# Output stream analysis in a queueing model with working vacation mechanism as a power reduction strategy

## TL;DR

This paper studies how a queueing system behaves when it uses a working vacation strategy to reduce power consumption.

## Contribution

The paper provides an explicit solution for the Laplace transform of the generating function of the departure process in a queueing model with working vacations.

## Key findings

- The time-dependent mean number of jobs served was computed using numerical Laplace transform inversion.
- Numerical examples show how the output stream depends on parameters like interarrival distribution and vacation duration.
- The model accounts for finite buffer and different workload modes.

## Abstract

The aim of this paper is to analyze the departure process of a queueing model with general independent input stream, exponentially distributed service time, finite buffer and working vacation mechanism. The explicit solution for a Laplace transform of generating function of this characteristic is determined. Utilizing numerical Laplace transform inversion, the time-dependent mean number of jobs served in a time interval is computed. The numerical examples show the behavior of the output stream in dependence on the model parameters, such as interarrival distribution, mean working vacation period duration, the workload in normal and in working vacation mode.