Asymptotically Optimal Job Assignment for Energy-Efficient Processor-Sharing Server Farms

We study the problem of job assignment in a large-scale realistically dimensioned server farm comprising multiple processor-sharing servers with different service rates, energy consumption rates, and buffer sizes. Our aim is to optimize the energy efficiency of such a server farm by effectively controlling carried load on networked servers. To this end, we propose a job assignment policy, called Most energy-efficient available server first Accounting for Idle Power (MAIP), which is both scalable and near optimal. MAIP focuses on reducing the productive power used to support the processing service rate. Using the framework of semi-Markov decision process, we show that, with exponentially distributed job sizes, MAIP is equivalent to the well-known Whittle's index policy. This equivalence and the methodology of Weber and Weiss enable us to prove that, in server farms where a loss of jobs happens if and only if all buffers are full, MAIP is asymptotically optimal, as the number of servers tends to infinity under certain conditions associated with the large number of servers, as we have in a real server farm. Through extensive numerical simulations, we demonstrate the effectiveness of MAIP and its robustness to different job-size distributions, and observe that significant improvement in energy efficiency can be achieved by utilizing the knowledge of energy consumption rate of idle servers.