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

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.

Analysis of Vacation Fluid M/M/1 Queue in Multi-Phase Random Environment

“…They achieved this by creating an explicit equation for buffer content distribution using the Laplace transform and generating function approaches, based on the modified Bessel function of the first type. In [19], the authors illustrated a fluid queue controlled by a multi-server queue featuring working vacations and vacation interruptions. Using the matrix geometric structure of the Laplace transform, they calculated the steady-state distribution of fluid buffer queue mean.…”