{
  "id": "1502.07218",
  "version": "v1",
  "published": "2015-02-25T16:01:29.000Z",
  "updated": "2015-02-25T16:01:29.000Z",
  "title": "Invariant measures and error bounds for random walks in the quarter-plane based on sums of geometric terms",
  "authors": [
    "Yanting Chen",
    "Richard J. Boucherie",
    "Jasper Goseling"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider homogeneous random walks in the quarter-plane. The necessary conditions which characterize random walks of which the invariant measure is a sum of geometric terms are provided in [2,3]. Based on these results, we first develop an algorithm to check whether the invariant measure of a given random walk is a sum of geometric terms. We also provide the explicit form of the invariant measure if it is a sum of geometric terms. Secondly, for random walks of which the invariant measure is not a sum of geometric terms, we provide an approximation scheme to obtain error bounds for the performance measures. Finally, some numerical examples are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-25T16:01:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60J10"
    ],
    "keywords": [
      "geometric terms",
      "invariant measure",
      "error bounds",
      "quarter-plane",
      "characterize random walks"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}