{
  "id": "1812.10163",
  "version": "v1",
  "published": "2018-12-25T20:11:12.000Z",
  "updated": "2018-12-25T20:11:12.000Z",
  "title": "Large deviations of the stationary distribution of a non Markov process",
  "authors": [
    "Anatolii A. Puhalskii"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-25T20:11:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "large deviation",
      "non markov process",
      "stationary distribution",
      "queue length process",
      "unique stationary idempotent distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}