{
  "id": "1312.6970",
  "version": "v2",
  "published": "2013-12-25T13:18:43.000Z",
  "updated": "2014-04-24T08:32:46.000Z",
  "title": "Heavy-traffic asymptotic formulas for the multiclass M${}^X$/G/1 queue",
  "authors": [
    "Hiroshi Miyawaki",
    "Hiroyuki Masuyama",
    "Yutaka Takahashi"
  ],
  "comment": "This paper has been withdrawn by the author because Conjecture 4.1 has turned out to be not true",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper studies the heavy-traffic asymptotics for the multiclass FIFO M${}^X$/G/1 queue. We first derive the probability generating function of the joint queue length distribution. Using the probability generating function, we then present heavy-traffic asymptotic formulas for the joint queue length distribution and its joint moments (i.e., the joint queue length moments). These formulas are proved under weaker conditions on the service time distributions, compared to the ones reported in the literature. This fact leads us to conjectures that some of the conditions made in the literature are relaxed.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2014-04-24T08:32:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "heavy-traffic asymptotic formulas",
      "joint queue length distribution",
      "probability generating function",
      "multiclass",
      "joint queue length moments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.6970M"
    }
  }
}