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Large fork-join queues with nearly deterministic arrival and service times (1912.11661v3)
Published 25 Dec 2019 in math.PR and cs.PF
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 $N\to\infty$. 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.
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