### Samenvatting

Motivated by a web-server model, we present a queueing network consisting of two layers. The first layer incorporates the arrival of customers at a network of two single-server nodes. We assume that the inter-arrival and the service times have general distributions. Customers are served according to their arrival order at each node and after finishing their service they can re-enter at nodes several times (as new customers) for new services. At the second layer, active servers act as jobs which are served by a single server working at speed one in a Processor-Sharing fashion. We further assume that the degree of resource sharing is limited by choice, leading to a Limited Processor-Sharing discipline. Our main result is a diffusion approximation for the process describing the number of customers in the system. Assuming a single bottleneck node and studying the system as it approaches heavy traffic, we prove a state-space collapse property. The key to derive this property is to study the model at the second layer and to prove a diffusion limit theorem, which yields an explicit approximation for the customers in the system.

Originele taal-2 | Engels |
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Pagina's (van-tot) | 497-532 |

Aantal pagina's | 36 |

Tijdschrift | Probability and Mathematical Statistics |

Volume | 37 |

Nummer van het tijdschrift | 2 |

DOI's | |

Status | Gepubliceerd - 30 dec 2017 |

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## Citeer dit

Aveklouris, A., Vlasiou, M., Zhang, J., & Zwart, A. P. (2017). Heavy-traffic approximations for a layered network with limited resources.

*Probability and Mathematical Statistics*,*37*(2), 497-532. https://doi.org/10.19195/0208-4147.37.2.15