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.
Ann. Appl. Probab.
8(4):
1070-1129
(November 1998).
DOI: 10.1214/aoap/1028903374