  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 processes. The
proof draws on developments in queueing network stability and idempotent
probability.
