Large Deviations for Large Capacity

In this paper, we study large deviations of large capacity loss networks with xed routing. We use two-level modelling for the loss networks: the call level and the cell level. At the call level, a call request is accepted if it succeeds an admission test. The test is based on a polyhedral set of the number of calls in progress when a new call arrives. After being accepted, a call then transmits a sequence of cells (random variables) during its holding period. We show that the uid limits and the conditional central limit theorems in Kelly 1991] can be extended to the large deviation regime. Moreover, there are corresponding uid ow explanations for our large deviation results. In particular, we derive the exponential decay rates of the call blocking probability and the cell loss probability. These decay rates are obtained by solving primal and dual convex programming problems.