IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-3-642-11492-2_5.html
   My bibliography  Save this book chapter

Markov Chains on Continuous State Space

In: Constructive Computation in Stochastic Models with Applications

Author

Listed:
  • Quan-Lin Li

    (Tsinghua University, Department of Industrial Engineering)

Abstract

In this chapter, we discuss Markov chains on continuous state space. We first analyze a discrete-time Markov chain on continuous state space, and then discuss a discrete-time Markov chain on a bivariate state space. Applying the censoring technique, we provide expression for the RG-factorizations, which are used to derive the stationary probability of the Markov chain. Further, we consider a continuous-time Markov chain on continuous state space. Specifically, we deal with a continuous-time level-dependent QBD process with continuous phase variable, and provide orthonormal representations for the R-, U- and G-measures, which lead to the matrix-structured computation of the stationary probability. As an application, we introduce continuousphase type (CPH) distribution and continuous-phase Markovian arrival process (CMAP), and then analyze a CMAP/CPH/1 queue. Finally, we study a piecewise deterministic Markov process, which is applied to deal with more general queues such as the GI/G/c queue.

Suggested Citation

  • Quan-Lin Li, 2010. "Markov Chains on Continuous State Space," Springer Books, in: Constructive Computation in Stochastic Models with Applications, chapter 5, pages 216-287, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-11492-2_5
    DOI: 10.1007/978-3-642-11492-2_5
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;
    ;

    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:spr:sprchp:978-3-642-11492-2_5. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.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.