Exact Tail Asymptotics of a Tandem Queue with LRD Service Times

2013 ◽  
Vol 196 (1) ◽  
pp. 102-114
Author(s):  
A. Villani
Keyword(s):  
Tail Asymptotics ◽  
Tandem Queue ◽  
Exact Tail Asymptotics ◽  
Service Times

scholarly journals Exact tail asymptotics for a three-dimensional Brownian-driven tandem queue with intermediate inputs

2021 ◽  
Author(s):  
Hongshuai Dai ◽  
Donald A. Dawson ◽  
Yiqiang Q. Zhao
Keyword(s):  
Stationary Distribution ◽  
Kernel Method ◽  
Three Dimensional ◽  
Value Theory ◽  
Tail Asymptotics ◽  
Tandem Queue ◽  
Intermediate Inputs ◽  
Exact Tail Asymptotics ◽  
Reflection Matrix ◽  
Joint Stationary Distribution

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.

scholarly journals The Saddle Point Method for the Integral of the Absolute Value of the Brownian Motion

2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Leonid Tolmatz
Keyword(s):  
Distribution Function ◽  
Brownian Motion ◽  
Saddle Point ◽  
Point Method ◽  
Saddle Point Method ◽  
Tail Asymptotics ◽  
Absolute Value ◽  
Exact Tail Asymptotics ◽  
International Audience ◽  
The Absolute

International audience The distribution function of the integral of the absolute value of the Brownian motion was expressed by L.Takács in the form of various series. In the present paper we determine the exact tail asymptotics of this distribution function. The proposed method is applicable to a variety of other Wiener functionals as well.

Exact tail asymptotics for a two-stage queue: Complete solution via kernel method

2017 ◽  
Vol 51 (4) ◽  
pp. 1211-1250
Author(s):  
Hongshuai Dai ◽  
Lingtao Kong ◽  
Yang Song
Keyword(s):  
Kernel Method ◽  
Complete Solution ◽  
Tail Asymptotics ◽  
Two Stage ◽  
Exact Tail Asymptotics

Stationary tail asymptotics of a tandem queue with feedback

2007 ◽  
Vol 160 (1) ◽  
pp. 173-189 ◽  
Author(s):  
Jiashan Tang ◽  
Yiqiang Q. Zhao
Keyword(s):  
Tail Asymptotics ◽  
Tandem Queue

scholarly journals Exact tail asymptotics for fluid models driven by an M/M/c queue

2019 ◽  
Vol 91 (3-4) ◽  
pp. 319-346 ◽  
Author(s):  
Wendi Li ◽  
Yuanyuan Liu ◽  
Yiqiang Q. Zhao
Keyword(s):  
Fluid Models ◽  
Tail Asymptotics ◽  
Exact Tail Asymptotics
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