Mathematics

We derive a large deviations principle for the trajectories generated by a class of ergodic Markov processes. Specifically, we work with M/M/∞ queueing processes. We study large deviations of these processes scaled equally in both space and time directions. Our main result is that the probabilities of long excursions originating at state 0 would converge to zero function with the rate proportional to the square of the scaling parameter. The rate function is expressed as an integral of a linear combination of trajectories.