  In this paper, we study the $G/\mathit{GI}/N$ queue in the Halfin--Whitt
regime. Our first result is to obtain a deterministic fluid limit for the
properly centered and scaled number of customers in the system which may be
used to provide a first-order approximation to the queue length process. Our
second result is to obtain a second-order stochastic approximation to the
number of customers in the system in the Halfin--Whitt regime. This is
accomplished by first centering the queue length process by its deterministic
fluid limit and then normalizing by an appropriate factor. We then proceed to
obtain an alternative but equivalent characterization of our limiting
approximation which involves the renewal function associated with the service
time distribution. This alternative characterization reduces to the diffusion
process obtained by Halfin and Whitt [Oper. Res. 29 (1981) 567--588] in the
case of exponentially distributed service times.
