  A many-server queueing system is considered in which customers with
independent and identically distributed service times enter service in the
order of arrival. The state of the system is represented by a process that
describes the total number of customers in the system, as well as a
measure-valued process that keeps track of the ages of customers in service,
leading to a Markovian description of the dynamics. Under suitable assumptions,
a functional central limit theorem is established for the sequence of (centered
and scaled) state processes as the number of servers goes to infinity. The
limit process describing the total number in system is shown to be an Ito
diffusion with a constant diffusion coefficient that is insensitive to the
service distribution. The limit of the sequence of (centered and scaled) age
processes is shown to be a Hilbert space valued diffusion that can also be
characterized as the unique solution of a stochastic partial differential
equation that is coupled with the Ito diffusion. Furthermore, the limit
processes are shown to be semimartingales and to possess a strong Markov
property.
