IDEAS home Printed from https://ideas.repec.org/a/ids/ijmore/v15y2019i1p1-25.html
   My bibliography  Save this article

Analysis of batch arrival bulk service queue with additional optional service multiple vacation and setup time

Author

Listed:
  • G. Ayyappan
  • T. Deepa

Abstract

This paper studies an M[x]/G(a, b)/1 queuing system with additional optional service, multiple vacation and setup time. After completing the first service, the customers may opt for the second service with probability α or leave the system with probability 1 − α. After completing a bulk service, if the queue size is less than 'α', then the server leaves for a vacation of random length. When he returns from the vacation, if the queue length is still less than 'α', he leaves for another vacation and so on. This process continues until he finds at least 'α' customer in the queue. After a vacation, if the server finds at least 'α' customer waiting for service, he requires a setup time 'G' to start the service. After this setup, he serves a batch of ξ customers (a ≤ ξ ≤ b). Using supplementary variable technique, the probability generating function (PGF) of the queue size, expected queue length, expected waiting time, expected busy period and expected idle period are derived. Numerical illustrations are presented to visualise the effect of system parameters.

Suggested Citation

  • G. Ayyappan & T. Deepa, 2019. "Analysis of batch arrival bulk service queue with additional optional service multiple vacation and setup time," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 15(1), pages 1-25.
    • Handle: RePEc:ids:ijmore:v:15:y:2019:i:1:p:1-25
    as

    Download full text from publisher

    File URL: http://www.inderscience.com/link.php?id=101609
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Anuradha Banerjee & Priti Lata, 2024. "Complete Analysis of $$M/G_{r}^{(a,b)}/1/N$$ M / G r ( a , b ) / 1 / N Queue with Second Optional Service," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-33, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ids:ijmore:v:15:y:2019:i:1:p:1-25. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sarah Parker (email available below). General contact details of provider: http://www.inderscience.com/browse/index.php?journalID=320 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.