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A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities

Author

Listed:
  • Seokjun Lee

    (Department of Management Information Systems, Sangji University, Wonju 26339, Korea)

  • Sergei Dudin

    (Laboratory of Applied Probabilistic Analysis, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

  • Olga Dudina

    (Laboratory of Applied Probabilistic Analysis, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

  • Chesoong Kim

    (Department of Business Administration, Sangji University, Wonju 26339, Korea)

  • Valentina Klimenok

    (Laboratory of Applied Probabilistic Analysis, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus)

Abstract

A single-server queueing system with a finite buffer, several types of impatient customers, and non-preemptive priorities is analyzed. The initial priority of a customer can increase during its waiting time in the queue. The behavior of the system is described by a multi-dimensional Markov chain. The generator of this chain, having essential dependencies between the components, is derived and formulas for computation of the most important performance indicators of the system are presented. The dependence of some of these indicators on the capacity of the buffer space is illustrated. The profound effect of the phenomenon of correlation of successive inter-arrival times and variance of the service time is numerically demonstrated. Results can be used for the optimization of dispatching various types of customers in information transmission systems, emergency departments and first aid stations, perishable foods supply chains, etc.

Suggested Citation

  • Seokjun Lee & Sergei Dudin & Olga Dudina & Chesoong Kim & Valentina Klimenok, 2020. "A Priority Queue with Many Customer Types, Correlated Arrivals and Changing Priorities," Mathematics, MDPI, vol. 8(8), pages 1-20, August.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:8:p:1292-:d:394728
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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. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    3. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    4. Sergei Dudin & Olga Dudina & Konstantin Samouylov & Alexander Dudin, 2020. "Improvement of the Fairness of Non-Preemptive Priorities in the Transmission of Heterogeneous Traffic," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    5. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    6. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 1.
    7. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 4.
    8. Dudin, A.N. & Dudin, S.A. & Dudina, O.S. & Samouylov, K.E., 2020. "Competitive queueing systems with comparative rating dependent arrivals," Operations Research Perspectives, Elsevier, vol. 7(C).
    9. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 3.
    10. Editorial Article, 0. "The Information for Authors," Economics of Contemporary Russia, Regional Public Organization for Assistance to the Development of Institutions of the Department of Economics of the Russian Academy of Sciences, issue 2.
    11. 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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    Cited by:

    1. V. Vinitha & N. Anbazhagan & S. Amutha & K. Jeganathan & Bhanu Shrestha & Hyoung-Kyu Song & Gyanendra Prasad Joshi & Hyeonjoon Moon, 2022. "Analysis of a Stochastic Inventory Model on Random Environment with Two Classes of Suppliers and Impulse Customers," Mathematics, MDPI, vol. 10(13), pages 1-18, June.
    2. A. N. Dudin & S. A. Dudin & O. S. Dudina, 2023. "Randomized Threshold Strategy for Providing Flexible Priority in Multi-Server Queueing System with a Marked Markov Arrival Process and Phase-Type Distribution of Service Time," Mathematics, MDPI, vol. 11(12), pages 1-23, June.
    3. Konstantin Samouylov & Olga Dudina & Alexander Dudin, 2023. "Analysis of Multi-Server Queueing System with Flexible Priorities," Mathematics, MDPI, vol. 11(4), pages 1-22, February.

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