### Abstract

Original language | English |
---|---|

Pages (from-to) | 497-532 |

Journal | Probability and Mathematical Statistics |

Volume | 37 |

Issue number | 2 |

DOIs | |

Publication status | Published - 30 Dec 2017 |

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### Keywords

- Layered queueing network
- limited processor sharing
- fluid model
- diffusion approximation
- heavy traffic

### Cite this

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*Probability and Mathematical Statistics*, vol. 37, no. 2, pp. 497-532. https://doi.org/10.19195/0208-4147.37.2.15

**Heavy-traffic approximations for a layered network with limited resources.** / Aveklouris, A.; Vlasiou, M.; Zhang, J.; Zwart, A.P.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Heavy-traffic approximations for a layered network with limited resources

AU - Aveklouris, A.

AU - Vlasiou, M.

AU - Zhang, J.

AU - Zwart, A.P.

PY - 2017/12/30

Y1 - 2017/12/30

N2 - 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.

AB - 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.

KW - Layered queueing network

KW - limited processor sharing

KW - fluid model

KW - diffusion approximation

KW - heavy traffic

U2 - 10.19195/0208-4147.37.2.15

DO - 10.19195/0208-4147.37.2.15

M3 - Article

VL - 37

SP - 497

EP - 532

JO - Probability and Mathematical Statistics

JF - Probability and Mathematical Statistics

SN - 0208-4147

IS - 2

ER -