{
  "id": "0809.4275",
  "version": "v3",
  "published": "2008-09-24T20:45:41.000Z",
  "updated": "2009-12-10T07:53:12.000Z",
  "title": "Heavy-traffic limits for waiting times in many-server queues with abandonment",
  "authors": [
    "Rishi Talreja",
    "Ward Whitt"
  ],
  "comment": "Published in at http://dx.doi.org/10.1214/09-AAP606 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)",
  "journal": "Annals of Applied Probability 2009, Vol. 19, No. 6, 2137-2175",
  "doi": "10.1214/09-AAP606",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish heavy-traffic stochastic-process limits for waiting times in many-server queues with customer abandonment. If the system is asymptotically critically loaded, as in the quality-and-efficiency-driven (QED) regime, then a bounding argument shows that the abandonment does not affect waiting-time processes. If instead the system is overloaded, as in the efficiency-driven (ED) regime, following Mandelbaum et al. [Proceedings of the Thirty-Seventh Annual Allerton Conference on Communication, Control and Computing (1999) 1095--1104], we treat customer abandonment by studying the limiting behavior of the queueing models with arrivals turned off at some time $t$. Then, the waiting time of an infinitely patient customer arriving at time $t$ is the additional time it takes for the queue to empty. To prove stochastic-process limits for virtual waiting times, we establish a two-parameter version of Puhalskii's invariance principle for first passage times. That, in turn, involves proving that two-parameter versions of the composition and inverse mappings appropriately preserve convergence.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-12-10T07:53:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F17",
      "60K25"
    ],
    "keywords": [
      "waiting time",
      "many-server queues",
      "heavy-traffic limits",
      "stochastic-process limits",
      "inverse mappings appropriately preserve convergence"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0809.4275T"
    }
  }
}