IDEAS home Printed from https://ideas.repec.org/a/hin/jnijsa/9152701.html
   My bibliography  Save this article

Analysis of a Priority Queue with Phase-Type Service and Failures

Author

Listed:
  • Alexander Dudin
  • Sergei Dudin

Abstract

We consider a single server queue with two types of customers. We propose a discipline of flexible priority in access that combines the features of randomization and the threshold type control. We introduce a new class of distributions, phase-type with failures ( ) distribution, that generalizes the well-known phase-type ( ) distribution to the case when failures can occur during service of a customer. The arrival flow is described by the marked Markovian arrival process. The service time distribution is of type with the parameters depending on the type of a customer. Customers of both types can be impatient. Behavior of the system is described by the multidimensional Markov chain. Problem of existence and computation of the stationary distribution of this Markov chain is discussed in brief as well as the problem of computation of the key performance measures of the system. Numerical examples are presented that give some insight into behavior of the system performance measures under different values of the parameters defining the strategy of customers access to service.

Suggested Citation

  • Alexander Dudin & Sergei Dudin, 2016. "Analysis of a Priority Queue with Phase-Type Service and Failures," International Journal of Stochastic Analysis, Hindawi, vol. 2016, pages 1-11, July.
    • Handle: RePEc:hin:jnijsa:9152701
    DOI: 10.1155/2016/9152701
    as

    Download full text from publisher

    File URL: http://downloads.hindawi.com/journals/IJSA/2016/9152701.pdf
    Download Restriction: no
    File URL: http://downloads.hindawi.com/journals/IJSA/2016/9152701.xml
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2016/9152701?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. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Single-Server Multi-Class Queue with Unreliable Service, Batch Correlated Arrivals, Customers Impatience, and Dynamical Change of Priorities," Mathematics, MDPI, vol. 9(11), pages 1-17, May.
    2. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Multi-Server Queue with Self-Sustained Servers," Mathematics, MDPI, vol. 9(17), pages 1-18, September.
    3. Sergei Dudin & Olga Dudina & Konstantin Samouylov & Alexander Dudin, 2020. "Improvement of the Fairness of Non-Preemptive Priorities in the Transmission of Heterogeneous Traffic," Mathematics, MDPI, vol. 8(6), pages 1-17, June.
    4. A. N. Dudin & S. A. Dudin & O. S. Dudina, 2023. "Randomized Threshold Strategy for Providing Flexible Priority in Multi-Server Queueing System with a Marked Markov Arrival Process and Phase-Type Distribution of Service Time," Mathematics, MDPI, vol. 11(12), pages 1-23, June.
    5. Sally McClean, 2021. "Using Markov Models to Characterize and Predict Process Target Compliance," Mathematics, MDPI, vol. 9(11), pages 1-12, 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:9152701. 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.