{
  "id": "math/0403318",
  "version": "v2",
  "published": "2004-03-19T11:30:11.000Z",
  "updated": "2005-01-27T10:24:43.000Z",
  "title": "The effect of service time variability on maximum queue lengths in M^X/G/1 queues",
  "authors": [
    "Ger Koole",
    "Misja Nuyens",
    "Rhonda Righter"
  ],
  "comment": "12 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study the impact of service-time distributions on the distribution of the maximum queue length during a busy period for the M^X/G/1 queue. The maximum queue length is an important random variable to understand when designing the buffer size for finite buffer (M/G/1/n) systems. We show the somewhat surprising result that for three variations of the preemptive LCFS discipline, the maximum queue length during a busy period is smaller when service times are more variable (in the convex sense).",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-01-27T10:24:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25",
      "90B22"
    ],
    "keywords": [
      "maximum queue length",
      "service time variability",
      "busy period",
      "important random",
      "convex sense"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......3318K"
    }
  }
}