{
  "id": "1811.09576",
  "version": "v1",
  "published": "2018-11-23T17:44:43.000Z",
  "updated": "2018-11-23T17:44:43.000Z",
  "title": "An alternative approach to heavy-traffic limits for finite-pool queues",
  "authors": [
    "Gianmarco Bet"
  ],
  "comment": "16 pages. Comments are welcome",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a model for transitory queues in which only a finite number of customers can join. The queue thus operates over a finite time horizon. In this system, also known as the $\\Delta_{(i)}/G/1$ queue, the customers decide independently when to join the queue by sampling their arrival time from a common distribution. We prove that, when the queue satisfies a certain heavy-traffic condition and under the additional assumption that the second moment of the service time is finite, the rescaled queue length process converges to a reflected Brownian motion with parabolic drift. Our result holds for general arrival times, thus improving on an earlier result which assumes exponential arrival times.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-23T17:44:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25",
      "60F17"
    ],
    "keywords": [
      "heavy-traffic limits",
      "finite-pool queues",
      "alternative approach",
      "assumes exponential arrival times",
      "rescaled queue length process converges"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}