{
  "id": "math/0512118",
  "version": "v7",
  "published": "2005-12-06T07:00:37.000Z",
  "updated": "2006-11-23T21:42:23.000Z",
  "title": "Optimal control of a large dam",
  "authors": [
    "Vyacheslav M. Abramov"
  ],
  "comment": "To appear in \"Journal of Applied Probability\" 44 (2007), No.1",
  "journal": "Journal of Applied Probability, 44 (2007), 249-258",
  "categories": [
    "math.PR",
    "math.CA",
    "math.OC"
  ],
  "abstract": "A large dam model is an object of study of this paper. The parameters $L^{lower}$ and $L^{upper}$ are its lower and upper levels, $L=L^{upper}-L^{lower}$ is large, and if a current level of water is between these bounds, then the dam is assumed to be in normal state. Passage one or other bound leads to damage. Let $J_1$ $(J_2)$ denote the damage cost of crossing the lower (upper) level. It is assumed that input stream of water is described by a Poisson process, while the output stream is state-dependent (the exact formulation of the problem is given in the paper). Let $L_t$ denote the dam level at time $t$, and let $p_1=\\lim_{t\\to\\infty}\\mathbf{P}\\{L_t= L^{lower}\\}$, $p_2=\\lim_{t\\to\\infty}\\mathbf{P}\\{L_t> L^{upper}\\}$ exist. The long-run average cost $J=p_1J_1+p_2J_2$ is a performance measure. The aim of the paper is to choose the parameter of output stream (exactly specified in the paper) minimizing $J$.",
  "revisions": [
    {
      "version": "v7",
      "updated": "2006-11-23T21:42:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K30",
      "40E05",
      "90B05",
      "60K25"
    ],
    "keywords": [
      "optimal control",
      "output stream",
      "large dam model",
      "long-run average cost",
      "upper levels"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math.....12118A"
    }
  }
}