Abstract
In this paper, we study an $N$ server forkjoin 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 steadystate result for the maximum queue length, as $N\to\infty$. These results have remarkable differences. The steadystate 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 language  English 

Article number  arXiv 1912.11661v1 
Number of pages  36 
Journal  arXiv.org, ePrint Archive, Mathematics 
Publication status  Published  25 Dec 2019 
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Stochactic processes on interacting networks
Maria Vlasiou (Content manager)
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