{
  "id": "1308.4227",
  "version": "v1",
  "published": "2013-08-20T04:36:39.000Z",
  "updated": "2013-08-20T04:36:39.000Z",
  "title": "A Computational Framework for the Mixing Times in the QBD Processes with Infinitely-Many Levels",
  "authors": [
    "Quan-Lin Li",
    "Jing Cao"
  ],
  "categories": [
    "math.PR",
    "cs.PF",
    "cs.SY",
    "math.OC"
  ],
  "abstract": "In this paper, we develop some matrix Poisson's equations satisfied by the mean and variance of the mixing time in an irreducible positive-recurrent discrete-time Markov chain with infinitely-many levels, and provide a computational framework for the solution to the matrix Poisson's equations by means of the UL-type of $RG$-factorization as well as the generalized inverses. In an important special case: the level-dependent QBD processes, we provide a detailed computation for the mean and variance of the mixing time. Based on this, we give new highlight on computation of the mixing time in the block-structured Markov chains with infinitely-many levels through the matrix-analytic method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-08-20T04:36:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J10",
      "60J22",
      "60J45",
      "90B15",
      "90B18",
      "90B22",
      "G.3",
      "C.4"
    ],
    "keywords": [
      "mixing time",
      "infinitely-many levels",
      "qbd processes",
      "computational framework",
      "matrix poissons equations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1308.4227L"
    }
  }
}