  We develop many-server asymptotics in the QED regime for models with
admission control. The admission control, designed to reduce the incoming
traffic in periods of congestion, scales with the size of the system. For a
class of Markovian models with this scaled control, we identify the QED limits
for two stationary performance measures. We also derive corrected QED
approximations, generalizing earlier results for the Erlang B, C and A models.
These results are useful for the dimensioning of large systems equipped with an
active control policy. In particular, the corrected approximations can be
leveraged to establish the optimality gaps related to square-root staffing and
asymptotic dimensioning with admission control.
