Brazilian Journal of Probability and Statistics

A Jackson network under general regime

Yair Y. Shaki

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Abstract

We consider a Jackson network in a general heavy traffic diffusion regime with the $\alpha$-parametrization. We also assume that each customer may abandon the system while waiting. We show that in this regime the queue-length process converges to a multi-dimensional regulated Ornstein–Uhlenbeck process.

Article information

Source
Braz. J. Probab. Stat., Volume 33, Number 3 (2019), 532-548.

Dates
Received: May 2017
Accepted: May 2018
First available in Project Euclid: 10 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1560153851

Digital Object Identifier
doi:10.1214/18-BJPS401

Mathematical Reviews number (MathSciNet)
MR3960275

Zentralblatt MATH identifier
07094816

Keywords
Jackson network diffusion limits many-server queue heavy traffic conventional diffusion regime Halfin–Whitt regime

Citation

Shaki, Yair Y. A Jackson network under general regime. Braz. J. Probab. Stat. 33 (2019), no. 3, 532--548. doi:10.1214/18-BJPS401. https://projecteuclid.org/euclid.bjps/1560153851


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