{
  "id": "1102.4707",
  "version": "v1",
  "published": "2011-02-23T10:13:29.000Z",
  "updated": "2011-02-23T10:13:29.000Z",
  "title": "The exact asymptotic for the stationary distribution of some unreliable systems",
  "authors": [
    "Pawel Lorek"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we find asymptotic distribution for some unreliable networks. Using Markov Additive Structure and Adan, Foley, McDonald method, we find the exact asymptotic for the stationary distribution. With the help of MA structure and matrix geometric approach, we also investigate the asymptotic when breakdown intensity is small. In particular, two different asymptotic regimes for small breakdown intensity suggest two different patterns of large deviations, which is confirmed by simulation study.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-02-23T10:13:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stationary distribution",
      "exact asymptotic",
      "unreliable systems",
      "matrix geometric approach",
      "small breakdown intensity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1102.4707L"
    }
  }
}