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

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A Correction to this article was published on 16 April 2022

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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.

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Acknowledgements

This research was supported by NSF CMMI 1634133. We thank Tomasz Rolski and an anonymous referee for exposing a gap in our first proof of Theorem 1.

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  1. Industrial Engineering and Operations Research, Columbia University, New York, USA

    Yan Chen & Ward Whitt

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  1. Yan Chen
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  2. Ward Whitt
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Correspondence to Ward Whitt.

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Chen, Y., Whitt, W. Extremal GI/GI/1 queues given two moments: exploiting Tchebycheff systems. Queueing Syst 97, 101–124 (2021). https://doi.org/10.1007/s11134-020-09675-7

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  • DOI: https://doi.org/10.1007/s11134-020-09675-7

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