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Performance analysis of service systems with priority upgrades

Author

Listed:
  • Jingui Xie

    (University of Science and Technology of China)

  • Taozeng Zhu

    (University of Science and Technology of China)

  • An-Kuo Chao

    (National University of Singapore)

  • Shuaian Wang

    (Hong Kong Polytechnic University)

Abstract

In this paper, we study the performance of service systems with priority upgrades. We model the service system as a single-server two-class priority queue, with queue 1 as the normal queue and queue 2 as the priority queue. The queueing model of interest has various applications in healthcare services, perishable inventory and project management. We comprehensively examine the system’s stationary distribution, computational algorithm design and sensitivity analysis. We observe that when queue 2 is large, the conditional distribution of queue 1 approximates a Poisson distribution. The tail probability of queue 2 decays geometrically, while the tail probability of queue 1 decays much faster than queue 2’s. This helps us design an algorithm that computed the stationary distribution. Finally, by using the algorithm, we perform a sensitivity analysis on various system parameters, i.e., the arrival rates, service rates and the upgrade rate. The numerical study provides helpful insights into designing such service systems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2370-6
    DOI: 10.1007/s10479-016-2370-6
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    References listed on IDEAS

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    1. Wang, Qinan, 2004. "Modeling and analysis of high risk patient queues," European Journal of Operational Research, Elsevier, vol. 155(2), pages 502-515, June.
    2. Borga Deniz & Itir Karaesmen & Alan Scheller-Wolf, 2010. "Managing Perishables with Substitution: Inventory Issuance and Replenishment Heuristics," Manufacturing & Service Operations Management, INFORMS, vol. 12(2), pages 319-329, July.
    3. Ronald W. Wolff, 1982. "Poisson Arrivals See Time Averages," Operations Research, INFORMS, vol. 30(2), pages 223-231, April.
    4. Mustafa Akan & Oguzhan Alagoz & Baris Ata & Fatih Safa Erenay & Adnan Said, 2012. "A Broader View of Designing the Liver Allocation System," Operations Research, INFORMS, vol. 60(4), pages 757-770, August.
    5. Tuan Phung-Duc & Ken'Ichi Kawanishi, 2014. "An Efficient Method For Performance Analysis Of Blended Call Centers With Redial," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-33.
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    Citations

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    Cited by:

    1. 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.
    2. Yue Hu & Carri W. Chan & Jing Dong, 2022. "Optimal Scheduling of Proactive Service with Customer Deterioration and Improvement," Management Science, INFORMS, vol. 68(4), pages 2533-2578, April.
    3. Jia Xu & Liwei Liu, 2024. "Analysis of a Two-Stage Tandem Queuing System with Priority and Clearing Service in the Second Stage," Mathematics, MDPI, vol. 12(10), pages 1-23, May.
    4. Valentina Klimenok & Alexander Dudin & Olga Dudina & Irina Kochetkova, 2020. "Queuing System with Two Types of Customers and Dynamic Change of a Priority," Mathematics, MDPI, vol. 8(5), pages 1-25, May.

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