{
  "id": "math/0406178",
  "version": "v1",
  "published": "2004-06-09T12:24:41.000Z",
  "updated": "2004-06-09T12:24:41.000Z",
  "title": "Exact asymptotics for fluid queues fed by multiple heavy-tailed on-off flows",
  "authors": [
    "Bert Zwart",
    "Sem Borst",
    "Michel Mandjes"
  ],
  "journal": "Annals of Probability 2004, Vol. 14, No. 2, 903-957",
  "doi": "10.1214/105051604000000161",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a fluid queue fed by multiple On-Off flows with heavy-tailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a ``dominant'' subset of the flows, with the original service rate subtracted by the mean rate of the other flows. We describe how a dominant set may be determined from a simple knapsack formulation. The dominant set consists of a ``minimally critical'' set of On-Off flows with regularly varying On periods. In case the dominant set contains just a single On-Off flow, the exact asymptotics for the reduced system follow from known results. For the case of several On-Off flows, we exploit a powerful intuitive argument to obtain the exact asymptotics. Combined with the reduced-load equivalence, the results for the reduced system provide a characterization of the tail of the workload distribution for a wide range of traffic scenarios.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-09T12:24:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25",
      "60F10",
      "90B22"
    ],
    "keywords": [
      "multiple heavy-tailed on-off flows",
      "exact asymptotics",
      "fluid queues",
      "reduced system",
      "dominant set"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6178Z"
    }
  }
}