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doi: 10.3934/jimo.2018195

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

 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

Received  October 2017 Revised  January 2018 Published  December 2018

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.

Citation: Yuan Zhao, Wuyi Yue. Performance analysis and optimization for cognitive radio networks with a finite primary user buffer and a probability returning scheme. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018195
##### References:
 [1] A. 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] A. Asheralieva and Y. Miyanaga, Joint bandwidth and power allocation for LTE-based cognitive radio network based on buffer occupancy, Mobile Information Systems, 2016 (2016), Article ID 6306580, 23 pages.Google Scholar [3] B. Benmammar, A. Amraoui and F. Krief, A survey on dynamic spectrum access techniques in cognitive radio networks, International Journal of Communication Networks and Information Security, 5 (2013), 68-79. Google Scholar [4] C. Do, N. Tran, M. Nguyen, C. Hong and S. Lee, Social optimization strategy in unobserved queueing systems in cognitive radio networks, IEEE Communications Letters, 16 (2012), 1944-1947. Google Scholar [5] A. Fakhrudeen and O. Alani, Comprehensive survey on quality of service provisioning approaches in cognitive radio networks: Part one, International Journal of Wireless Information Networks, 24 (2017), 356-388. Google Scholar [6] M. Hassan, G. Karmakar, J. Kamruzzaman and B. Srinivasan, Exclusive use spectrum access trading models in cognitive radio networks: A survey, Tutorials, 19 (2017), 2192-2231. Google Scholar [7] R. Hassin, Rational Queueing, CRC Press, New York, 2016. doi: 10.1201/b20014. [8] 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 [9] S. Jin, S. Chen and J. Zhang, Social optimization and pricing policy in cognitive radio networks with an energy saving strategy, Mobile Information Systems, 2016 (2016), Article ID 2426580, 10 pages.Google Scholar [10] H. Li and Z. Han, Socially optimal queuing control in cognitive radio networks subject to service interruptions: To queue or not to queue?, IEEE Transactions on Wireless Communications, 10 (2011), 1656-1666. Google Scholar [11] M. Naeem, A. Anpalagan, M. Jaseemuddin and D. Lee, Resource allocation techniques in cooperative cognitive radio networks, Tutorials, 16 (2014), 729-744. Google Scholar [12] S. Pandit and G. Singh, An overview of spectrum sharing techniques in cognitive radio communication system, Wireless Networks, 23 (2017), 497-518. Google Scholar [13] Y. Saleem and M. Rehmani, Primary radio user activity models for cognitive radio networks: A survey, Journal of Network and Computer Applications, 43 (2014), 1-16. Google Scholar [14] A. Sultana, X. Fernando and L. Zhao, An overview of medium access control strategies for opportunistic spectrum access in cognitive radio networks, Peer-to-Peer Networking and Applications, 10 (2017), 1113-1141. Google Scholar [15] N. Tian and G. Zhang, Vacation Queueing Models: Theory and Applications, Springer, New York, 2006. Google Scholar [16] E. Tragos, S. Zeadally, A. Fragkiadakis and V. Siris, Spectrum assignment in cognitive radio networks: A comprehensive survey, Tutorials, 15 (2013), 1108-1135. Google Scholar [17] 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. Google Scholar [18] Y. Zhao, S. Jin and W. Yue, A novel spectrum access strategy with α-retry policy in cognitive radio networks: A queueing-based analysis, Journal of Communications and Networks, 16 (2014), 193-201. Google Scholar [19] Y. Zhao and W. Yue, Performance evaluation of cognitive radio networks with a finite buffer setting for primary users, in Queueing Theory and Network Applications (eds. W. Yue, Q. Li, S. Jin and Z. Ma), Springer, (2017), 168-179.Google Scholar [20] Y. Zhao and W. Yue, Performance analysis and optimization of cognitive radio networks with retransmission control, Optimization Letters, 12 (2018), 1281-1300. doi: 10.1007/s11590-017-1119-8. Google Scholar

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##### References:
 [1] A. 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] A. Asheralieva and Y. Miyanaga, Joint bandwidth and power allocation for LTE-based cognitive radio network based on buffer occupancy, Mobile Information Systems, 2016 (2016), Article ID 6306580, 23 pages.Google Scholar [3] B. Benmammar, A. Amraoui and F. Krief, A survey on dynamic spectrum access techniques in cognitive radio networks, International Journal of Communication Networks and Information Security, 5 (2013), 68-79. Google Scholar [4] C. Do, N. Tran, M. Nguyen, C. Hong and S. Lee, Social optimization strategy in unobserved queueing systems in cognitive radio networks, IEEE Communications Letters, 16 (2012), 1944-1947. Google Scholar [5] A. Fakhrudeen and O. Alani, Comprehensive survey on quality of service provisioning approaches in cognitive radio networks: Part one, International Journal of Wireless Information Networks, 24 (2017), 356-388. Google Scholar [6] M. Hassan, G. Karmakar, J. Kamruzzaman and B. Srinivasan, Exclusive use spectrum access trading models in cognitive radio networks: A survey, Tutorials, 19 (2017), 2192-2231. Google Scholar [7] R. Hassin, Rational Queueing, CRC Press, New York, 2016. doi: 10.1201/b20014. [8] 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 [9] S. Jin, S. Chen and J. Zhang, Social optimization and pricing policy in cognitive radio networks with an energy saving strategy, Mobile Information Systems, 2016 (2016), Article ID 2426580, 10 pages.Google Scholar [10] H. Li and Z. Han, Socially optimal queuing control in cognitive radio networks subject to service interruptions: To queue or not to queue?, IEEE Transactions on Wireless Communications, 10 (2011), 1656-1666. Google Scholar [11] M. Naeem, A. Anpalagan, M. Jaseemuddin and D. Lee, Resource allocation techniques in cooperative cognitive radio networks, Tutorials, 16 (2014), 729-744. Google Scholar [12] S. Pandit and G. Singh, An overview of spectrum sharing techniques in cognitive radio communication system, Wireless Networks, 23 (2017), 497-518. Google Scholar [13] Y. Saleem and M. Rehmani, Primary radio user activity models for cognitive radio networks: A survey, Journal of Network and Computer Applications, 43 (2014), 1-16. Google Scholar [14] A. Sultana, X. Fernando and L. Zhao, An overview of medium access control strategies for opportunistic spectrum access in cognitive radio networks, Peer-to-Peer Networking and Applications, 10 (2017), 1113-1141. Google Scholar [15] N. Tian and G. Zhang, Vacation Queueing Models: Theory and Applications, Springer, New York, 2006. Google Scholar [16] E. Tragos, S. Zeadally, A. Fragkiadakis and V. Siris, Spectrum assignment in cognitive radio networks: A comprehensive survey, Tutorials, 15 (2013), 1108-1135. Google Scholar [17] 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. Google Scholar [18] Y. Zhao, S. Jin and W. Yue, A novel spectrum access strategy with α-retry policy in cognitive radio networks: A queueing-based analysis, Journal of Communications and Networks, 16 (2014), 193-201. Google Scholar [19] Y. Zhao and W. Yue, Performance evaluation of cognitive radio networks with a finite buffer setting for primary users, in Queueing Theory and Network Applications (eds. W. Yue, Q. Li, S. Jin and Z. Ma), Springer, (2017), 168-179.Google Scholar [20] Y. Zhao and W. Yue, Performance analysis and optimization of cognitive radio networks with retransmission control, Optimization Letters, 12 (2018), 1281-1300. doi: 10.1007/s11590-017-1119-8. Google Scholar
System actions of PU packets and SU packets
Average queue length $E_{PU}$ of PU packets
Throughput $\theta_{PU}$ of PU packets
Blocking rate $\beta_{SU}$ of SU packets
Average delay $\delta_{SU}$ of SU packets
Function $F_I(\lambda_2)$ of the individual net benefit
Function $F_S(\lambda_2)$ of the social net benefit
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 $t=n^+$
 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 $t=n^+$
Numerical results for the individually and socially optimal strategies
 $K_1$ $K_2$ $q$ $\lambda_i$ $r_i$ $\lambda_s$ $r_s$ min max min max 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
 $K_1$ $K_2$ $q$ $\lambda_i$ $r_i$ $\lambda_s$ $r_s$ min max min max 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
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
 $K_1$ $K_2$ $q$ $\lambda_s$ $f$ 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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