IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v31y2014i02ns0217595914400090.html
   My bibliography  Save this article

Multiserver Retrial Queues With Two Types Of Nonpersistent Customers

Author

Listed:
  • TUAN PHUNG-DUC

    (Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Tokyo 152-8552, Japan)

Abstract

We consider M/M/c/K (K ≥ c ≥ 1) retrial queues with two types of nonpersistent customers, which are motivated from modeling of service systems such as call centers. Arriving customers that see the system fully occupied either join the orbit or abandon receiving service forever. After an exponentially distributed time in the orbit, each customer either abandons the system forever or retries to occupy a server again. For the case of K = c = 1, we present an analytical solution for the generating functions in terms of confluent hypegeometric functions. In the general case, the number of customers in the system and that in the orbit form a level-dependent quasi-birth-and-death (QBD) process whose structure is sparse. Based on this sparse structure, we develop a numerically stable algorithm to compute the joint stationary distribution. We show that the computational complexity of the algorithm is linear to the capacity of the queue. Furthermore, we present a simple fixed point approximation model for the case where the algorithm is time consuming. Numerical results show various insights into the system behavior.

Suggested Citation

  • Tuan Phung-Duc, 2014. "Multiserver Retrial Queues With Two Types Of Nonpersistent Customers," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-27.
    • Handle: RePEc:wsi:apjorx:v:31:y:2014:i:02:n:s0217595914400090
    DOI: 10.1142/S0217595914400090
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595914400090
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595914400090?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
    ---><---

    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. Phung-Duc, Tuan, 2015. "Asymptotic analysis for Markovian queues with two types of nonpersistent retrial customers," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 768-784.

    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:wsi:apjorx:v:31:y:2014:i:02:n:s0217595914400090. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    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.