IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v201y2012i1p307-32310.1007-s10479-012-1254-7.html
   My bibliography  Save this article

Computation of the steady state distribution for multi-server retrial queues with phase type service process

Author

Listed:
  • Che Kim
  • Vilena Mushko
  • Alexander Dudin

Abstract

We consider a multi-server retrial queueing system with the Batch Markovian Arrival Process and phase type service time distribution. Such a general queueing system suits for modeling and decision making in many real life objects including modern wireless communication networks. Behavior of such a system is described by the level dependent multi-dimensional Markov chain. Blocks of the generator of this chain, which is the block structured matrix of infinite size, can have large size if the number of servers is large and distribution of service time is not exponential. Due to this fact, the existing in literature algorithms allow to compute key performance measures of such a system only for a small number of servers. Here we describe the algorithm that allows to compute the stationary distribution of the system for larger number of servers and numerically illustrate its advantage. Importance of taking into account correlation in the arrival process is numerically demonstrated. Copyright Springer Science+Business Media New York 2012

Suggested Citation

  • Che Kim & Vilena Mushko & Alexander Dudin, 2012. "Computation of the steady state distribution for multi-server retrial queues with phase type service process," Annals of Operations Research, Springer, vol. 201(1), pages 307-323, December.
    • Handle: RePEc:spr:annopr:v:201:y:2012:i:1:p:307-323:10.1007/s10479-012-1254-7
    DOI: 10.1007/s10479-012-1254-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10479-012-1254-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10479-012-1254-7?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. Valentina I. Klimenok & Dmitry S. Orlovsky & Alexander N. Dudin, 2007. "Abmap/Ph/Nsystem With Impatient Repeated Calls," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 24(03), pages 293-312.
    2. A. Gómez-Corral, 2006. "A bibliographical guide to the analysis of retrial queues through matrix analytic techniques," Annals of Operations Research, Springer, vol. 141(1), pages 163-191, January.
    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. 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.
    2. Alexander Moiseev & Anatoly Nazarov & Svetlana Paul, 2020. "Asymptotic Diffusion Analysis of Multi-Server Retrial Queue with Hyper-Exponential Service," Mathematics, MDPI, vol. 8(4), pages 1-16, April.
    3. Samira Taleb & Amar Aissani, 2016. "Preventive maintenance in an unreliable M/G/1 retrial queue with persistent and impatient customers," Annals of Operations Research, Springer, vol. 247(1), pages 291-317, December.
    4. Alexander N. Dudin & Sergey A. Dudin & Valentina I. Klimenok & Olga S. Dudina, 2024. "Stability of Queueing Systems with Impatience, Balking and Non-Persistence of Customers," Mathematics, MDPI, vol. 12(14), pages 1-16, July.
    5. K. R. Rejitha & K. P. Jose, 2018. "A stochastic inventory system with two modes of service and retrial of customers," OPSEARCH, Springer;Operational Research Society of India, vol. 55(1), pages 134-149, March.
    6. Qi-Ming He & Attahiru Sule Alfa, 2018. "Space Reduction for a Class of Multidimensional Markov Chains: A Summary and Some Applications," INFORMS Journal on Computing, INFORMS, vol. 30(1), pages 1-10, February.
    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.
    8. Wanlu Gu & Neng Fan & Haitao Liao, 2019. "Evaluating readmission rates and discharge planning by analyzing the length-of-stay of patients," Annals of Operations Research, Springer, vol. 276(1), pages 89-108, May.
    9. Alexander Dudin & Chesoong Kim & Olga Dudina & Sergey Dudin, 2016. "Multi-server queueing system with a generalized phase-type service time distribution as a model of call center with a call-back option," Annals of Operations Research, Springer, vol. 239(2), pages 401-428, April.
    10. 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.

    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. Chesoong Kim & Valentina Klimenok & Alexander Dudin, 2014. "A G/M/1 retrial queue with constant retrial rate," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 509-529, July.
    2. Ioannis Dimitriou, 2016. "A queueing model with two classes of retrial customers and paired services," Annals of Operations Research, Springer, vol. 238(1), pages 123-143, March.
    3. B. Krishna Kumar & R. Sankar & R. Navaneetha Krishnan & R. Rukmani, 2022. "Performance Analysis of Multi-processor Two-Stage Tandem Call Center Retrial Queues with Non-Reliable Processors," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 95-142, March.
    4. Kim, Chesoong & Klimenok, Valentina I. & Orlovsky, Dmitry S., 2008. "The BMAP/PH/N retrial queue with Markovian flow of breakdowns," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1057-1072, September.
    5. Efrosinin, Dmitry & Winkler, Anastasia, 2011. "Queueing system with a constant retrial rate, non-reliable server and threshold-based recovery," European Journal of Operational Research, Elsevier, vol. 210(3), pages 594-605, May.
    6. Valentina I. Klimenok & Alexander N. Dudin & Vladimir M. Vishnevsky & Olga V. Semenova, 2022. "Retrial BMAP / PH / N Queueing System with a Threshold-Dependent Inter-Retrial Time Distribution," Mathematics, MDPI, vol. 10(2), pages 1-21, January.
    7. C. D’Apice & A. N. Dudin & O. S. Dudina & R. Manzo, 2024. "Analysis of Queueing System with Dynamic Rating-Dependent Arrival Process and Price of Service," Mathematics, MDPI, vol. 12(7), pages 1-20, April.
    8. Artalejo, J.R. & Economou, A. & Lopez-Herrero, M.J., 2007. "Algorithmic approximations for the busy period distribution of the M/M/c retrial queue," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1687-1702, February.
    9. Lyes Ikhlef & Ouiza Lekadir & Djamil Aïssani, 2016. "MRSPN analysis of Semi-Markovian finite source retrial queues," Annals of Operations Research, Springer, vol. 247(1), pages 141-167, December.
    10. Ioannis Dimitriou, 2016. "A queueing model with two classes of retrial customers and paired services," Annals of Operations Research, Springer, vol. 238(1), pages 123-143, March.
    11. Tuan Phung-Duc & Hiroyuki Masuyama & Shoji Kasahara & Yutaka Takahashi, 2013. "A matrix continued fraction approach to multiserver retrial queues," Annals of Operations Research, Springer, vol. 202(1), pages 161-183, January.
    12. Anastasia Winkler, 2013. "Dynamic scheduling of a single-server two-class queue with constant retrial policy," Annals of Operations Research, Springer, vol. 202(1), pages 197-210, January.
    13. Alexander N. Dudin & Sergey A. Dudin & Valentina I. Klimenok & Olga S. Dudina, 2024. "Stability of Queueing Systems with Impatience, Balking and Non-Persistence of Customers," Mathematics, MDPI, vol. 12(14), pages 1-16, July.

    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:annopr:v:201:y:2012:i:1:p:307-323:10.1007/s10479-012-1254-7. 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.