{
  "id": "1502.00885",
  "version": "v1",
  "published": "2015-02-03T15:14:58.000Z",
  "updated": "2015-02-03T15:14:58.000Z",
  "title": "A large deviations principle for infinite-server queues in a random environment",
  "authors": [
    "H. M. Jansen",
    "M. R. H. Mandjes",
    "K. De Turck",
    "S. Wittevrongel"
  ],
  "comment": "28 pages, 2 figures",
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper studies an infinite-server queue in a random environment, meaning that the arrival rate, the service requirements and the server work rate are modulated by a general c\\`{a}dl\\`{a}g stochastic background process. To prove a large deviations principle, the concept of attainable parameters is introduced. Scaling both the arrival rates and the background process, a large deviations principle for the number of jobs in the system is derived using attainable parameters. Finally, some known results about Markov-modulated infinite-server queues are generalized and new results for several background processes and scalings are established in examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-02-03T15:14:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25",
      "60F10"
    ],
    "keywords": [
      "large deviations principle",
      "infinite-server queue",
      "random environment",
      "arrival rate",
      "attainable parameters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150200885J"
    }
  }
}