We consider a discrete-time queue with general service distribution
and characterize a class of arrival processes that possess a large deviation
rate function that remains unchanged in passing through the queue. This
invariant rate function corresponds to a kind of exponential
tilting of the service distribution. We establish a large
deviations analogue of quasireversibility for this class of arrival
processes. Finally, we prove the existence of stationary point
processes that have a probability law that is preserved by the queueing
operator and conjecture that they have large deviation rate
functions which belong to the class of invariant rate functions
described above.