Using large deviation techniques, we analyze the tail behavior of the stationary distribution of the buffer content process for a two-station communication network. We also show how the associated rate function can be expressed as the solution to a finite-dimensional variational problem. Along the way, we develop a number of results and techniques that are of independent interest, including continuity results for the input-output mapping for certain multiclass fluid models and a new technique for obtaining large deviation principles for invariant distributions from sample path large deviation results.
"Large deviation properties of data streams that share a buffer." Ann. Appl. Probab. 8 (4) 1070 - 1129, November 1998. https://doi.org/10.1214/aoap/1028903374