On the control of power consumption in server farms via heavy traffic approximation

In this paper, we investigate optimal power management in parallel processing systems composed of one queue and several identical processing stations. Power consumption is controlled by putting some of the stations into an inactive state, where they consume less power but are unable to provide service. This way, we are faced with the conflicting objective of minimizing power consumption while maintaining a desired quality of service. The approach taken in this paper is to construct a diffusion model of the system. It is shown that, under limiting conditions, the system can be approximated by a reflected Brownian motion with a Markov jump drift parameter. The optimization problem is set as a stochastic optimal control problem and it is solved via the Markov chain approximation method. Some numerical data is also presented.