Invariant rate functions for discrete-time queues

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.