Large Fork-Join Queues with Nearly Deterministic Arrival and Service Times

Dennis Schol*, Maria Vlasiou, Bert Zwart

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

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Abstract

In this paper, we study an N server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as N → ∞. This fluid limit depends on the initial number of tasks. In order to prove these results, we develop extreme value theory and diffusion approximations for the queue lengths.

Original languageEnglish
Pages (from-to)1335-1364
Number of pages30
JournalMathematics of operations research
Volume47
Issue number2
Early online date14 Dec 2021
DOIs
Publication statusPublished - May 2022

Keywords

  • extreme value theory
  • fluid limit
  • fork-join queue
  • heavy traffic
  • nearly deterministic
  • queueing network
  • 22/3 OA procedure

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