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Queues with Service in Random Order

Author

Listed:
  • Grace M. Carter

    (The Rand Corporation, Santa Monica, California)

  • Robert B. Cooper

    (Georgia Institute of Technology, Atlanta, Georgia)

Abstract

We consider two models, the GI / M / s queue and the M / G /1 queue, in which waiting customers are served in random order. For each model we derive expressions for the calculation of the stationary waiting-time distribution function. Our methods differ from those of previous authors in that we do not use transforms, and consequently our results may be better suited for calculation. We illustrate our methods by deriving previously known results for the M / M / s and M / D /1 random-service queues, and by making sample calculations for the M / E k /1 random-service queue for various values of the utilization factor and the index k .

Suggested Citation

  • Grace M. Carter & Robert B. Cooper, 1972. "Queues with Service in Random Order," Operations Research, INFORMS, vol. 20(2), pages 389-405, April.
    • Handle: RePEc:inm:oropre:v:20:y:1972:i:2:p:389-405
    DOI: 10.1287/opre.20.2.389
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    Cited by:

    1. Souvik Ghosh & A. D. Banik, 2018. "Computing conditional sojourn time of a randomly chosen tagged customer in a $$\textit{BMAP/MSP/}1$$ BMAP / MSP / 1 queue under random order service discipline," Annals of Operations Research, Springer, vol. 261(1), pages 185-206, February.
    2. Jesus R. Artalejo & A. Gómez‐Corral, 2007. "Waiting time analysis of the M/G/1 queue with finite retrial group," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 524-529, August.
    3. Field, A. J. & Harrison, P. G., 1999. "Sojourn times in a random queue with and without preemption," European Journal of Operational Research, Elsevier, vol. 112(3), pages 646-653, February.

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