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Queues with correlated inter-arrival and service times

Author

Listed:
  • Qixin Wang

    (Fudan University)

  • Jian-Qiang Hu

    (Fudan University)

Abstract

We study a type of correlated queue in which its inter-arrival and service times are correlated, with their joint distribution being characterized by a copula function. This characterization allows for very generally correlated inter-arrival and service times. For such a queue, we first derive an infinite system of linear equations for the moments of the waiting time, based on which we design an algorithm to calculate the moments of the waiting time. In contrast with traditional methods, our algorithm incorporates a recursive procedure which is computationally much more efficient. Furthermore, we show how the moments and covariances of the inter-departure times of the queue can be obtained based on the moments of the waiting time. Numerical experiments are provided to validate our method.

Suggested Citation

  • Qixin Wang & Jian-Qiang Hu, 2024. "Queues with correlated inter-arrival and service times," Queueing Systems: Theory and Applications, Springer, vol. 108(1), pages 1-30, October.
    • Handle: RePEc:spr:queues:v:108:y:2024:i:1:d:10.1007_s11134-024-09913-2
    DOI: 10.1007/s11134-024-09913-2
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    References listed on IDEAS

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    1. Weimin Dai & Jian-Qiang Hu, 2022. "Correlated queues with service times depending on inter-arrival times," Queueing Systems: Theory and Applications, Springer, vol. 100(1), pages 41-60, February.
    2. B. W. Conolly, 1968. "The Waiting Time Process for a Certain Correlated Queue," Operations Research, INFORMS, vol. 16(5), pages 1006-1015, October.
    3. Lei Lei & Jian-Qiang Hu & Chenbo Zhu, 2022. "Discrete-event stochastic systems with copula correlated input processes," IISE Transactions, Taylor & Francis Journals, vol. 54(4), pages 321-331, April.
    4. B. W. Conolly & N. Hadidi, 1969. "A Comparison of the Operational Features of Conventional Queues with a Self‐Regulating System," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 18(1), pages 41-53, March.
    5. Nasser Hadidi, 1985. "Further Results on Queues with Partial Correlation," Operations Research, INFORMS, vol. 33(1), pages 203-209, February.
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