{
  "id": "1404.5549",
  "version": "v1",
  "published": "2014-04-22T16:43:17.000Z",
  "updated": "2014-04-22T16:43:17.000Z",
  "title": "On queues with service and interarrival times depending on waiting times",
  "authors": [
    "Onno J. Boxma",
    "Maria Vlasiou"
  ],
  "comment": "19 pages, 1 figure, 24 references",
  "journal": "Queueing Systems, 56(3-4), 121-132, August 2007",
  "doi": "10.1007/s11134-007-9011-3",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider an extension of the standard G/G/1 queue, described by the equation $W\\stackrel{\\mathcal{D}}{=}\\max\\{0, B-A+YW\\}$, where $\\mathbb{P}[Y=1]=p$ and $\\mathbb{P}[Y=-1]=1-p$. For $p=1$ this model reduces to the classical Lindley equation for the waiting time in the G/G/1 queue, whereas for $p=0$ it describes the waiting time of the server in an alternating service model. For all other values of $p$ this model describes a FCFS queue in which the service times and interarrival times depend linearly and randomly on the waiting times. We derive the distribution of $W$ when $A$ is generally distributed and $B$ follows a phase-type distribution, and when $A$ is exponentially distributed and $B$ deterministic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-04-22T16:43:17.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25"
    ],
    "keywords": [
      "waiting time",
      "model reduces",
      "alternating service model",
      "fcfs queue",
      "service times"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1404.5549B"
    }
  }
}