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Analysis of Multi-Server Priority Queueing System with Hysteresis Strategy of Server Reservation and Retrials

Author

Listed:
  • Alexander Dudin

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

  • Sergey Dudin

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

  • Rosanna Manzo

    (Department of Information and Electrical Engineering and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, Fisciano, 84084 Salerno, Italy)

  • Luigi Rarità

    (Dipartimento di Scienze Aziendali—Management and Innovation Systems, University of Salerno, Via Giovanni Paolo II, 132, Fisciano, 84084 Salerno, Italy)

Abstract

A multi-server queueing system with two types of requests and preemptive priority of one type is considered as a model of a cell of a cognitive radio system under practical suggestions about the arrival flows. A hysteresis type strategy for server reservation is suggested to mitigate the effect of interruption of service of low priority requests. Under the arbitrarily fixed values of the sets of the thresholds defining this strategy, the behavior of the system is described by a level-dependent multi-dimensional Markov chain. Formulas for computation of values of performance characteristics of the system are derived. Numerical examples illustrating the dependence of the main performance characteristics on the thresholds defining the strategy of control and the numerical solution of the problem of the optimal choice of the thresholds are reported.

Suggested Citation

  • Alexander Dudin & Sergey Dudin & Rosanna Manzo & Luigi Rarità, 2022. "Analysis of Multi-Server Priority Queueing System with Hysteresis Strategy of Server Reservation and Retrials," Mathematics, MDPI, vol. 10(20), pages 1-19, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3747-:d:939698
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    References listed on IDEAS

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    1. A.D. Banik, 2015. "Some aspects of stationary characteristics and optimal control of the BMAP ∕ G − G ∕ 1 ∕ N( ∞ ) oscillating queueing system," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 31(2), pages 204-230, March.
    2. Huamin Zhang & Feng Ding, 2013. "On the Kronecker Products and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, June.
    3. Bin Sun & Moon Ho Lee & Sergey A. Dudin & Alexander N. Dudin, 2014. "Analysis of Multiserver Queueing System with Opportunistic Occupation and Reservation of Servers," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-13, May.
    4. Amir Elalouf & Guy Wachtel, 2022. "Queueing Problems in Emergency Departments: A Review of Practical Approaches and Research Methodologies," SN Operations Research Forum, Springer, vol. 3(1), pages 1-46, March.
    5. Yuan Zhao & Wuyi Yue & Zsolt Saffer, 2022. "Spectrum allocation strategy with a probabilistic preemption scheme in cognitive radio networks: analysis and optimization," Annals of Operations Research, Springer, vol. 310(2), pages 621-639, March.
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