{
  "id": "1104.0167",
  "version": "v2",
  "published": "2011-04-01T13:30:06.000Z",
  "updated": "2011-12-06T10:47:23.000Z",
  "title": "Gaussian queues in light and heavy traffic",
  "authors": [
    "Krzysztof Debicki",
    "Kamil Marcin Kosinski",
    "Michel Mandjes"
  ],
  "journal": "Queueing Systems 71 (2012) 137-149",
  "doi": "10.1007/s11134-011-9270-x",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we investigate Gaussian queues in the light-traffic and in the heavy-traffic regime. The setting considered is that of a centered Gaussian process $X\\equiv\\{X(t):t\\in\\mathbb R\\}$ with stationary increments and variance function $\\sigma^2_X(\\cdot)$, equipped with a deterministic drift $c>0$, reflected at 0: \\[Q_X^{(c)}(t)=\\sup_{-\\infty<s\\le t}(X(t)-X(s)-c(t-s)).\\] We study the resulting stationary workload process $Q^{(c)}_X\\equiv\\{Q_X^{(c)}(t):t\\ge0\\}$ in the limiting regimes $c\\to 0$ (heavy traffic) and $c\\to\\infty$ (light traffic). The primary contribution is that we show for both limiting regimes that, under mild regularity conditions on the variance function, there exists a normalizing function $\\delta(c)$ such that $Q^{(c)}_X(\\delta(c)\\cdot)/\\sigma_X(\\delta(c))$ converges to a non-trivial limit in $C[0,\\infty)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-12-06T10:47:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60F17",
      "60K25"
    ],
    "keywords": [
      "heavy traffic",
      "gaussian queues",
      "variance function",
      "limiting regimes",
      "resulting stationary workload process"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.0167D"
    }
  }
}