{
  "id": "math/0312335",
  "version": "v2",
  "published": "2003-12-17T14:57:10.000Z",
  "updated": "2004-03-31T13:13:34.000Z",
  "title": "Out of equilibrium functional central limit theorems for a large network where customers join the shortest of several queues",
  "authors": [
    "Carl Graham"
  ],
  "comment": "A new preprint math.PR/0403538, has been written as a combined version of the present preprint and the preprint math.PR/0312334. It is recommended to read the new combined version instead of the two others",
  "categories": [
    "math.PR"
  ],
  "abstract": "Customers arrive at rate N times alpha on a network of N single server infinite buffer queues, choose L queues uniformly, join the shortest one, and are served there in turn at rate beta. We let N go to infinity.We prove a functional central limit theorem (CLT) for the tails of the empirical measures of the queue occupations,in a Hilbert space with the weak topology, with limit given by an Ornstein-Uhlenbeck process. The a priori assumption is that the initial data converge.This completes a recent functional CLT in equilibrium result for which convergence for the initial data was not known in advance, but was deduced a posteriori from the functional CLT.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2004-03-31T13:13:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60K25"
    ],
    "keywords": [
      "equilibrium functional central limit theorems",
      "large network",
      "customers join",
      "single server infinite buffer queues"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math.....12335G"
    }
  }
}