Large deviations of the long term distribution of a non Markov process
Probability
2019-05-16 v6
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 processes. The proof draws on developments in queueing network stability and idempotent probability.
Keywords
Cite
@article{arxiv.1812.10163,
title = {Large deviations of the long term distribution of a non Markov process},
author = {Anatolii A. Puhalskii},
journal= {arXiv preprint arXiv:1812.10163},
year = {2019}
}