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We formulate a control problem for a GI/GI/N+GI queue, whose objective is totrade off the long-run average operational costs (i.e., abandonment costs andholding costs) with server utilization costs. To solve the control problem, weconsider an asymptotic regime in which the arrival rate and the number ofservers grow large. The solution to an associated fluid control problemmotivates that non-idling service disciplines are not in general optimal,unless some arrivals are turned away. We propose an admission control policydesigned to ensure servers have sufficient idle time that we show isasymptotically optimal.

Asymptotically Optimal Idling in the GI/GI/N+GI Queue