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→∞. 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.
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