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- Title
Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times.
- Authors
Bazhba, Mihail; Blanchet, Jose; Rhee, Chang-Han; Zwart, Bert
- 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.
- Subjects
LEVY processes; RANDOM walks; STOCHASTIC processes
- Publication
Queueing Systems, 2019, Vol 93, Issue 3/4, p195
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-019-09640-z