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Stationary analysis for the fluid model driven by the working vacation queue.

Authors :
Xu, Xiuli
Geng, Jie
Liu, Mingxin
Guo, Hongxia
Source :
Journal of Mathematical Analysis & Applications. Jul2013, Vol. 403 Issue 2, p423-433. 11p.
Publication Year :
2013

Abstract

Abstract: We first analyze a multi-server queue with working vacations. Using a quasi birth-and-death (QBD) process and a matrix-geometric solution method, the steady state distribution of the queue length is derived. Furthermore, a fluid flow model driven by this working vacation queue is discussed, we obtain the sets of differential equations satisfied by the stationary joint distribution of the buffer content, by which we gain the simple structure of the Laplace transform (LT) of the stationary distribution of the buffer content. Finally, we give the probability of empty buffer content and the mean of the buffer content based on the relationship between the LT and the Laplace–Stieltjes transform (LST) of the stationary distribution. [Copyright &y& Elsevier]

Details

Language :
English
ISSN :
0022247X
Volume :
403
Issue :
2
Database :
Academic Search Index
Journal :
Journal of Mathematical Analysis & Applications
Publication Type :
Academic Journal
Accession number :
88978454
Full Text :
https://doi.org/10.1016/j.jmaa.2013.02.021