In this paper, we consider a three-dimensional Brownian-driven tandem queue with intermediate inputs, which corresponds to a three-dimensional semimartingale reflecting Brownian motion whose reflection matrix is triangular. For this three-node tandem queue, no closed form formula is known, not only for its stationary distribution but also for the corresponding transform. We are interested in exact tail asymptotics for stationary distributions. By generalizing the kernel method, and using extreme value theory and copula, we obtain exact tail asymptotics for the marginal stationary distribution of the buffer content in the third buffer and for the joint stationary distribution.
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DOI : 10.1051/ps/2021018
Keywords: Brownian-driven tandem queue, stationary distribution, exact tail asymptotics, kernel method, extreme value theory
@article{PS_2022__26_1_26_0,
author = {Dai, Hongshuai and Dawson, Donald A. and Zhao, Yiqiang Q.},
title = {Exact tail asymptotics for a three-dimensional {Brownian-driven} tandem queue with intermediate inputs},
journal = {ESAIM: Probability and Statistics},
pages = {26--68},
year = {2022},
publisher = {EDP-Sciences},
volume = {26},
doi = {10.1051/ps/2021018},
mrnumber = {4363454},
zbl = {1495.60081},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2021018/}
}
TY - JOUR AU - Dai, Hongshuai AU - Dawson, Donald A. AU - Zhao, Yiqiang Q. TI - Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs JO - ESAIM: Probability and Statistics PY - 2022 SP - 26 EP - 68 VL - 26 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ps/2021018/ DO - 10.1051/ps/2021018 LA - en ID - PS_2022__26_1_26_0 ER -
%0 Journal Article %A Dai, Hongshuai %A Dawson, Donald A. %A Zhao, Yiqiang Q. %T Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs %J ESAIM: Probability and Statistics %D 2022 %P 26-68 %V 26 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ps/2021018/ %R 10.1051/ps/2021018 %G en %F PS_2022__26_1_26_0
Dai, Hongshuai; Dawson, Donald A.; Zhao, Yiqiang Q. Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs. ESAIM: Probability and Statistics, Tome 26 (2022), pp. 26-68. doi: 10.1051/ps/2021018
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