{
  "id": "2304.09279",
  "version": "v1",
  "published": "2023-04-18T20:34:04.000Z",
  "updated": "2023-04-18T20:34:04.000Z",
  "title": "Heavy Loads and Heavy Tails",
  "authors": [
    "Sem Borst"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The present paper is concerned with the stationary workload of queues with heavy-tailed (regularly varying) characteristics. We adopt a transform perspective to illuminate a close connection between the tail asymptotics and heavy-traffic limit in infinite-variance scenarios. This serves as a tribute to some of the pioneering results of J.W. Cohen in this domain. We specifically demonstrate that reduced-load equivalence properties established for the tail asymptotics of the workload naturally extend to the heavy-traffic limit.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-18T20:34:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25",
      "68M20",
      "90B22"
    ],
    "keywords": [
      "heavy tails",
      "heavy loads",
      "tail asymptotics",
      "heavy-traffic limit",
      "reduced-load equivalence properties"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}