  A parallel server system with $n$ identical servers is considered. The
service time distribution has a finite mean $1/\mu$, but otherwise is
arbitrary. Arriving customers are be routed to one of the servers immediately
upon arrival. Join-Idle-Queue routing algorithm is studied, under which an
arriving customer is sent to an idle server, if such is available, and to a
randomly uniformly chosen server, otherwise. We consider the asymptotic regime
where $n\to\infty$ and the customer input flow rate is $\lambda n$. Under the
condition $\lambda/\mu<1/2$, we prove that, as $n\to\infty$, the sequence of
(appropriately scaled) stationary distributions concentrates at the natural
equilibrium point, with the fraction of occupied servers being constant equal
$\lambda/\mu$. In particular, this implies that the steady-state probability of
an arriving customer waiting for service vanishes.
