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Correlated queues with service times depending on inter-arrival times

Author

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  • Weimin Dai

    (Fudan University)

  • Jian-Qiang Hu

    (Fudan University)

Abstract

We consider a type of correlated queue in which the service time of a customer depends on the inter-arrival time between him and the previous customer. We first derive an infinite system of linear equations for the moments of the system time, based on which we then develop several methods to calculate the moments of the system time by using MacLaurin series expansion and Padé approximation. In addition, we show how the moments and covariances of the inter-departure times of the correlated queue can be calculated based on the moments of the system time. Finally, numerical examples are provided to validate our methods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:queues:v:100:y:2022:i:1:d:10.1007_s11134-021-09718-7
    DOI: 10.1007/s11134-021-09718-7
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    References listed on IDEAS

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    1. Jian-Qiang Hu, 1996. "The Departure Process of the GI / G /1 Queue and Its MacLaurin Series," Operations Research, INFORMS, vol. 44(5), pages 810-815, October.
    2. Shun‐Chen Niu, 1981. "On queues with dependent interarrival and service times," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(3), pages 497-501, September.
    3. Vlasiou, M. & Adan, I.J.B.F. & Boxma, O.J., 2009. "A two-station queue with dependent preparation and service times," European Journal of Operational Research, Elsevier, vol. 195(1), pages 104-116, May.
    4. B. W. Conolly, 1968. "The Waiting Time Process for a Certain Correlated Queue," Operations Research, INFORMS, vol. 16(5), pages 1006-1015, October.
    5. Civelek, Ismail & Biller, Bahar & Scheller-Wolf, Alan, 2021. "Impact of dependence on single-server queueing systems," European Journal of Operational Research, Elsevier, vol. 290(3), pages 1031-1045.
    6. 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.
    7. Nasser Hadidi, 1985. "Further Results on Queues with Partial Correlation," Operations Research, INFORMS, vol. 33(1), pages 203-209, February.
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    Cited by:

    1. 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.
    2. Sindhu S & Achyutha Krishnamoorthy & Dmitry Kozyrev, 2023. "A Two-Server Queue with Interdependence between Arrival and Service Processes," Mathematics, MDPI, vol. 11(22), pages 1-25, November.

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