IDEAS home Printed from https://ideas.repec.org/a/hin/jnijsa/582154.html
   My bibliography  Save this article

A first passage problem and its applications to the analysis of a class of stochastic models

Author

Listed:
  • Lev Abolnikov
  • Jewgeni H. Dshalalow

Abstract

A problem of the first passage of a cumulative random process with generally distributed discrete or continuous increments over a fixed level is considered in the article as an essential part of the analysis of a class of stochastic models (bulk queueing systems, inventory control and dam models). Using direct probability methods the authors find various characteristics of this problem: the magnitude of the first excess of the process over a fixed level, the shortage before the first excess, the levels of the first and pre-first excesses, the index of the first excess and others. The results obtained are illustrated by a number of numerical examples and then are applied to a bulk queueing system with a service delay discipline.

Suggested Citation

  • Lev Abolnikov & Jewgeni H. Dshalalow, 1992. "A first passage problem and its applications to the analysis of a class of stochastic models," International Journal of Stochastic Analysis, Hindawi, vol. 5, pages 1-15, January.
    • Handle: RePEc:hin:jnijsa:582154
    DOI: 10.1155/S1048953392000066
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJSA/5/582154.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJSA/5/582154.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/S1048953392000066?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Citations

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


    Cited by:

    1. Jewgeni H. Dshalalow & Ryan T. White, 2021. "Current Trends in Random Walks on Random Lattices," Mathematics, MDPI, vol. 9(10), pages 1-38, May.

    More about this item

    Statistics

    Access and download statistics

    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:hin:jnijsa:582154. 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: Mohamed Abdelhakeem (email available below). General contact details of provider: https://www.hindawi.com .

    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.