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

Dennis Schol (), Maria Vlasiou () and Bert Zwart ()
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Dennis Schol: Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands
Maria Vlasiou: Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands; University of Twente, 7522 NB Enschede, Netherlands
Bert Zwart: Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands; Centrum Wiskunde & Informatica, 1098 XG Amsterdam, Netherlands

Mathematics of Operations Research, 2022, vol. 47, issue 2, 1335-1364

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: Primary: 60K25; heavy traffic; fluid limit; extreme value theory; queueing network; fork-join queue; nearly deterministic (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormoor:v:47:y:2022:i:2:p:1335-1364

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