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

Dennis Schol; Maria Vlasiou; Bert Zwart

doi:10.1287/moor.2021.1171

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

Dennis Schol^*
, Maria Vlasiou
, Bert Zwart

^*Corresponding author for this work

Mathematics of Operations Research

Research output: Contribution to journal › Article › Academic › peer-review

7 Citations (Scopus)

132 Downloads (Pure)

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 language	English
Pages (from-to)	1335-1364
Number of pages	30
Journal	Mathematics of operations research
Volume	47
Issue number	2
Early online date	14 Dec 2021
DOIs	https://doi.org/10.1287/moor.2021.1171
Publication status	Published - 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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10.1287/moor.2021.1171

moor.2021.1171Final published version, 1.4 MBLicence: Taverne

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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.",

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

author = "Dennis Schol and Maria Vlasiou and Bert Zwart",

note = "Funding Information: Funding: This research is supported by the Netherlands Organization for Scientific Research through the programs Grip on Complexity (Schol) [Grant 438.16.121], MEERVOUD (Vlasiou) [Grant 632.003.002], and Talent VICI (Zwart) [Grant 639.033.413]. Publisher Copyright: Copyright: {\textcopyright} 2021 INFORMS.",

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KW - queueing network

KW - 22/3 OA procedure

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

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Keywords

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