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Technical Note—Delays in Single-Server Queues with Batch Input

Author

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  • P. J. Burke

    (Bell Laboratories, Holmdel, New Jersey)

Abstract

Standard works on queuing theory are in error in the calculation of the equilibrium delay distribution—and even of the average delay—in a single-server system with batch input, when the batches are not of constant size. This paper corrects the error, which occurs in connection with that portion of the delay of a customer due to the service times of other members of the same batch.

Suggested Citation

  • P. J. Burke, 1975. "Technical Note—Delays in Single-Server Queues with Batch Input," Operations Research, INFORMS, vol. 23(4), pages 830-833, August.
    • Handle: RePEc:inm:oropre:v:23:y:1975:i:4:p:830-833
    DOI: 10.1287/opre.23.4.830
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    Cited by:

    1. Tuan Phung-Duc, 2017. "Exact solutions for M/M/c/Setup queues," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 64(2), pages 309-324, February.
    2. Mohan L. Chaudhry & James J. Kim, 2016. "Analytically elegant and computationally efficient results in terms of roots for the $$GI^{X}/M/c$$ G I X / M / c queueing system," Queueing Systems: Theory and Applications, Springer, vol. 82(1), pages 237-257, February.
    3. Miaomiao Yu & Yinghui Tang, 2022. "Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method," Operational Research, Springer, vol. 22(3), pages 2831-2858, July.
    4. Justus Arne Schwarz & Martin Epp, 2016. "Performance evaluation of a transportation-type bulk queue with generally distributed inter-arrival times," International Journal of Production Research, Taylor & Francis Journals, vol. 54(20), pages 6251-6264, October.

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