Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times

Mihail Bazhba (), Jose Blanchet (), Chang-Han Rhee () and Bert Zwart ()
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Mihail Bazhba: Centrum Wiskunde & Informatica
Jose Blanchet: Stanford University 475 Via Ortega
Chang-Han Rhee: Northwestern University
Bert Zwart: Centrum Wiskunde & Informatica

Queueing Systems: Theory and Applications, 2019, vol. 93, issue 3, No 2, 195-226

Abstract: Abstract We study the occurrence of large queue lengths in the GI / GI / d queue with heavy-tailed Weibull-type service times. Our analysis hinges on a recently developed sample path large-deviations principle for Lévy processes and random walks, following a continuous mapping approach. Also, we identify and solve a key variational problem which provides physical insight into the way a large queue length occurs. In contrast to the regularly varying case, we observe several subtle features such as a non-trivial trade-off between the number of big jobs and their sizes and a surprising asymmetric structure in asymptotic job sizes leading to congestion.

Keywords: Multiple-server queue; Queue length asymptotics; Heavy tails; Weibull service times; 60K25; 68M20 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11134-019-09640-z

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