{
  "id": "2202.05428",
  "version": "v1",
  "published": "2022-02-11T03:30:01.000Z",
  "updated": "2022-02-11T03:30:01.000Z",
  "title": "Quasi-stationary distributions for queueing and other models",
  "authors": [
    "Phil. Pollett"
  ],
  "comment": "3 pages. To appear in \"100 Views on Queues\", a special issue (Vol. 100) of Queueing Systems (QUESTA) on open problems",
  "categories": [
    "math.PR"
  ],
  "abstract": "This note presents conjectures on polynomial/algebraic/sub-exponential convergence of transition probabilities for $\\lambda$-null recurrent and $\\lambda$-transient Markov chains in continuous time. The only known positive examples are in queueing, branching, and related models. Implications for the existence of limiting conditional distributions for $\\lambda$-transient chains are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-02-11T03:30:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "60K25",
      "60J80"
    ],
    "keywords": [
      "quasi-stationary distributions",
      "transient markov chains",
      "limiting conditional distributions",
      "polynomial/algebraic/sub-exponential convergence",
      "transient chains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 3,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}