Large fork-join networks with nearly deterministic service times

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In this paper, we study an $N$ server fork-join queueing network with nearly deterministic arrivals and service times. Specifically, we aim to approximate the length of the largest of the $N$ queues in the network. From a practical point of view, this has interesting applications, such as modeling the delays in a large supply chain. We present a fluid limit and a steady-state result for the maximum queue length, as $N\to\infty$. These results have remarkable differences. The steady-state result depends on two model parameters, while the fluid limit only depends on one model parameter. In addition, the fluid limit requires a different spatial scaling than the backlog in steady state. In order to prove these results, we use extreme value theory and diffusion approximations for the queue lengths.
Original languageEnglish
Article numberarXiv 1912.11661v1
Number of pages36, e-Print Archive, Mathematics
Publication statusPublished - 25 Dec 2019


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