  In this paper, we study the stability of queues with impatient customers.
Under general stationary ergodic assumptions, we first provide some conditions
for such a queue to be regenerative (i.e. to empty a.s. an infinite number of
times). In the particular case of a single server operating in First in, First
out, we prove the existence (in some cases, on an enlarged probability space)
of a stationary workload. This is done by studying a non-monotonic stochastic
recursion under the Palm settings, and by stochastic comparison of stochastic
recursions.
