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

This paper obtains logarithmic asymptotics of moderate deviations of the stochastic process of the number of customers in a many–server queue with generally distributed interarrival and service times in the Halfin–Whitt heavy traffic regime. The deviation function is expressed in terms of the solution to a Fredholm equation of the second kind. The proof uses characterisation of large deviation relatively compact sequences of probability measures as exponentially tight ones.