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Waiting Time Distributions in the Preemptive Accumulating Priority Queue

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  • Val Andrei Fajardo

    (University of Waterloo)

  • Steve Drekic

    (University of Waterloo)

Abstract

We consider a queueing system in which a single server attends to N priority classes of customers. Upon arrival to the system, a customer begins to accumulate priority linearly at a rate which is distinct to the class to which it belongs. Customers with greater accumulated priority levels are given preferential treatment in the sense that at every service selection instant, the customer with the greatest accumulated priority level is selected next for servicing. Furthermore, the system is preemptive so that the servicing of a customer is interrupted for customers with greater accumulated priority levels. The main objective of the paper is to characterize the waiting time distributions of each class. Numerical examples are also provided which exemplify the true benefit of incorporating an accumulating prioritization structure, namely the ability to control waiting times.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:19:y:2017:i:1:d:10.1007_s11009-015-9476-1
    DOI: 10.1007/s11009-015-9476-1
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    References listed on IDEAS

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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. Na Li & David A. Stanford & Peter Taylor & Ilze Ziedins, 2017. "Nonlinear Accumulating Priority Queues with Equivalent Linear Proxies," Operations Research, INFORMS, vol. 65(6), pages 1712-1721, December.
    3. 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.
    4. Chen, Wanying & Wu, Peng & Gong, Yeming & Zhang, Zhengmin & Wang, Kun, 2025. "The role of energy consumption in robotic mobile fulfillment systems: Performance evaluation and operating policies with dynamic priority," Omega, Elsevier, vol. 130(C).
    5. Raina Raj & Vidyottama Jain, 2023. "Resource optimization in $$\textit{MMAP[2]/PH[2]/S}$$ MMAP [ 2 ] / PH [ 2 ] / S priority queueing model with threshold $$\textit{PH}$$ PH retrial times and the preemptive resume policy," Annals of Operations Research, Springer, vol. 331(2), pages 1119-1148, December.
    6. 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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