Mean Field Approximations to a Queueing System with Threshold-Based Workload Control Scheme

TL;DR

This paper models a cloud computing queueing system with threshold-based workload control, using mean field approximations to analyze performance and energy efficiency, supported by numerical and simulation validation.

Contribution

It introduces a mean field approximation approach for analyzing a threshold-based workload control in queueing systems, providing iterative solutions and performance insights.

Findings

Mean field approximations effectively model system performance.

System parameters significantly influence energy and utilization metrics.

Numerical and simulation results validate the approximation method.

Abstract

In this paper, motivated by considerations of server utilization and energy consumptions in cloud computing, we investigate a homogeneous queueing system with a threshold-based workload control scheme. In this system, a virtual machine will be turned off when there are no tasks in its buffer upon the completion of a service by the machine, and turned on when the number of tasks in its buffer reaches a pre-set threshold value. Due to complexity of this system, we propose approximations to system performance measures by mean field limits. An iterative algorithm is suggested for the solution to the mean field limit equations. In addition, numerical and simulation results are presented to justify the proposed approximation method and to provide a numerical analysis on the impact of the system performances by system parameters.