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.
Original language | English (US) |
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Pages (from-to) | 195-226 |
Number of pages | 32 |
Journal | Queueing Systems |
Volume | 93 |
Issue number | 3-4 |
DOIs | |
State | Published - Dec 1 2019 |
Keywords
- Heavy tails
- Multiple-server queue
- Queue length asymptotics
- Weibull service times
ASJC Scopus subject areas
- Statistics and Probability
- Computer Science Applications
- Management Science and Operations Research
- Computational Theory and Mathematics