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

Yan Chen () and Ward Whitt ()
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Yan Chen: Columbia University
Ward Whitt: Columbia University

Queueing Systems: Theory and Applications, 2021, vol. 97, issue 1, No 5, 124 pages

Abstract: 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.

Keywords: GI/GI/1 queue; Tight bounds; Extremal queues; Bounds for the mean steady-state mean waiting time; Moment problem; 60K25; 65C50; 90B22 (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11134-020-09675-7

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