{
  "id": "1309.3962",
  "version": "v1",
  "published": "2013-09-16T13:59:40.000Z",
  "updated": "2013-09-16T13:59:40.000Z",
  "title": "A functional central limit theorem for a Markov-modulated infinite-server queue",
  "authors": [
    "D. Anderson",
    "J. Blom",
    "M. Mandjes",
    "H. Thorsdottir",
    "K. de Turck"
  ],
  "comment": "4 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "The production of molecules in a chemical reaction network is modelled as a Poisson process with a Markov-modulated arrival rate and an exponential decay rate. We analyze the distributional properties of $M$, the number of molecules, under specific time-scaling; the background process is sped up by $N^{\\alpha}$, the arrival rates are scaled by $N$, for $N$ large. A functional central limit theorem is derived for $M$, which after centering and scaling, converges to an Ornstein-Uhlenbeck process. A dichotomy depending on $\\alpha$ is observed. For $\\alpha\\leq1$ the parameters of the limiting process contain the deviation matrix associated with the background process.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-16T13:59:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25",
      "60K37",
      "60F05",
      "60F17",
      "60J60"
    ],
    "keywords": [
      "functional central limit theorem",
      "markov-modulated infinite-server queue",
      "background process",
      "exponential decay rate",
      "markov-modulated arrival rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.3962A"
    }
  }
}