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The Waiting Time Process for a Certain Correlated Queue

Author

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  • B. W. Conolly

    (Virginia Polytechnic Institute, Blacksburg, Virginia)

Abstract

A brief description is given of a problem that arose in a nonqueuing context but that can be interpreted in queuing terms. The result is the unusual single-server system in which the length of a customer's service is determined by the length of the interarrival interval separating himself and his predecessor. The main result is the distribution of waiting time, and its moments. It is shown numerically that this pattern of server behavior results in a drastic reduction of the mean and variance of the waiting time as compared with a conventional M/M/l system.

Suggested Citation

  • B. W. Conolly, 1968. "The Waiting Time Process for a Certain Correlated Queue," Operations Research, INFORMS, vol. 16(5), pages 1006-1015, October.
    • Handle: RePEc:inm:oropre:v:16:y:1968:i:5:p:1006-1015
    DOI: 10.1287/opre.16.5.1006
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Peter Buchholz & Jan Kriege, 2017. "Fitting correlated arrival and service times and related queueing performance," Queueing Systems: Theory and Applications, Springer, vol. 85(3), pages 337-359, April.

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