Large deviations of the long term distribution of a non Markov process

Abstract

We prove that the long term distribution of the queue length process in an ergodic generalised Jackson network obeys the Large Deviation Principle with a deviation function given by the quasipotential. The latter is related to the unique long term idempotent distribution, which is also a stationary idempotent distribution, of the large deviation limit of the queue length process. The proof draws on developments in queueing network stability and idempotent probability.