We consider an M/G/1 queue that is idle at time 0. The number of
customers sampled at an independent exponential time is shown to
have the same geometric distribution under the preemptive-resume
last-in-first-out and the processor-sharing disciplines. Hence,
the marginal distribution of the queue length at any time is
identical for both disciplines. We then give a detailed analysis
of the time until the first departure for any symmetric
queueing discipline. We characterize its distribution and show
that it is insensitive to the service discipline. Finally, we
study the tail behavior of this distribution.
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