  We study a job-assignment problem in a large-scale server farm system with
geographically deployed servers as abstracted computer components (e.g.,
storage, network links, and processors) that are potentially diverse. We aim to
maximize the energy efficiency of the entire system by effectively controlling
carried load on networked servers. A scalable, near-optimal job-assignment
policy is proposed. The optimality is gauged as, roughly speaking, energy cost
per job. Our key result is an upper bound on the deviation between the proposed
policy and the asymptotically optimal energy efficiency, when job sizes are
exponentially distributed and blocking probabilities are positive. Relying on
Whittle relaxation and the asymptotic optimality theorem of Weber and Weiss,
this bound is shown to decrease exponentially as the number of servers and the
arrival rates of jobs increase arbitrarily and in proportion. In consequence,
the proposed policy is asymptotically optimal and, more importantly, approaches
asymptotic optimality quickly (exponentially). This suggests that the proposed
policy is close to optimal even for relatively small systems (and indeed any
larger systems), and this is consistent with the results of our simulations.
Simulations indicate that the policy is effective, and robust to variations in
job-size distributions.
