{
  "id": "1111.4846",
  "version": "v4",
  "published": "2011-11-21T12:12:34.000Z",
  "updated": "2015-03-23T19:21:48.000Z",
  "title": "Greedy Walk on the Real Line",
  "authors": [
    "Sergey Foss",
    "Leonardo T. Rolla",
    "Vladas Sidoravicius"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a self-interacting process described in terms of a single-server system with service stations at each point of the real line. The customer arrivals are given by a Poisson point processes on the space-time half plane. The server adopts a greedy routing mechanism, traveling towards the nearest customer, and ignoring new arrivals while in transit. We study the trajectories of the server and show that its asymptotic position diverges logarithmically in time.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-12-02T17:11:30.000Z",
      "title": "Transience of a Server with Greedy Strategy on the Real Line",
      "abstract": "We consider a single-server system with stations at each point of the real line. The customer arrivals are given by a Poisson point processes on the space-time half plane. The server adopts a greedy routing mechanism, traveling towards the nearest customer, and ignoring new arrivals while in transit. We study the trajectories of the server and show that its asymptotic position diverges logarithmically in time.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-03-23T19:21:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "real line",
      "greedy strategy",
      "transience",
      "asymptotic position diverges",
      "space-time half plane"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.4846F"
    }
  }
}