# American Institute of Mathematical Sciences

January  2019, 15(1): 1-14. doi: 10.3934/jimo.2018029

## Performance evaluation and optimization of cognitive radio networks with adjustable access control for multiple secondary users

 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  February 2017 Revised  July 2017 Published  February 2018

Fund Project: The reviewing process of this paper was handled by Yutaka Takahashi.

In this paper, we consider a cognitive radio network with multiple secondary users (SUs). The SU packets in the system can be divided into two categories: SU1 packets and SU2 packets, where SU1 packets have transmission priority over SU2 packets. Considering the absolute priority of the primary users (PUs), the PU packets have the highest priority in the system to transmit. In order to guarantee the Quality of Service (QoS) of the network users, as well as reduce the average delay of the SU2 packets, we propose an adjustable access control scheme for the SU2 packets. A newly arriving SU2 packet can access the system with an access probability related to the total number of packets in the system. A variable factor is also introduced to adjust the access probability dynamically. Based on the working principle of the adjustable access control scheme, we build a discrete-time queueing model with a finite waiting room and an adjustable joining rate. With a steady-state analysis of the queueing model, using a three-dimensional Markov chain, we derive some performance measures, such as the total channel utilization, the interruption rate, the throughput, and the average delay of the SU2 packets. Moreover, we show the influence of the adjustment factor on different system performance measures by using numerical results. Finally, considering the trade-off between the throughput and the average delay of the SU2 packets with respect to the adjustment factor, we build a net benefit function and show an optimal algorithm to optimize the adjustment factor.

Citation: Yuan Zhao, Wuyi Yue. Performance evaluation and optimization of cognitive radio networks with adjustable access control for multiple secondary users. Journal of Industrial & Management Optimization, 2019, 15 (1) : 1-14. doi: 10.3934/jimo.2018029
##### References:
 [1] S. Aghajeri, A. Sharafat and K. Navaie, Primary service outage degradation in dynamic spectrum sharing with non-ideal spectrum sensing, IET Communications, 6 (2012), 1252-1261.  doi: 10.1049/iet-com.2011.0476.  Google Scholar [2] A. Alfa, Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System ,Springer, New York, 2010.  Google Scholar [3] E. P. Chong and S.${{\rm{\dot Z}}}$ak, An Introduction to Optimization, Third Edition, Wiley, Hoboken, 2008. doi: 10.1002/9781118033340.  Google Scholar [4] C. Ding, K. Wang and S. Lai, Channel coordination mechanism with retailers having fairness preference-An improved quantity discount mechanism, Journal of Industrial and Management Optimization, 9 (2013), 967-982.  doi: 10.3934/jimo.2013.9.967.  Google Scholar [5] A. Greenbaum, Iterative Methods for Solving Linear Systems, Society for Industrial and Applied Mathematics, Philadelphia, 1997.  Google Scholar [6] S. Jin, Y. Zhao, W. Yue and Z. Saffer, Performance analysis and optimization of an adaptive admission control scheme in cognitive radio networks, Mathematical Problems in Engineering, 2013 (2013), Article ID 727310, 10 pages. doi: 10.1155/2013/727310.  Google Scholar [7] Y. Lee, C. Park and D. Sim, Cognitive radio spectrum access with prioritized secondary users, Applied Mathematics & Information Sciences, 6 (2012), 595S-601S.   Google Scholar [8] 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 [9] J. Marinho and E. Monteiro, Cognitive radio: Survey on communication protocols, spectrum decision issues, and future research directions, Wireless Networks, 18 (2012), 147-164.  doi: 10.1007/s11276-011-0392-1.  Google Scholar [10] M. Naeem, A. Anpalagan, M. Jaseemuddin and D. Lee, Resource allocation techniques in cooperative cognitive radio networks, IEEE Communications Surveys & Tutorials, 16 (2014), 729-744.  doi: 10.1109/SURV.2013.102313.00272.  Google Scholar [11] N. Nguyen-Thanh, A. Pham and V. T. Nguyen, Medium access control design for cognitive radio networks: A survey, IEICE Transactions on Communications, E97-B (2014), 359-374.  doi: 10.1587/transcom.E97.B.359.  Google Scholar [12] S. Sharma, T. Bogale, S. Chatzinotas, B. Ottersten, L. Le and X. Wang, Cognitive radio techniques under practical imperfections: A survey, IEEE Communications Surveys & Tutorials, 17 (2015), 1858-1884.  doi: 10.1109/COMST.2015.2452414.  Google Scholar [13] N. Tian and Z. Zhang, Vacation Queueing Models: Theory and Applications, Springer, New York, 2006.  Google Scholar [14] E. Tragos, S. Zeadally, A. Fragkiadakis and V. Siris, Spectrum assignment in cognitive radio networks: A comprehensive survey, IEEE Communications Surveys & Tutorials, 15 (2013), 1108-1135.  doi: 10.1109/SURV.2012.121112.00047.  Google Scholar [15] D. Willkomm and A. Wolisz, Efficient QoS support for secondary users in cognitive radio systems, IEEE Wireless Communications, 17 (2010), 16-23.   Google Scholar [16] Y. Zhao and W. Yue, Cognitive radio networks with multiple secondary users under two kinds of priority schemes: Performance comparison and optimization, Journal of IndustrialI and Management Optimization, 13 (2017), 1449-1466.   Google Scholar [17] Y. Zhao and W. Yue, An adjustable access control scheme in cognitive radio networks with multiple secondary users in Proceesings of 11th International Conference on Queueing Theory and Network Applications, ACM, (2016), Article No. 10, 5 pages. doi: 10.1145/3016032.3016040.  Google Scholar

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##### References:
 [1] S. Aghajeri, A. Sharafat and K. Navaie, Primary service outage degradation in dynamic spectrum sharing with non-ideal spectrum sensing, IET Communications, 6 (2012), 1252-1261.  doi: 10.1049/iet-com.2011.0476.  Google Scholar [2] A. Alfa, Queueing Theory for Telecommunications: Discrete Time Modelling of a Single Node System ,Springer, New York, 2010.  Google Scholar [3] E. P. Chong and S.${{\rm{\dot Z}}}$ak, An Introduction to Optimization, Third Edition, Wiley, Hoboken, 2008. doi: 10.1002/9781118033340.  Google Scholar [4] C. Ding, K. Wang and S. Lai, Channel coordination mechanism with retailers having fairness preference-An improved quantity discount mechanism, Journal of Industrial and Management Optimization, 9 (2013), 967-982.  doi: 10.3934/jimo.2013.9.967.  Google Scholar [5] A. Greenbaum, Iterative Methods for Solving Linear Systems, Society for Industrial and Applied Mathematics, Philadelphia, 1997.  Google Scholar [6] S. Jin, Y. Zhao, W. Yue and Z. Saffer, Performance analysis and optimization of an adaptive admission control scheme in cognitive radio networks, Mathematical Problems in Engineering, 2013 (2013), Article ID 727310, 10 pages. doi: 10.1155/2013/727310.  Google Scholar [7] Y. Lee, C. Park and D. Sim, Cognitive radio spectrum access with prioritized secondary users, Applied Mathematics & Information Sciences, 6 (2012), 595S-601S.   Google Scholar [8] 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 [9] J. Marinho and E. Monteiro, Cognitive radio: Survey on communication protocols, spectrum decision issues, and future research directions, Wireless Networks, 18 (2012), 147-164.  doi: 10.1007/s11276-011-0392-1.  Google Scholar [10] M. Naeem, A. Anpalagan, M. Jaseemuddin and D. Lee, Resource allocation techniques in cooperative cognitive radio networks, IEEE Communications Surveys & Tutorials, 16 (2014), 729-744.  doi: 10.1109/SURV.2013.102313.00272.  Google Scholar [11] N. Nguyen-Thanh, A. Pham and V. T. Nguyen, Medium access control design for cognitive radio networks: A survey, IEICE Transactions on Communications, E97-B (2014), 359-374.  doi: 10.1587/transcom.E97.B.359.  Google Scholar [12] S. Sharma, T. Bogale, S. Chatzinotas, B. Ottersten, L. Le and X. Wang, Cognitive radio techniques under practical imperfections: A survey, IEEE Communications Surveys & Tutorials, 17 (2015), 1858-1884.  doi: 10.1109/COMST.2015.2452414.  Google Scholar [13] N. Tian and Z. Zhang, Vacation Queueing Models: Theory and Applications, Springer, New York, 2006.  Google Scholar [14] E. Tragos, S. Zeadally, A. Fragkiadakis and V. Siris, Spectrum assignment in cognitive radio networks: A comprehensive survey, IEEE Communications Surveys & Tutorials, 15 (2013), 1108-1135.  doi: 10.1109/SURV.2012.121112.00047.  Google Scholar [15] D. Willkomm and A. Wolisz, Efficient QoS support for secondary users in cognitive radio systems, IEEE Wireless Communications, 17 (2010), 16-23.   Google Scholar [16] Y. Zhao and W. Yue, Cognitive radio networks with multiple secondary users under two kinds of priority schemes: Performance comparison and optimization, Journal of IndustrialI and Management Optimization, 13 (2017), 1449-1466.   Google Scholar [17] Y. Zhao and W. Yue, An adjustable access control scheme in cognitive radio networks with multiple secondary users in Proceesings of 11th International Conference on Queueing Theory and Network Applications, ACM, (2016), Article No. 10, 5 pages. doi: 10.1145/3016032.3016040.  Google Scholar
Diagram for the proposed adjustable access control scheme
Total channel utilization $\delta$ vs. adjustment factor $\tau$
Interruption rate $\gamma$ of the SU2 packets vs. adjustment factor $\tau$
Throughput $\theta$ of the SU2 packets vs. adjustment factor $\tau$
Average delay $\sigma$ of the SU2 packets vs. adjustment factor $\tau$
Optimal adjustment factor $\tau^*$ and the maximum net benefit $B(\tau^*)$
 Buffer capacity Arrival rates of packets Optimal adjustment factor Maximum net benefit $K$ $\lambda_1, \lambda_{21}, \lambda_{22}$ $\tau^*$ $B(\tau^*)$ $5$ $\lambda_1=0.1, \lambda_{21}=0.1, \lambda_{22}=0.2$ 0.0006 7.4084 $\lambda_1=0.2, \lambda_{21}=0.1, \lambda_{22}=0.2$ 0.1178 3.5230 $\lambda_1=0.2, \lambda_{21}=0.2, \lambda_{22}=0.2$ 0.3232 0.0113 $\lambda_1=0.2, \lambda_{21}=0.2, \lambda_{22}=0.3$ 0.5887 2.4589 $10$ $\lambda_1=0.1, \lambda_{21}=0.1, \lambda_{22}=0.2$ 0.0252 7.3280 $\lambda_1=0.2, \lambda_{21}=0.1, \lambda_{22}=0.2$ 0.1341 3.4942 $\lambda_1=0.2, \lambda_{21}=0.2, \lambda_{22}=0.2$ 0.3342 0.0031 $\lambda_1=0.2, \lambda_{21}=0.2, \lambda_{22}=0.3$ 0.6012 2.4494
 Buffer capacity Arrival rates of packets Optimal adjustment factor Maximum net benefit $K$ $\lambda_1, \lambda_{21}, \lambda_{22}$ $\tau^*$ $B(\tau^*)$ $5$ $\lambda_1=0.1, \lambda_{21}=0.1, \lambda_{22}=0.2$ 0.0006 7.4084 $\lambda_1=0.2, \lambda_{21}=0.1, \lambda_{22}=0.2$ 0.1178 3.5230 $\lambda_1=0.2, \lambda_{21}=0.2, \lambda_{22}=0.2$ 0.3232 0.0113 $\lambda_1=0.2, \lambda_{21}=0.2, \lambda_{22}=0.3$ 0.5887 2.4589 $10$ $\lambda_1=0.1, \lambda_{21}=0.1, \lambda_{22}=0.2$ 0.0252 7.3280 $\lambda_1=0.2, \lambda_{21}=0.1, \lambda_{22}=0.2$ 0.1341 3.4942 $\lambda_1=0.2, \lambda_{21}=0.2, \lambda_{22}=0.2$ 0.3342 0.0031 $\lambda_1=0.2, \lambda_{21}=0.2, \lambda_{22}=0.3$ 0.6012 2.4494
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