Abstract
In cognitive radio networks (CRNs), multiple secondary users may send out requests simultaneously and one secondary user may send out multiple requests at one time, i.e., request arrivals usually show an aggregate manner. Moreover, a secondary user packet waiting in the buffer may leave the system due to impatience before it is transmitted, and this impatient behavior inevitably has an impact on the system performance. Aiming to investigate the influence of the aggregate behavior of requests and the likelihood of impatience on a dynamic spectrum allocation scheme in CRNs, in this paper a batch arrival queueing model with possible reneging and potential transmission interruption is established. By constructing a Markov chain and presenting a transition rate matrix, the steady-state distribution of the queueing model along with a dynamic spectrum allocation scheme is derived to analyze the stochastic behavior of the system. Accordingly, some important performance measures such as the loss rate, the balk rate and the average delay of secondary user packets are given. Moreover, system experiments are carried out to show the change trends of the performance measures with respect to batch arrival rates of secondary user packets for different impatience parameters, different batch sizes of secondary user packets, and different arrival rates of primary user packets. Finally, a pricing policy for secondary users is presented and the dynamic spectrum allocation scheme is socially optimized.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Domenico A D, Strinati E C, Benedetto M G D (2012). A survey on MAC strategies for cognitive radio networks. IEEE Communications Surveys & Tutorials 14(1): 21–44.
Farraj A.K (2013). Queue model analysis for spectrum sharing cognitive systems under outage probability constraint. Wireless Personal Communications 73(3): 1021–1035.
Geirhofer S, Lang T, Sadler B M (2007). Cognitive radios for dynamic spectrum access-dynamic spectrum access in the time domain: Modeling and exploiting white space. IEEE Communication Magazine 45(5): 66–72.
Ghosh G, Das P, Chatterjee S (2014). Cognitive radio and dynamic spectrum access-Astudy. International Journal of Next-Generation Networks 6(1): 43–60.
Hassin R, Haviv M (2003). To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Kluwer Academic Publishers, New York.
** S, Ge S, Yue W (2015). Performance evaluation for an opportunistic spectrum access mechanism with impatience behavior and imperfect sensing results. Proceedings of the Seventh International Conference on Ubiquitous and Future Networks. Sapporo, Japan, July 7–10, 2015.
** S, Yue W (2016). A dynamic spectrum allocation strategy in CRNs and its performance evaluation. Proceedings of the 17th International Symposium on Knowledge and Systems Sciences. Kobe, Japan, November 4–6, 2016.
** S, Hao S, Qie X (2019). A virtual machine scheduling strategy with a speed switch and a multi-sleep mode in cloud data centers. Journal of Systems Science and Systems Engineering 28(2): 194–210.
Li H, Han Z (2011). Socially optimal queuing control in cognitive radio networks subject to service interruptions: To queue or not to queue? IEEE Transactions on Wireless Communications 10(5): 1656–1666.
Liu C, Wang J, Liu X, Liang Y (2019). Deep CM-CNN for spectrum sensing in cognitive radio. IEEE Journal on Selected Areas in Communications 37(10): 2306–2321.
Liu C, Wang J, Liu X, Liang Y (2019). Maximum eigenvalue-based goodness-of-fit detection for spectrum sensing in cognitive radio. IEEE Transactions on Vehicular Technology 68(8): 7747–7760.
Martinez-Bauset J, Popescu A, Pla V, Popescu A (2012). Cognitive radio networks with elastic traffic. Proceedings of the 8th Euro-NF Conference on Next Generation Internet. Karlskrona, Sweden, June 25–27, 2012.
Oklander B, Sidi M (2014). On cognitive processes in cognitive radio networks. Wireless Networks 20(2): 319–330.
Rajesh G, Raa**i X.M, Sagayam K, Bhushan B, Kse U (2020). Fuzzy genetic based dynamic spectrum allocation approach for cognitive radio sensor networks. Turkish Journal of Electrical Engineering and Computer Sciences 28(5): 2416–2432.
Ramzan M R, Qadri N N, Ahmed A, Naeem M (2017). Multi-objective optimization for spectrum sharing in cognitive radio networks: A review. Pervasive and Mobile Computing 41: 106–131.
Ratnaparkhi S C, Venkatesan M, Kulkarni A.V (2016). Realization of dynamic spectrum allocation using PSO. Proceedings of the Conference on Advances in Signal Processing. Pune, India, June 9–11, 2016.
Saha R.K (2020). Licensed countrywide full-spectrum allocation: A new paradigm for millimeter-wave mobile systems in 5G/6G era. IEEE Access 8: 166612–166629.
Shekhar C, Varshney S, Kumar A (2021). Matrix-geometric solution of multi-server queueing systems with Bernoulli scheduled modified vacation and retention of reneged customers: A meta-heuristic approach. Quality Technology & Quantitative Management 18(1): 39–66.
Wang B, Liu K.J.R (2011). Advances in cognitive radio networks: A survey. IEEE Journal of Selected Topics in Signal Processing 5(1): 5–23.
Wang J, Zhang F (2011). Equilibrium analysis of the observable queues with balking and delayed repairs. Applied Mathematics and Computation 218(6): 2716–2729.
Wang J, Huang A, Wang W, Quek T (2013). Admission control in cognitive radio networks with finite queue and user impatience. IEEE Wireless Communications Letters 2(2): 175–178.
Wang J, Zhang Y, Li W (2017). Strategic joining and optimal pricing in the cognitive radio system with delay-sensitive secondary users. IEEE Transactions on Cognitive Communications and Networking 3(3): 298–312.
Wu Z, Xu H, Ke G.Y (2019). The strategy of third-party mediation based on the option prioritization in the graph model. Journal of Systems Science and Systems Engineering 28(4): 399–414.
**e J, Liu C, Liang Y, Fang J (2019). Activity pattern aware spectrum sensing: A CNN-based deep learning approach. IEEE Communications Letters 23(6): 1025–1028.
Yadav P, Chaterjee S, Bhattacharya P P (2012). A survey on dynamic spectrum access techniques in cognitive radio. International Journal of Next-Generation Networks 4(1): 27–46.
Yang Y, Zhang Q, Wang Y, Emoto T, Akutagawa M, Konaka S (2019). Multi-strategy dynamic spectrum access in cognitive radio networks: Modeling, analysis and optimization. China Communications 16(3): 103–121.
Zhang W, Sun Y, Deng L, Yeo C, Yang L (2019). Dynamic spectrum allocation for heterogeneous cognitive radio networks with multiple channels. IEEE Systems Journal 13(1): 53–64.
Zeng Z, Liu M, Wang J, Lan D (2019). Non-cooperative spectrum access strategy based on impatient behavior of secondary users in cognitive radio networks. Electronics 8(9): 995–1008.
Acknowledgments
This work was supported in part by National Natural Science Foundation of China under Grant Nos. 61872311, 61973261 and 62006069, and was supported in part by MEXT, Japan. Also, the authors sincerely thank the referees for their much valuable and practical help to improve the quality of this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Haixing Wu is a PhD candidate at School of Information Science and Engineering, Yanshan University, Qinhuangdao, China. She received the B.Eng. degree in internet of things engineering from Agricultural University of Hebei, Baoding China, and M.Eng. degree in computer technology from Yanshan University, Qinhuangdao, China. Haixing Wu’s research interests are mathematical modeling, performance evaluation and resource allocation of cloud computing and mobile edge computing.
Shunfu ** is a professor at School of Information Science and Engineering, Yanshan University, Qinhuangdao, China. She received the B.Eng. degree in computer science from North-East Heavier Machinery College, Qiqihar, China, M.Eng. degree in computer science from Yanshan University, Qinhuangdao, China, and Dr.Eng degree in circuits and system from Yanshan University. Dr. **’s research interests include stochastic modeling for telecommunication, performance evaluation for computer system and network and application for queueing system. Dr. **’s papers have appeared in journals including Telecommunication System, Communications Networks, IEICE Transactions on Communications, Performance Evaluation, etc.
Wuyi Yue is a professor at Department of Intelligence and Informatics, Konan University, Kobe, Japan. She received the B.Eng. degree in electronic engineering from Tsinghua University, Bei**g, China, and the M.Eng. and Dr.Eng. degrees in applied mathematics and physics from Kyoto University, Kyoto, Japan. She was a researcher and a chief researcher of ASTEM RI, an associate professor of Wakayama University, an associate professor and a professor at the Department of Applied Mathematics, a professor at Department of Information Science and Systems Engineering, Konan University, Japan. She is also the dean of the faculty of Intelligence and Informatics, Konan University, Japan, now. Dr. Yue is a senior member of IEICE of Japan, a fellow of the Operations Research Society of Japan, a life member of the IEEE, the System Engineers Society of China and the Operations Research Society of China. She has been serving many international conferences and symposia as chair (co-chair) of organizing committee, technical program committee, steering committee and local committee, member of technical program committee and program committee. Dr. Yue’s research interests include queueing theory, stochastic processes and optimal methods as applied to system modeling, performance analysis and evaluation, and optimal resource allocation of wired and wireless/mobile communication networks (including mobile cellular, multi-hop, multi-traffic mobile communication networks), multimedia communication networks, traffic systems, stochastic systems, information systems, systems engineering and operations research.
Rights and permissions
About this article
Cite this article
Wu, H., **, S. & Yue, W. Pricing Policy for a Dynamic Spectrum Allocation Scheme with Batch Requests and Impatient Packets in Cognitive Radio Networks. J. Syst. Sci. Syst. Eng. 31, 133–149 (2022). https://doi.org/10.1007/s11518-022-5521-0
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11518-022-5521-0