Past exam of the mathematics course of the University of Cambridge / 2004 / iii / Paper 31 / 4 / a

Use the stated continuity of the infinite-buffer and finite-buffer queue workload maps on the input path space. The contraction principle for large deviations gives, at the same speed as the input sequence,Empty fibers have infimum infinity. Both rates are good because they are continuous contractions of the good rate function I. In particular, at speed L the infinite-buffer queue workload satisfies, for every Borel set E,and the identical bounds with bars give the finite-buffer queue workload LDP. This states the entire principles, not just an informal tail approximation.