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

Mihail Bazhba, Jose Blanchet, Chang Han Rhee, Bert Zwart*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 languageEnglish (US)
Pages (from-to)195-226
Number of pages32
JournalQueueing Systems
Volume93
Issue number3-4
DOIs
StatePublished - 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

Fingerprint

Dive into the research topics of 'Queue length asymptotics for the multiple-server queue with heavy-tailed Weibull service times'. Together they form a unique fingerprint.

Cite this