Mean field approximations to a queueing system with threshold-based workload control scheme

Qihui Bu, Liwei Liu and Yiqiang Q. Zhao

Communications in Statistics - Theory and Methods, 2023, vol. 52, issue 11, 3960-3981

Abstract: In this paper, motivated by considerations of server utilization and energy consumption 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, which suggests that the proposed system saves about (1−λμ)×100% of the energy consumption compared to the ordinary supermarket models.

Date: 2023
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DOI: 10.1080/03610926.2021.1983601

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