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Extremal GI/GI/1 queues given two moments: exploiting Tchebycheff systems

Author

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  • Yan Chen

    (Columbia University)

  • Ward Whitt

    (Columbia University)

Abstract

This paper studies tight upper bounds for the mean and higher moments of the steady-state waiting time in the GI/GI/1 queue given the first two moments of the interarrival-time and service-time distributions. We apply the theory of Tchebycheff systems to obtain sufficient conditions for classical two-point distributions to yield the extreme values. These distributions are determined by having one mass at 0 or at the upper limit of support.

Suggested Citation

  • Yan Chen & Ward Whitt, 2021. "Extremal GI/GI/1 queues given two moments: exploiting Tchebycheff systems," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 101-124, February.
    • Handle: RePEc:spr:queues:v:97:y:2021:i:1:d:10.1007_s11134-020-09675-7
    DOI: 10.1007/s11134-020-09675-7
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    References listed on IDEAS

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    1. Teunis J. Ott, 1987. "Simple Inequalities for the D / G /1 Queue," Operations Research, INFORMS, vol. 35(4), pages 589-597, August.
    2. A. E. Eckberg, 1977. "Sharp Bounds on Laplace-Stieltjes Transforms, with Applications to Various Queueing Problems," Mathematics of Operations Research, INFORMS, vol. 2(2), pages 135-142, May.
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    Cited by:

    1. Wouter Eekelen & Johan S. H. Leeuwaarden, 2022. "Distributionally robust views on extremal queues," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 485-487, April.

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