This paper presents a large deviations principle for the average of real-valued processes indexed by the positive integers, one which is particularly suited to queueing systems with many traffic flows. Examples are given of how it may be applied to standard queues with finite and infinite buffers, to priority queues and to finding most likely paths to overflow.
"Sample path large deviations for queues with many inputs." Ann. Appl. Probab. 11 (2) 379 - 404, May 2001. https://doi.org/10.1214/aoap/1015345296