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In “A Restless Bandit Model for Resource Allocation, Competition and Reservation,” J. Fu, B. Moran, and P. G. Taylor study a resource allocation problem with varying requests and with resources of limited capacity shared by multiple requests. This problem is modeled as a set of heterogeneous restless multi-armed bandit problems (RMABPs) connected by constraints imposed by resource capacity. Following Whittle’s idea of relaxing the constraints and Weber and Weiss’s proof of asymptotic optimality, the authors propose an index policy and establish conditions for it to be asymptotically optimal in a regime where both arrival rates and capacities increase. In particular, they provide a simple sufficient condition for asymptotic optimality of the policy and, in complete generality, propose a method that generates a set of candidate policies for which asymptotic optimality can be checked. Via numerical experiments, they demonstrate the effectiveness of these results even in the pre-limit case.

We study a job-assignment problem in a largescale 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 jobassignment 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.Index Terms-server farm, energy efficiency, restless multiarmed bandit problem.

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