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In this paper, we study an $N$ server fork-join queue with nearlydeterministic arrival and service times. Specifically, we present a fluid limitfor the maximum queue length as $N\to\infty$. This fluid limit depends on theinitial number of tasks. In order to prove these results, we develop extremevalue theory and diffusion approximations for the queue lengths.

Large fork-join queues with nearly deterministic arrival and service times