{
  "id": "1601.03489",
  "version": "v1",
  "published": "2016-01-14T04:53:26.000Z",
  "updated": "2016-01-14T04:53:26.000Z",
  "title": "Error Bounds for Last-Block-Column-Augmented Truncations of Block-Structured Markov Chains",
  "authors": [
    "Hiroyuki Masuyama"
  ],
  "comment": "This paper has been submitted for review",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper considers the estimation of the difference between the time-averaged functionals of a continuous-time block-structured Markov chain (BSMC) and its last-blockcolumn-augmented northwest-corner truncation (called the LBC-augmented truncation, for short). The stationary probability vectors of a BSMC and its LBC-augmented truncation can be connected through the deviation matrix of the BSMC, which is a solution to a certain Poisson equation. Combining this fact with Dynkin's formula, we derive error bounds for the time-averaged functional obtained by LBC-augmented truncation, under the assumption that the BSMC satisfies the general f-modulated drift condition. We also establish computable bounds for a special case where the BSMC is exponentially ergodic. To derive such computable bounds for the general case, we propose a method that reduces BSMCs to be exponential ergodic. Furthermore, we focus on the level-dependent quasi-birth-and-death process (LD-QBD), which is a typical example of BSMCs connected with queueing theory. As an application of our results, we consider a retrial queueing model and provide some numerical examples. Finally, we provide some remarks on the perturbation analysis of the stationary probability vectors BSMCs.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-14T04:53:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "error bounds",
      "last-block-column-augmented truncations",
      "lbc-augmented truncation",
      "stationary probability vectors bsmcs",
      "level-dependent quasi-birth-and-death process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160103489M"
    }
  }
}