Large Deviation Properties of Data Streams That Share a Buuer

Using large deviation techniques, we analyze the tail behavior of the stationary distribution of the buuer content process for a two-station communication network. We also show how the associated rate function can be expressed as the solution to a nite-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 uid models, a method for the construction of Lyapunov functions for such models, and a new technique for obtaining large deviation principles for invariant distributions from sample path large deviation results. The results can easily be extended to more general network models.