Swinburne
Browse

Analysis of multiserver retrial queueing system: a martingale approach and an algorithm of solution

Download (371.5 kB)
journal contribution
posted on 2024-07-13, 05:59 authored by Vyacheslav M. Abramov
The paper studies a multiserver retrial queueing system withm servers. Arrival process is a point process with strictly stationary and ergodic increments. A customer arriving to the system occupies one of the free servers. If upon arrival all servers are busy, then the customer goes to the secondary queue, orbit, and after some random time retries more and more to occupy a server. A service time of each customer is exponentially distributed random variable with parameter μ1. A time between retrials is exponentially distributed with parameter μ2 for each customer. Using a martingale approach the paper provides an analysis of this system. The paper establishes the stability condition and studies a behavior of the limiting queue-length distributions as μ2 increases to infinity. As μ2→∞, the paper also proves the convergence of appropriate queue-length distributions to those of the associated “usual” multiserver queueing system without retrials. An algorithm for numerical solution of the equations, associated with the limiting queue-length distribution of retrial systems, is provided.

History

Available versions

PDF (Accepted manuscript)

ISSN

0254-5330

Journal title

Annals of Operations Research

Volume

141

Pagination

31 pp

Publisher

Springer

Copyright statement

Copyright © 2006 Springer Science + Business Media, Inc. The accepted manuscript is reproduced in accordance with the copyright policy of the publisher. The definitive version is available at www.springer.com.

Language

eng

Usage metrics

    Publications

    Categories

    No categories selected

    Keywords

    Exports

    RefWorks
    BibTeX
    Ref. manager
    Endnote
    DataCite
    NLM
    DC