IDEAS home Printed from https://ideas.repec.org/a/ids/ijmore/v15y2019i1p92-109.html
   My bibliography  Save this article

Exact stationary solution for a fluid queue driven by an M/M/ 1 queue with disaster and subsequent repair

Author

Listed:
  • K.V. Vijayashree
  • A. Anjuka

Abstract

This paper deals with the stationary analysis of a fluid queuing model driven by an M/M/1 queue subject to disaster and subsequent repair. Further, arrivals are allowed to join the background queuing model during the period of repair at a slower rate as compared to the arrivals during regular busy period of the server. Such a model was analysed earlier by Ammar (2014), however the model formulation and hence the main results are found to be incorrect. In this paper, the assumptions are suitably modified to ensure correctness, detailed mathematical analysis is carried out to find an explicit analytical expression for the buffer content distribution. The underlying system of differential difference equations that govern the process are solved using Laplace transform and generating function methodologies. The closed form expressions for the joint steady state probabilities of the state of the background queuing model and the content of the buffer are obtained in terms of modified Bessel function of the first kind.

Suggested Citation

  • K.V. Vijayashree & A. Anjuka, 2019. "Exact stationary solution for a fluid queue driven by an M/M/ 1 queue with disaster and subsequent repair," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 15(1), pages 92-109.
    • Handle: RePEc:ids:ijmore:v:15:y:2019:i:1:p:92-109
    as

    Download full text from publisher

    File URL: http://www.inderscience.com/link.php?id=101614
    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.

    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:92-109. 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.