We consider an infinite tandem of first-come-first-served queues. The service
times have unit mean, and are independent and identically distributed across
queues and customers. Let $\bI$ be a stationary and ergodic interarrival sequence with marginals
of mean $\tau>1$, and suppose it is independent of all service times. The process $\bI$ is said to
be a fixed point for the first, and hence
for each, queue if the corresponding interdeparture sequence is
distributed as $\bI$. Assuming that
such a fixed point exists, we show that it is the distributional limit of passing an arbitrary stationary
and ergodic interarrival process of mean $\tau$ through the infinite
queueing tandem.