@article{a4b2c53b000346d7aaf46fd65a3b1212,
title = "Large fork-join networks with nearly deterministic service times",
abstract = "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. ",
keywords = "math.PR, cs.PF",
author = "Dennis Schol and Maria Vlasiou and Bert Zwart",
year = "2019",
month = dec,
day = "25",
doi = "10.48550/arXiv.1912.11661",
language = "English",
volume = "2019",
journal = "arXiv",
issn = "2331-8422",
publisher = "Cornell University Library",
}