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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Dennis Schol & Maria Vlasiou & Bert Zwart, 2022. "Large Fork-Join Queues with Nearly Deterministic Arrival and Service Times," Mathematics of Operations Research, INFORMS, vol. 47(2), pages 1335-1364, May.
    • Handle: RePEc:inm:ormoor:v:47:y:2022:i:2:p:1335-1364
    DOI: 10.1287/moor.2021.1171
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