{
  "id": "math/0501291",
  "version": "v2",
  "published": "2005-01-19T16:06:24.000Z",
  "updated": "2007-07-30T06:32:23.000Z",
  "title": "Stationary distributions of multi-type totally asymmetric exclusion processes",
  "authors": [
    "Pablo A. Ferrari",
    "James B. Martin"
  ],
  "comment": "Published at http://dx.doi.org/10.1214/009117906000000944 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Probability 2007, Vol. 35, No. 3, 807-832",
  "doi": "10.1214/009117906000000944",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider totally asymmetric simple exclusion processes with n types of particle and holes ($n$-TASEPs) on $\\mathbb {Z}$ and on the cycle $\\mathbb {Z}_N$. Angel recently gave an elegant construction of the stationary measures for the 2-TASEP, based on a pair of independent product measures. We show that Angel's construction can be interpreted in terms of the operation of a discrete-time $M/M/1$ queueing server; the two product measures correspond to the arrival and service processes of the queue. We extend this construction to represent the stationary measures of an n-TASEP in terms of a system of queues in tandem. The proof of stationarity involves a system of n 1-TASEPs, whose evolutions are coupled but whose distributions at any fixed time are independent. Using the queueing representation, we give quantitative results for stationary probabilities of states of the n-TASEP on $\\mathbb {Z}_N$, and simple proofs of various independence and regeneration properties for systems on $\\mathbb {Z}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-07-30T06:32:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22",
      "90B22"
    ],
    "keywords": [
      "multi-type totally asymmetric exclusion processes",
      "stationary distributions",
      "totally asymmetric simple exclusion processes",
      "stationary measures"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......1291F"
    }
  }
}