A Restless Bandit Model for Energy-Efficient Job Assignments in Server Farms

We aim to maximize the energy efficiency, gauged as average energy cost per job, in a large-scale server farm with various storage or/and computing components modeled as parallel abstracted servers. Each server operates in multiple power modes characterized by potentially different service and energy consumption rates. The heterogeneity of servers and multiple power modes complicate the maximization problem, where optimal solutions are generally intractable. Relying on the Whittle relaxation technique, we resort to a near-optimal, scalable job-assignment policy. Under a mild condition related to the service and energy consumption rates of the servers, we prove that our proposed policy approaches optimality as the size of the entire system tends to infinity; that is, it is asymptotically optimal. For the nonasymptotic regime, we show the effectiveness of the proposed policy through numerical simulations, where the policy outperforms all the tested baselines, and we numerically demonstrate its robustness against heavy-tailed job-size distributions.