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In this paper, motivated by considerations of server utilization and energyconsumptions in cloud computing, we investigate a homogeneous queueing systemwith a threshold-based workload control scheme. In this system, a virtualmachine will be turned off when there are no tasks in its buffer upon thecompletion of a service by the machine, and turned on when the number of tasksin its buffer reaches a pre-set threshold value. Due to complexity of thissystem, we propose approximations to system performance measures by mean fieldlimits. An iterative algorithm is suggested for the solution to the mean fieldlimit equations. In addition, numerical and simulation results are presented tojustify the proposed approximation method and to provide a numerical analysison the impact of the system performances by system parameters.

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