{
  "id": "math/0601010",
  "version": "v1",
  "published": "2005-12-31T22:16:23.000Z",
  "updated": "2005-12-31T22:16:23.000Z",
  "title": "A large deviation principle for join the shortest queue",
  "authors": [
    "Anatolii A. Puhalskii",
    "Alexander A. Vladimirov"
  ],
  "comment": "14 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a join-the-shortest-queue model which is as follows. There are $K$ single FIFO servers and $M$ arrival processes. The customers from a given arrival process can be served only by servers from a certain subset of all servers. The actual destination is the server with the smallest weighted queue length. The arrival processes are assumed to obey a large deviation principle while the service is exponential. A large deviation principle is established for the queue-length process. The action functional is expressed in terms of solutions to mathematical programming problems. The large deviation limit point is identified as a weak solution to a system of idempotent equations. Uniqueness of the weak solution is proved by establishing trajectorial uniqueness.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2005-12-31T22:16:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60K25"
    ],
    "keywords": [
      "large deviation principle",
      "shortest queue",
      "arrival processes",
      "weak solution",
      "large deviation limit point"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......1010P"
    }
  }
}