Asymptotically optimal idling in the GI/GI/N+GI queue

We formulate a control problem for a GI/GI/N+GI queue, whose objective is to trade off the long-run average operational costs with server utilization costs. To solve the control problem, we consider an asymptotic regime in which the arrival rate and the number of servers grow large. The solution to an associated fluid control problem motivates that non-idling service disciplines are not in general optimal, unless some arrivals are turned away. We propose an admission control policy designed to ensure that servers have sufficient idle time, which we show is asymptotically optimal.