  We consider Markovian many-server systems with admission control operating in
a QED regime, where the relative utilization approaches unity while the number
of servers grows large, providing natural Economies-of-Scale. In order to
determine the optimal admission control policy, we adopt a revenue maximization
framework, and suppose that the revenue rate attains a maximum when no
customers are waiting and no servers are idling. When the revenue function
scales properly with the system size, we show that a nondegenerate optimization
problem arises in the limit. Detailed analysis demonstrates that the revenue is
maximized by nontrivial policies that bar customers from entering when the
queue length exceeds a certain threshold of the order of the typical
square-root level variation in the system occupancy. We identify a fundamental
equation characterizing the optimal threshold, which we extensively leverage to
provide broadly applicable upper/lower bounds for the optimal threshold,
establish its monotonicity, and examine its asymptotic behavior, all for
general revenue structures. For linear and exponential revenue structures, we
present explicit expressions for the optimal threshold.
