Service center trade-offs between customer impatience and power consumption

We consider the problem of managing a service center where it is desirable to keep power consumption low. Customers defect (i.e. leave the system) if they have to wait too long before starting service. A block of servers is designated as ‘reserve’. The reserves are powered up when the number of jobs in the system is sufficiently high, and are powered down when that number is sufficiently low. Powering up takes an interval of time during which the reserves consume power but do not serve jobs. The objective function to be minimized takes into account both the number of servers that are powered up and the number of jobs that are lost through defections. The question of how to choose the number of reserves, and the up and down thresholds, is answered by analyzing a suitable queueing model. Heuristics and numerical results are also presented.