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Analysis of Single-Server Multi-Class Queue with Unreliable Service, Batch Correlated Arrivals, Customers Impatience, and Dynamical Change of Priorities

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  • Alexander Dudin

    (Department of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus
    Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia)

  • Olga Dudina

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

  • Sergei Dudin

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

  • Konstantin Samouylov

    (Applied Mathematics and Communications Technology Institute, Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St., 117198 Moscow, Russia)

Abstract

A single-server non-pre-emptive priority queueing system of a finite capacity with many types of customers is analyzed. Inter-arrival times can be correlated and batch arrivals are allowed. Possible unreliability of the server, implying the loss of a customer or the necessity of its service from the early beginning or some phase of the service, is taken into account. Initial priorities provided to various types of customers at the arrival moment can be varied (increased or decreased) after the random amount of time during the customer stay in the buffer. Such a type of queues arises in the modeling operation of various emergency care systems, information, and perishable goods delivering systems, etc. The stationary behavior of the system is described by the finite state multi-dimensional continuous-time Markov chain with the upper-Hessenberg block structure of the generator. The stationary distribution of the system states and some important characteristics of the system are calculated. The presented numerical examples illustrate opportunities to quantitatively evaluate the impact of the buffer capacity and customers’ mean arrival rate on the most important characteristics of the system. The possibility of solving optimization problems is briefly shown.

Suggested Citation

  • Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Single-Server Multi-Class Queue with Unreliable Service, Batch Correlated Arrivals, Customers Impatience, and Dynamical Change of Priorities," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1257-:d:566004
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    References listed on IDEAS

    as
    1. Qi‐Ming He & Jingui Xie & Xiaobo Zhao, 2012. "Priority queue with customer upgrades," Naval Research Logistics (NRL), John Wiley & Sons, vol. 59(5), pages 362-375, August.
    2. Alexander Dudin & Sergei Dudin, 2016. "Analysis of a Priority Queue with Phase-Type Service and Failures," International Journal of Stochastic Analysis, Hindawi, vol. 2016, pages 1-11, July.
    3. Jingui Xie & Taozeng Zhu & An-Kuo Chao & Shuaian Wang, 2017. "Performance analysis of service systems with priority upgrades," Annals of Operations Research, Springer, vol. 253(1), pages 683-705, June.
    4. Ping Cao & Jingui Xie, 2016. "Optimal control of a multiclass queueing system when customers can change types," Queueing Systems: Theory and Applications, Springer, vol. 82(3), pages 285-313, April.
    5. Val Andrei Fajardo & Steve Drekic, 2017. "Waiting Time Distributions in the Preemptive Accumulating Priority Queue," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 255-284, March.
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