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In this paper, we develop optimal sleep/wake scheduling algorithms for smart mobile devices that are powered by batteries and are capable of harvesting energy from the environment. Using a novel combination of the two-timescale Lyapunov optimization approach and weight perturbation, we first design the Optimal Sleep/wake scheduling Algorithm (OSA), which does not require any knowledge of the harvestable energy process. We prove that OSA is able to achieve any system performance that is within $O(\epsilon)$ of the optimal, and explicitly compute the required battery size, which is $O(1/\epsilon)$ . We then extend our results to incorporate system information into algorithm design. Specifically, we develop the Information-aided OSA algorithm (IOSA) by introducing a novel drift augmenting idea in Lyapunov optimization. We show that IOSA is able to achieve the $O(\epsilon)$ close-to-optimal utility performance and ensures that the required traffic buffer and energy storage size are $O(\log (1/\epsilon)^2)$ with high probability. [ABSTRACT FROM AUTHOR]

This paper considers a stochastic optimization approach for job scheduling and server management in large-scale, geographically distributed data centers. Randomly arriving jobs are routed to a choice of servers. The number of active servers depends on server activation decisions that are updated at a slow time scale, and the service rates of the servers are controlled by power scaling decisions that are made at a faster time scale. We develop a two-time-scale decision strategy that offers provable power cost and delay guarantees. The performance and robustness of the approach is illustrated through simulations. [ABSTRACT FROM AUTHOR]