  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.
