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Analysis of a Pre-Emptive Two-Priority Queuing System with Impatient Customers and Heterogeneous Servers

Author

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  • Mingang Yin

    (School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China)

  • Ming Yan

    (School of Mechanical Engineering, Shenyang University of Technology, Shenyang 110870, China)

  • Yu Guo

    (School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110819, China)

  • Minghe Liu

    (School of Mechanical Engineering, Shenyang Jianzhu University, Shenyang 110168, China)

Abstract

This paper presents a queuing system model that incorporates multiple priorities, multiple abandonments, and heterogeneous servers. Waiting for service easily leads to impatient behaviors. The impact of two kinds of impatient behaviors, balking and reneging, on queueing system performance is examined. The problem is formulated as continuous-time Markov chains. It also introduces a special state called the non-sojourn state to record the number of customers who abandon the system. The state transition rate matrix is transformed into a block tridiagonal matrix by appropriately setting the state numbers. A novel indicator called interstate transition frequency is proposed, which aids in distinguishing state transitions during the system evaluation process. Based on the interstate transition frequency, a set of indicators is derived to offer additional analytical perspectives for the queuing system. Finally, the proposed model is applied to an automobile repair shop to validate its effectiveness in practical scenarios.

Suggested Citation

  • Mingang Yin & Ming Yan & Yu Guo & Minghe Liu, 2023. "Analysis of a Pre-Emptive Two-Priority Queuing System with Impatient Customers and Heterogeneous Servers," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:18:p:3878-:d:1237658
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    References listed on IDEAS

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    1. Yaolei Wang & Yiming Fan & Taozeng Zhu & Ping Cao & Jingui Xie, 2019. "An approximation method for 2-chain flexible queues with preemptive priority," International Journal of Production Research, Taylor & Francis Journals, vol. 57(19), pages 5935-5950, October.
    2. Shlomo Halfin & Ward Whitt, 1981. "Heavy-Traffic Limits for Queues with Many Exponential Servers," Operations Research, INFORMS, vol. 29(3), pages 567-588, June.
    3. Wei Chang, 1965. "Queuing with Nonpreemptive and Preemptive-Resume Priorities," Operations Research, INFORMS, vol. 13(6), pages 1020-1022, December.
    4. N. K. Jaiswal, 1961. "Preemptive Resume Priority Queue," Operations Research, INFORMS, vol. 9(5), pages 732-742, October.
    5. O Jouini & A Roubos, 2014. "On multiple priority multi-server queues with impatience," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 65(5), pages 616-632, May.
    6. Kuo-Hsiung Wang & Ying-Chung Chang, 2002. "Cost analysis of a finite M/M/R queueing system with balking, reneging, and server breakdowns," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 169-180, November.
    7. Leonard Kleinrock & Roy P. Finkelstein, 1967. "Time Dependent Priority Queues," Operations Research, INFORMS, vol. 15(1), pages 104-116, February.
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    Cited by:

    1. Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.

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