### 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.

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 -