  A many-server queueing system is considered in which customers arrive
according to a renewal process and have service and patience times that are
drawn from two independent sequences of independent, identically distributed
random variables. Customers enter service in the order of arrival and are
assumed to abandon the queue if the waiting time in queue exceeds the patience
time. The state of the system with $N$ servers is represented by a
four-component process that consists of the forward recurrence time of the
arrival process, a pair of measure-valued processes, one that keeps track of
the waiting times of customers in queue and the other that keeps track of the
amounts of time customers present in the system have been in service and a
real-valued process that represents the total number of customers in the
system. Under general assumptions, it is shown that the state process is a
Feller process, admits a stationary distribution and is ergodic. It is also
shown that the associated sequence of scaled stationary distributions is tight,
and that any subsequence converges to an invariant state for the fluid limit.
In particular, this implies that when the associated fluid limit has a unique
invariant state, then the sequence of stationary distributions converges, as
$N\rightarrow \infty$, to the invariant state. In addition, a simple example is
given to illustrate that, both in the presence and absence of abandonments, the
$N\rightarrow \infty$ and $t\rightarrow \infty$ limits cannot always be
interchanged.
