Abstract
| Original language | English |
|---|---|
| Article number | arXiv 1912.11661v1 |
| Number of pages | 36 |
| Journal | arXiv.org,e-Print Archive, Mathematics |
| Publication status | Published - 25 Dec 2019 |
Fingerprint
Cite this
}
Large fork-join networks with nearly deterministic service times. / Schol, Dennis; Vlasiou, Maria; Zwart, Bert.
In: arXiv.org,e-Print Archive, Mathematics, 25.12.2019.Research output: Contribution to journal › Article › Academic
TY - JOUR
T1 - Large fork-join networks with nearly deterministic service times
AU - Schol, Dennis
AU - Vlasiou, Maria
AU - Zwart, Bert
PY - 2019/12/25
Y1 - 2019/12/25
N2 - 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.
AB - 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.
KW - math.PR
KW - cs.PF
M3 - Article
JO - arXiv.org,e-Print Archive, Mathematics
JF - arXiv.org,e-Print Archive, Mathematics
M1 - arXiv 1912.11661v1
ER -