Whittle Index Approach to Energy-Aware Dispatching

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 so-called Whittle index approach. As our main result, we rigorously prove, under 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 energy-aware Whittle index policy is able to perform very close to the numerically obtained optimal policy.