{
  "id": "1104.3192",
  "version": "v2",
  "published": "2011-04-16T03:44:09.000Z",
  "updated": "2012-08-18T06:13:12.000Z",
  "title": "On Large Delays in Multi-Server Queues with Heavy Tails",
  "authors": [
    "Sergey Foss",
    "Dmitry Korshunov"
  ],
  "journal": "Mathematics of Operations Research, 37 (2012) 201-218",
  "doi": "10.1287/moor.1120.0539",
  "categories": [
    "math.PR"
  ],
  "abstract": "We present upper and lower bounds for the tail distribution of the stationary waiting time $D$ in the stable $GI/GI/s$ FCFS queue. These bounds depend on the value of the traffic load $\\rho$ which is the ratio of mean service and mean interarrival times. For service times with intermediate regularly varying tail distribution the bounds are exact up to a constant, and we are able to establish a `principle of $s-k$ big jumps' in this case (here $k$ is the integer part of $\\rho$), which gives the most probable way for the stationary waiting time to be large. Another corollary of the bounds obtained is to provide a new proof of necessity and sufficiency of conditions for the existence of moments of the stationary waiting time.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2012-08-18T06:13:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25",
      "90B22",
      "60F10"
    ],
    "keywords": [
      "stationary waiting time",
      "heavy tails",
      "large delays",
      "multi-server queues",
      "intermediate regularly varying tail distribution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.3192F"
    }
  }
}