Large deviations of the stationary distribution of a non Markov process

Anatolii A. Puhalskii

Published 2018-12-25Version 1

We prove that the stationary 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 a unique stationary idempotent distribution of the large deviation limit of the queue length processes. The proof draws on developments in queueing network stability and idempotent probability.