Extremal GI/GI/1 queues given two moments: exploiting Tchebycheff systems.
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| Title: | Extremal GI/GI/1 queues given two moments: exploiting Tchebycheff systems. |
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| Authors: | Chen, Yan1 (AUTHOR), Whitt, Ward1 (AUTHOR) ww2040@columbia.edu |
| Source: | Queueing Systems. Feb2021, Vol. 97 Issue 1/2, p101-124. 24p. |
| Subjects: | Chebyshev systems, Distribution (Probability theory), Classical conditioning, Extreme value theory, Systems theory |
| 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. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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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. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 02570130 |
| DOI: | 10.1007/s11134-020-09675-7 |
