagrangian heuristic algorithm
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 & 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.  Google Scholar [2] I. A. M. Balapuwaduge, L. Jiao, V. 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.  Google Scholar [3] X. Chen, H. 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.  Google Scholar [4] J. Chu, R. 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.  Google Scholar [5] C. T. Do, N. H. Tran, M. V. Nguyen, C. 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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [8] K. J. Kim, K. 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.  Google Scholar [9] Y. Lee, C. G. Park and D. B. Sim, Cognitive radio spectrum access with prioritized secondary users, Applied Mathematics & Information Sciences, 6 (2012), 595S-601S.   Google Scholar [10] X. Xu, X. 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.  Google Scholar [11] Y. Zhang, T. Jiang, L. Zhang, D. 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.   Google Scholar [12] Z. Zhang, K. 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.  Google Scholar [13] Y. Zhao, S. 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.  Google Scholar [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.  Google Scholar

show all references

##### 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.  Google Scholar [2] I. A. M. Balapuwaduge, L. Jiao, V. 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.  Google Scholar [3] X. Chen, H. 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.  Google Scholar [4] J. Chu, R. 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.  Google Scholar [5] C. T. Do, N. H. Tran, M. V. Nguyen, C. 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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [8] K. J. Kim, K. 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.  Google Scholar [9] Y. Lee, C. G. Park and D. B. Sim, Cognitive radio spectrum access with prioritized secondary users, Applied Mathematics & Information Sciences, 6 (2012), 595S-601S.   Google Scholar [10] X. Xu, X. 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.  Google Scholar [11] Y. Zhang, T. Jiang, L. Zhang, D. 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.   Google Scholar [12] Z. Zhang, K. 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.  Google Scholar [13] Y. Zhao, S. 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.  Google Scholar [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.  Google Scholar
Flow diagram for the proposed non-preemptive priority scheme.
Time diagram of the system model.
State transition diagram for the number of SU2 packets in the system model.
Change trend of the channel utilization $\xi$.
Change trend of the interruption probability $\gamma_{21}$ of the SU1 packets.
Change trend of the interruption probability $\gamma_{22}$ of the SU2 packets.
Change trend of the normalized throughput $\theta_{21}$ of the SU1 packets.
Change trend of the average latency $\delta_{22}$ of the SU2 packets.
Individual net benefit $W_I(\lambda_{22})$ vs. arrival rate $\lambda_{22}$ of the SU2 packets.
Social net benefit $W_S(\lambda_{22})$ vs. arrival rate $\lambda_{22}$ of the SU2 packets.
Numerical results with Nash equilibrium strategy
 $\lambda_1$ $\lambda_{21}$ $\lambda_e$ $q_e$ Min Max Min Max 0.15 0.20 0.16 0.17 0.80 0.85 Scheme Ⅰ 0.20 0.20 0.13 0.14 0.65 0.70 0.20 0.25 0.11 0.12 0.55 0.60 0.15 0.20 0.20 0.20 1.00 1.00 Scheme Ⅱ 0.20 0.20 0.17 0.18 0.85 0.90 0.20 0.25 0.15 0.16 0.75 0.80
 $\lambda_1$ $\lambda_{21}$ $\lambda_e$ $q_e$ Min Max Min Max 0.15 0.20 0.16 0.17 0.80 0.85 Scheme Ⅰ 0.20 0.20 0.13 0.14 0.65 0.70 0.20 0.25 0.11 0.12 0.55 0.60 0.15 0.20 0.20 0.20 1.00 1.00 Scheme Ⅱ 0.20 0.20 0.17 0.18 0.85 0.90 0.20 0.25 0.15 0.16 0.75 0.80
Numerical results with socially optimal strategy
 $\lambda_1$ $\lambda_{21}$ $\lambda^*$ $q^*$ 0.15 0.20 0.10 0.50 Scheme Ⅰ 0.20 0.20 0.08 0.40 0.20 0.25 0.07 0.35 0.15 0.20 0.13 0.65 Scheme Ⅱ 0.20 0.20 0.11 0.55 0.20 0.25 0.10 0.50
 $\lambda_1$ $\lambda_{21}$ $\lambda^*$ $q^*$ 0.15 0.20 0.10 0.50 Scheme Ⅰ 0.20 0.20 0.08 0.40 0.20 0.25 0.07 0.35 0.15 0.20 0.13 0.65 Scheme Ⅱ 0.20 0.20 0.11 0.55 0.20 0.25 0.10 0.50
Numerical results with admission fee
 $\lambda_1$ $\lambda_{21}$ $\lambda^*$ $f$ 0.15 0.20 0.10 6.9918 Scheme Ⅰ 0.20 0.20 0.08 6.5472 0.20 0.25 0.07 5.4116 0.15 0.20 0.13 8.1169 Scheme Ⅱ 0.20 0.20 0.11 7.1114 0.20 0.25 0.10 6.4127
 $\lambda_1$ $\lambda_{21}$ $\lambda^*$ $f$ 0.15 0.20 0.10 6.9918 Scheme Ⅰ 0.20 0.20 0.08 6.5472 0.20 0.25 0.07 5.4116 0.15 0.20 0.13 8.1169 Scheme Ⅱ 0.20 0.20 0.11 7.1114 0.20 0.25 0.10 6.4127
 [1] Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006 [2] Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 209-220. doi: 10.3934/naco.2020022 [3] Xiaoyi Zhou, Tong Ye, Tony T. Lee. Designing and analysis of a Wi-Fi data offloading strategy catering for the preference of mobile users. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021038 [4] Liqin Qian, Xiwang Cao. Character sums over a non-chain ring and their applications. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2020134 [5] Juan Manuel Pastor, Javier García-Algarra, José M. Iriondo, José J. Ramasco, Javier Galeano. Dragging in mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 37-52. doi: 10.3934/nhm.2015.10.37 [6] Alessandro Gondolo, Fernando Guevara Vasquez. Characterization and synthesis of Rayleigh damped elastodynamic networks. Networks & Heterogeneous Media, 2014, 9 (2) : 299-314. doi: 10.3934/nhm.2014.9.299 [7] Juan Manuel Pastor, Javier García-Algarra, Javier Galeano, José María Iriondo, José J. Ramasco. A simple and bounded model of population dynamics for mutualistic networks. Networks & Heterogeneous Media, 2015, 10 (1) : 53-70. doi: 10.3934/nhm.2015.10.53 [8] Juliang Zhang, Jian Chen. Information sharing in a make-to-stock supply chain. Journal of Industrial & Management Optimization, 2014, 10 (4) : 1169-1189. doi: 10.3934/jimo.2014.10.1169 [9] Y. Latushkin, B. Layton. The optimal gap condition for invariant manifolds. Discrete & Continuous Dynamical Systems - A, 1999, 5 (2) : 233-268. doi: 10.3934/dcds.1999.5.233 [10] Min Li, Jiahua Zhang, Yifan Xu, Wei Wang. Effects of disruption risk on a supply chain with a risk-averse retailer. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021024 [11] Martin Bohner, Sabrina Streipert. Optimal harvesting policy for the Beverton--Holt model. Mathematical Biosciences & Engineering, 2016, 13 (4) : 673-695. doi: 10.3934/mbe.2016014 [12] Diana Keller. Optimal control of a linear stochastic Schrödinger equation. Conference Publications, 2013, 2013 (special) : 437-446. doi: 10.3934/proc.2013.2013.437 [13] Xingchun Wang, Yongjin Wang. Variance-optimal hedging for target volatility options. Journal of Industrial & Management Optimization, 2014, 10 (1) : 207-218. doi: 10.3934/jimo.2014.10.207 [14] Alberto Bressan, Ke Han, Franco Rampazzo. On the control of non holonomic systems by active constraints. Discrete & Continuous Dynamical Systems - A, 2013, 33 (8) : 3329-3353. doi: 10.3934/dcds.2013.33.3329 [15] Mohsen Abdolhosseinzadeh, Mir Mohammad Alipour. Design of experiment for tuning parameters of an ant colony optimization method for the constrained shortest Hamiltonian path problem in the grid networks. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 321-332. doi: 10.3934/naco.2020028 [16] Zengyun Wang, Jinde Cao, Zuowei Cai, Lihong Huang. Finite-time stability of impulsive differential inclusion: Applications to discontinuous impulsive neural networks. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2677-2692. doi: 10.3934/dcdsb.2020200 [17] Wen-Bin Yang, Yan-Ling Li, Jianhua Wu, Hai-Xia Li. Dynamics of a food chain model with ratio-dependent and modified Leslie-Gower functional responses. Discrete & Continuous Dynamical Systems - B, 2015, 20 (7) : 2269-2290. doi: 10.3934/dcdsb.2015.20.2269 [18] Benrong Zheng, Xianpei Hong. Effects of take-back legislation on pricing and coordination in a closed-loop supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021035 [19] Reza Lotfi, Yahia Zare Mehrjerdi, Mir Saman Pishvaee, Ahmad Sadeghieh, Gerhard-Wilhelm Weber. A robust optimization model for sustainable and resilient closed-loop supply chain network design considering conditional value at risk. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 221-253. doi: 10.3934/naco.2020023 [20] Paula A. González-Parra, Sunmi Lee, Leticia Velázquez, Carlos Castillo-Chavez. A note on the use of optimal control on a discrete time model of influenza dynamics. Mathematical Biosciences & Engineering, 2011, 8 (1) : 183-197. doi: 10.3934/mbe.2011.8.183

2019 Impact Factor: 1.366

## Metrics

• PDF downloads (109)
• HTML views (461)
• Cited by (3)

## Other articlesby authors

• on AIMS
• on Google Scholar

[Back to Top]