IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v25y2023i2d10.1007_s11009-023-10042-1.html
   My bibliography  Save this article

Analysis of a Queueing System with Mixed Service Discipline

Author

Listed:
  • Alexander Dudin

    (Belarusian State University)

  • Sergei Dudin

    (Belarusian State University)

  • Olga Dudina

    (Belarusian State University)

Abstract

In this paper, we analyse a queueing model with two types of requests arriving in a marked Markov arrival process. Type-1 requests require a constant service rate, while type-2 requests admit a flexible service rate. Mixed service discipline is considered. It is defined as follows. The number of type-1 requests that can be processed by the system simultaneously is restricted. Type-2 requests receive service according to the classical processor sharing discipline and use all currently available (not occupied by type-1 requests) system bandwidth. Type-2 requests can be impatient and leave the system without receiving complete service. The system behavior is described by a multidimensional Markov chain. The infinitesimal generator of this chain is derived. The transparent ergodicity condition is obtained, and the stationary performance measures of the system are computed. A numerical example is presented, including consideration of the problem of choosing the optimal values of the system bandwidth and its share dedicated to the service of type-1 requests.

Suggested Citation

  • Alexander Dudin & Sergei Dudin & Olga Dudina, 2023. "Analysis of a Queueing System with Mixed Service Discipline," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-19, June.
    • Handle: RePEc:spr:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10042-1
    DOI: 10.1007/s11009-023-10042-1
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-023-10042-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-023-10042-1?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.

    References listed on IDEAS

    as
    1. Mor Harchol-Balter, 2021. "Open problems in queueing theory inspired by datacenter computing," Queueing Systems: Theory and Applications, Springer, vol. 97(1), pages 3-37, February.
    2. Arnaud Devos & Joris Walraevens & Dieter Fiems & Herwig Bruneel, 2021. "Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue," Mathematics, MDPI, vol. 9(21), pages 1-25, October.
    3. Kim, Chesoong & Dudin, Alexander & Dudina, Olga & Dudin, Sergey, 2014. "Tandem queueing system with infinite and finite intermediate buffers and generalized phase-type service time distribution," European Journal of Operational Research, Elsevier, vol. 235(1), pages 170-179.
    4. R. Núñez-Queija & O. J. Boxma, 1998. "Analysis of a multi-server queueing model of ABR," International Journal of Stochastic Analysis, Hindawi, vol. 11, pages 1-16, January.
    5. Dudin, A.N. & Dudin, S.A. & Dudina, O.S. & Samouylov, K.E., 2018. "Analysis of queueing model with processor sharing discipline and customers impatience," Operations Research Perspectives, Elsevier, vol. 5(C), pages 245-255.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Mario Lefebvre, 2024. "A Controlled Discrete-Time Queueing System as a Model for the Orders of Two Competing Companies," Games, MDPI, vol. 15(3), pages 1-8, May.
    2. Sindhu S & Achyutha Krishnamoorthy & Dmitry Kozyrev, 2023. "A Two-Server Queue with Interdependence between Arrival and Service Processes," Mathematics, MDPI, vol. 11(22), pages 1-25, November.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Youri Raaijmakers & Sem Borst & Onno Boxma, 2023. "Fork–join and redundancy systems with heavy-tailed job sizes," Queueing Systems: Theory and Applications, Springer, vol. 103(1), pages 131-159, February.
    2. Samuli Aalto & Ziv Scully, 2023. "Minimizing the mean slowdown in the M/G/1 queue," Queueing Systems: Theory and Applications, Springer, vol. 104(3), pages 187-210, August.
    3. Neil Walton, 2022. "Queueing: a perennial theory," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 557-559, April.
    4. Pala, Ali & Zhuang, Jun, 2018. "Security screening queues with impatient applicants: A new model with a case study," European Journal of Operational Research, Elsevier, vol. 265(3), pages 919-930.
    5. Sergei A. Dudin & Olga S. Dudina & Olga I. Kostyukova, 2023. "Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    6. Baumann, Hendrik & Sandmann, Werner, 2017. "Multi-server tandem queue with Markovian arrival process, phase-type service times, and finite buffers," European Journal of Operational Research, Elsevier, vol. 256(1), pages 187-195.
    7. 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.

    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:metcap:v:25:y:2023:i:2:d:10.1007_s11009-023-10042-1. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.