Fluid model driven by an M/M/1 queue with multiple exponential vacations

This paper studies a fluid model driven by an M/M/1 queue with multiple exponential vacations. 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 is obtained. Finally, using some numerical examples, we present the parameter effect on the mean buffer content.