Volume 26, 2022
|Page(s)||26 - 68|
|Published online||13 January 2022|
Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs
School of Statistics, Shandong University of Finance and Economics,
250014, P.R. China.
2 School of Mathematics and Statistics, Carleton University, Ottawa, ON, Canada K1S 5B6.
* Corresponding author: firstname.lastname@example.org
Accepted: 17 December 2021
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.
Mathematics Subject Classification: 60K25
Key words: Brownian-driven tandem queue / stationary distribution / exact tail asymptotics / kernel method / extreme value theory
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.