---
_id: '33358'
abstract:
- lang: eng
  text: 'We study the workload processes of two M/G/1 queueing systems with restricted
    capacity: in Model 1 any service requirement that would exceed a certain capacity
    threshold is truncated; in Model 2 new arrivals do not enter the system if they
    have to wait more than a fixed threshold time in line. For Model 1 we obtain several
    results concerning the rate of convergence to equilibrium. In particular, we derive
    uniform bounds for geometric ergodicity with respect to certain subclasses. For
    Model 2 geometric ergodicity follows from the finiteness of the moment-generating
    function of the service time distribution. We derive bounds for the convergence
    rates in special cases. The proofs use the coupling method.'
author:
- first_name: Martin
  full_name: Kolb, Martin
  id: '48880'
  last_name: Kolb
- first_name: Wolfgang
  full_name: Stadje, Wolfgang
  last_name: Stadje
- first_name: Achim
  full_name: Wübker, Achim
  last_name: Wübker
citation:
  ama: Kolb M, Stadje W, Wübker A. The rate of convergence to stationarity for M/G/1
    models with admission controls via coupling. <i>Stochastic Models</i>. 2015;32(1):121-135.
    doi:<a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>
  apa: Kolb, M., Stadje, W., &#38; Wübker, A. (2015). The rate of convergence to stationarity
    for M/G/1 models with admission controls via coupling. <i>Stochastic Models</i>,
    <i>32</i>(1), 121–135. <a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>
  bibtex: '@article{Kolb_Stadje_Wübker_2015, title={The rate of convergence to stationarity
    for M/G/1 models with admission controls via coupling}, volume={32}, DOI={<a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>},
    number={1}, journal={Stochastic Models}, publisher={INFORMS}, author={Kolb, Martin
    and Stadje, Wolfgang and Wübker, Achim}, year={2015}, pages={121–135} }'
  chicago: 'Kolb, Martin, Wolfgang Stadje, and Achim Wübker. “The Rate of Convergence
    to Stationarity for M/G/1 Models with Admission Controls via Coupling.” <i>Stochastic
    Models</i> 32, no. 1 (2015): 121–35. <a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>.'
  ieee: 'M. Kolb, W. Stadje, and A. Wübker, “The rate of convergence to stationarity
    for M/G/1 models with admission controls via coupling,” <i>Stochastic Models</i>,
    vol. 32, no. 1, pp. 121–135, 2015, doi: <a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>.'
  mla: Kolb, Martin, et al. “The Rate of Convergence to Stationarity for M/G/1 Models
    with Admission Controls via Coupling.” <i>Stochastic Models</i>, vol. 32, no.
    1, INFORMS, 2015, pp. 121–35, doi:<a href="http://dx.doi.org/10.1080/15326349.2015.1090322">http://dx.doi.org/10.1080/15326349.2015.1090322</a>.
  short: M. Kolb, W. Stadje, A. Wübker, Stochastic Models 32 (2015) 121–135.
date_created: 2022-09-14T04:52:15Z
date_updated: 2022-09-14T04:52:19Z
department:
- _id: '96'
doi: http://dx.doi.org/10.1080/15326349.2015.1090322
intvolume: '        32'
issue: '1'
language:
- iso: eng
page: 121-135
publication: Stochastic Models
publication_status: published
publisher: INFORMS
status: public
title: The rate of convergence to stationarity for M/G/1 models with admission controls
  via coupling
type: journal_article
user_id: '85821'
volume: 32
year: '2015'
...