A data center can be modeled as a set of parallel queues, and the dispatcher decides to which queue the arriving jobs are routed. We consider an energy-aware dispatching system in a Markovian setting, where each server upon becoming empty enters a sleep mode to save energy and to activate the server after sleep incurs an additional setup delay cost. We seek to optimize the performance-energy trade-off by applying the socalled Whittle index approach. As our main result, we rigorously prove,

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... a certain technical assumption, that the problem is indexable, and derive the explicit form of the Whittle index. Our numerical examples demonstrate that the resulting energyaware Whittle index policy is able to perform very close to the numerically obtained optimal policy.