{
  "id": "0707.4600",
  "version": "v1",
  "published": "2007-07-31T12:36:34.000Z",
  "updated": "2007-07-31T12:36:34.000Z",
  "title": "Heavy traffic limit for a processor sharing queue with soft deadlines",
  "authors": [
    "H. Christian Gromoll",
    "Łukasz Kruk"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/105051607000000014 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2007, Vol. 17, No. 3, 1049-1101",
  "doi": "10.1214/105051607000000014",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled using a random counting measure on the right half-plane. The limit of this measure valued process is obtained under diffusion scaling and heavy traffic conditions and is characterized as a deterministic function of the limiting queue length process. As special cases, one obtains diffusion approximations for the lead time profile and the profile of times in queue. One also obtains a snapshot principle for sojourn times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2007-07-31T12:36:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25",
      "60F17",
      "68M20",
      "90B22"
    ],
    "keywords": [
      "processor sharing queue",
      "heavy traffic limit",
      "soft deadlines",
      "residual service times",
      "limiting queue length process"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0707.4600G"
    }
  }
}