{
  "id": "1106.0964",
  "version": "v2",
  "published": "2011-06-06T06:21:09.000Z",
  "updated": "2011-10-17T10:42:37.000Z",
  "title": "Queue lengths and workloads in polling systems",
  "authors": [
    "Onno Boxma",
    "Offer Kella",
    "Kamil Marcin Kosinski"
  ],
  "journal": "Operations Research Letters 39 (2011) 401-405",
  "doi": "10.1016/j.orl.2011.10.006",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a polling system: a queueing system of $N\\ge 1$ queues with Poisson arrivals $Q_1,...,Q_N$ visited in a cyclic order (with or without switchover times) by a single server. For this system we derive the probability generating function $\\mathscr Q(\\cdot)$ of the joint queue length distribution at an arbitrary epoch in a stationary cycle, under no assumptions on service disciplines. We also derive the Laplace-Stieltjes transform $\\mathscr W(\\cdot)$ of the joint workload distribution at an arbitrary epoch. We express $\\mathscr Q$ and $\\mathscr W$ in the probability generating functions of the joint queue length distribution at visit beginnings, ${\\mathscr V}_{b_i}(\\cdot)$, and visit completions, ${\\mathscr V}_{c_i}(\\cdot)$, at $Q_i$, $i=1,...,N$. It is well known that ${\\mathscr V}_{b_i}$ and ${\\mathscr V}_{c_i}$ can be computed in a broad variety of cases. Furthermore, we establish a workload decomposition result.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-10-17T10:42:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K25",
      "90B22"
    ],
    "keywords": [
      "polling system",
      "joint queue length distribution",
      "probability generating function",
      "arbitrary epoch",
      "joint workload distribution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1106.0964B"
    }
  }
}