Fluid Model Driven by an M/M/1 Queue with Exponential Vacation

Abstract

This paper studies a fluid model driven by an M/M/1 queue with single exponential vacation. The Laplace transform of the steady-state distribution of the buffer content is expressed through the minimal positive solution to a crucial quadratic equation. Then the performance measure—mean buffer content which is independent of the vacation parameter, is obtained. Finally, using some numerical examples, we present the parameter effect on the mean buffer content.