{
  "id": "2010.14582",
  "version": "v1",
  "published": "2020-10-27T19:45:41.000Z",
  "updated": "2020-10-27T19:45:41.000Z",
  "title": "Jackson network in a random environment: strong approximation",
  "authors": [
    "Elena Bashtova",
    "Elena Lenena"
  ],
  "comment": "Submitted to Far Eastern Mathematical Journal (Dal'nevostochnyi Matematicheskii Zhurnal)",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a Jackson network with regenerative input flows in which every server is subject to a random environment influence generating breakdowns and repairs. They occur in accordance with two independent sequences of i.i.d. random variables. We establish a theorem on the strong approximation of the vector of queue lengths by a reflected Brownian motion in positive orthant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-27T19:45:41.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "strong approximation",
      "jackson network",
      "random environment influence generating breakdowns",
      "regenerative input flows",
      "reflected brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}