{
  "id": "1212.5291",
  "version": "v1",
  "published": "2012-12-20T22:45:52.000Z",
  "updated": "2012-12-20T22:45:52.000Z",
  "title": "Products of random matrices and queueing system performance evaluation",
  "authors": [
    "N. K. Krivulin"
  ],
  "comment": "Simulation 2001: St. Petersburg Workshop on Simulation, St. Petersburg, Russia, June 18-22, 2001. ISBN 5-7997-0304-9",
  "journal": "Proc. 4th St. Petersburg Workshop on Simulation, 2001, pp. 304-309",
  "categories": [
    "math.OC",
    "cs.SY"
  ],
  "abstract": "We consider (max,+)-algebra products of random matrices, which arise from performance evaluation of acyclic fork-join queueing networks. A new algebraic technique to examine properties of the product and investigate its limiting behaviour is proposed based on an extension of the standard matrix (max,+)-algebra by endowing it with the ordinary matrix addition as an external operation. As an application, we derive bounds on the (max,+)-algebra maximal Lyapunov exponent which can be considered as the cycle time of the networks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-12-20T22:45:52.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "15A80",
      "68M20",
      "93C65",
      "90B15",
      "37H15"
    ],
    "keywords": [
      "queueing system performance evaluation",
      "random matrices",
      "acyclic fork-join queueing networks",
      "ordinary matrix addition",
      "maximal lyapunov exponent"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1212.5291K"
    }
  }
}