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.
|Translated title of the contribution||Invariant rate functions for discrete-time queues|
|Pages (from-to)||446 - 474|
|Number of pages||29|
|Journal||Annals of Applied Probability|
|Publication status||Published - May 2003|