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Modified Erlang Loss System for Cognitive Wireless Networks

Author

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  • Evsey Morozov

    (Institute of Applied Mathematical Research, Karelian Research Centre RAS, 185910 Petrozavodsk, Russia
    Institute of Mathematics and Information Technologies, Petrozavodsk State University, 185910 Petrozavodsk, Russia
    Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 119991 Moscow, Russia)

  • Stepan Rogozin

    (Institute of Applied Mathematical Research, Karelian Research Centre RAS, 185910 Petrozavodsk, Russia
    Institute of Mathematics and Information Technologies, Petrozavodsk State University, 185910 Petrozavodsk, Russia)

  • Hung Q. Nguyen

    (Graduate School of Science and Technology, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Ibaraki, Japan)

  • Tuan Phung-Duc

    (Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8573, Ibaraki, Japan)

Abstract

This paper considers a modified Erlang loss system for cognitive wireless networks and related applications. A primary user has pre-emptive priority over secondary users, and the primary customer is lost if upon arrival all the channels are used by other primary users. Secondary users cognitively use idle channels, and they can stay (either in an infinite buffer or in an orbit) in cases where idle channels are not available upon arrival or they are interrupted by primary users. While the infinite buffer model represents the case with zero sensing time, the infinite orbit model represents the case with positive sensing time. We obtain an explicit stability condition for the cases where arrival processes of primary users and secondary users follow Poisson processes, and their service times follow two distinct arbitrary distributions. The stability condition is insensitive to the service time distributions and implies the maximal throughout of secondary users. Moreover, we extend the stability analysis to the system with outgoing calls. For a special case of exponential service time distributions, we analyze the buffered system in depth to show the effect of parameters on the delay performance and the mean number of interruptions of secondary users. Our simulations for distributions rather than exponential reveal that the mean number of terminations for secondary users is less sensitive to the service time distribution of primary users.

Suggested Citation

  • Evsey Morozov & Stepan Rogozin & Hung Q. Nguyen & Tuan Phung-Duc, 2022. "Modified Erlang Loss System for Cognitive Wireless Networks," Mathematics, MDPI, vol. 10(12), pages 1-20, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2101-:d:840919
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    References listed on IDEAS

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    1. Arash Ostovar & Hengameh Keshavarz & Zhi Quan, 2021. "Cognitive radio networks for green wireless communications: an overview," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 76(1), pages 129-138, January.
    2. Osama Salameh & Herwig Bruneel & Sabine Wittevrongel, 2020. "Performance Evaluation of Cognitive Radio Networks with Imperfect Spectrum Sensing and Bursty Primary User Traffic," Mathematical Problems in Engineering, Hindawi, vol. 2020, pages 1-11, June.
    3. Jianping Liu & Shunfu Jin & Wuyi Yue, 2019. "Performance evaluation and system optimization of Green cognitive radio networks with a multiple-sleep mode," Annals of Operations Research, Springer, vol. 277(2), pages 371-391, June.
    4. I. L. Mitrany & B. Avi-Itzhak, 1968. "A Many-Server Queue with Service Interruptions," Operations Research, INFORMS, vol. 16(3), pages 628-638, June.
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