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This paper obtains logarithmic asymptotics of moderate deviations of thestochastic process of the number of customers in a many--server queue withgenerally distributed interarrival and service times in the Halfin--Whitt heavytraffic regime. The deviation function is expressed in terms of the solution toa Fredholm equation of the second kind. The proof uses characterisation oflarge deviation relatively compact sequences of probability measures asexponentially tight ones.

Moderate deviations of many-server queues in the Halfin-Whitt regime and weak convergence methods