  It is well-known that large deviations of random walks driven by independent
and identically distributed heavy-tailed random variables are governed by the
so-called principle of one large jump. We note that further subtleties hold for
such random walks in the large deviation scale which we call hidden large
deviation. We apply this idea in the context of queueing processes with
heavy-tailed service times and study approximations of severe congestion times
for (buffered) queues. We conclude with simulated examples to verify our
results.
