Fluid queue driven by a multi-server queue with multiple vacations and vacation interruption

School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, P.R. China.
yusenlin@csu.edu.cn; mathlzm@csu.edu.cn; wujinbiao@csu.edu

Received: 25 April 2016
Accepted: 24 December 2016

Abstract

This paper studies a fluid queue driven by a multi-server queue with multiple working vacations and vacation interruption. The stationary distribution of the background environment is obtained after some manipulation. A system of differential equations satisfied by the fluid queue is presented, by which we gain the matrix-geometric structure of the Laplace transform of the stationary buffer content. Furthermore, we derive the explicit expression of the mean buffer content. Finally, the numerical example is employed to illustrate our results.