IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v250y2015icp287-297.html
   My bibliography  Save this article

Algorithmic approach to Markovian multi-server retrial queues with vacations

Author

Listed:
  • Shin, Yang Woo

Abstract

There are many practical situations that have both features of customer retrials and server vacations. The vacation policy is characterized by the vacation startup rules and vacation termination rules. The queueing system with retrials and vacations has been described in variety of ways according to the vacation rules and retrial policies such as constant retrial policy and linear retrial policy and analyzed for each specific model. In this paper, we model the Markovian multi-server queues with customers’ retrials and vacations with level dependent quasi-birth-and-death (LDQBD) process in a unified manner and present an algorithmic approach to compute the performance measures of the system.

Suggested Citation

  • Shin, Yang Woo, 2015. "Algorithmic approach to Markovian multi-server retrial queues with vacations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 287-297.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:287-297
    DOI: 10.1016/j.amc.2014.10.079
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300314014544
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2014.10.079?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. 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.
    2. Srinivas R. Chakravarthy, 2009. "Analysis Of A Multi-Server Queue With Markovian Arrivals And Synchronous Phase Type Vacations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(01), pages 85-113.
    3. Yang Woo Shin, 2009. "Fundamental Matrix Of Transient Qbd Generator With Finite States And Level Dependent Transitions," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(05), pages 697-714.
    4. Vladimir Anisimov & Jesus Artalejo, 2002. "Approximation of multiserver retrial queues by means of generalized truncated models," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 51-66, June.
    5. Jeffrey Diamond & Attahiru Alfa, 1999. "Matrix analytic methods for a multi-server retrial queue with buffer," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 249-266, December.
    6. Tuan Phung-Duc & Ken'Ichi Kawanishi, 2014. "An Efficient Method For Performance Analysis Of Blended Call Centers With Redial," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-33.
    7. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
    8. J.R. Artalejo & M. Pozo, 2002. "Numerical Calculation of the Stationary Distribution of the Main Multiserver Retrial Queue," Annals of Operations Research, Springer, vol. 116(1), pages 41-56, October.
    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. Shekhar, Chandra & Kumar, Neeraj & Gupta, Amit & Kumar, Amit & Varshney, Shreekant, 2020. "Warm-spare provisioning computing network with switching failure, common cause failure, vacation interruption, and synchronized reneging," Reliability Engineering and System Safety, Elsevier, vol. 199(C).
    2. Gabi Hanukov & Michael Hassoun & Oren Musicant, 2021. "On the Benefits of Providing Timely Information in Ticket Queues with Balking and Calling Times," Mathematics, MDPI, vol. 9(21), pages 1-16, October.

    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. Vyacheslav Abramov, 2006. "Analysis of multiserver retrial queueing system: A martingale approach and an algorithm of solution," Annals of Operations Research, Springer, vol. 141(1), pages 19-50, January.
    2. Chakravarthy, Srinivas R. & Shruti, & Kulshrestha, Rakhee, 2020. "A queueing model with server breakdowns, repairs, vacations, and backup server," Operations Research Perspectives, Elsevier, vol. 7(C).
    3. B. Krishna Kumar & R. Sankar & R. Navaneetha Krishnan & R. Rukmani, 2023. "Multiserver call center retrial queue under Bernoulli vacation schedule with two-way communication and orbital search," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 84(1), pages 23-51, September.
    4. 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.
    5. 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.
    6. 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.
    7. Alka Choudhary & Srinivas R. Chakravarthy & Dinesh C. Sharma, 2021. "Analysis of MAP / PH /1 Queueing System with Degrading Service Rate and Phase Type Vacation," Mathematics, MDPI, vol. 9(19), pages 1-17, September.
    8. Priyanka Kalita & Gautam Choudhury & Dharmaraja Selvamuthu, 2020. "Analysis of Single Server Queue with Modified Vacation Policy," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 511-553, June.
    9. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    10. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    11. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    12. Yi Peng & Jinbiao Wu, 2020. "A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations," Mathematics, MDPI, vol. 8(8), pages 1-12, July.
    13. Niek Baer & Ahmad Al Hanbali & Richard J. Boucherie & Jan-Kees van Ommeren, 2022. "A successive censoring algorithm for a system of connected LDQBD-processes," Annals of Operations Research, Springer, vol. 310(2), pages 389-410, March.
    14. Srinivas R. Chakravarthy & Serife Ozkar, 2016. "Crowdsourcing and Stochastic Modeling," Business and Management Research, Business and Management Research, Sciedu Press, vol. 5(2), pages 19-30, June.
    15. Zsolt Saffer & Sergey Andreev & Yevgeni Koucheryavy, 2016. "$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network," Annals of Operations Research, Springer, vol. 239(2), pages 497-520, April.
    16. Shunfu Jin & Xiuchen Qie & Wenjuan Zhao & Wuyi Yue & Yutaka Takahashi, 2020. "A clustered virtual machine allocation strategy based on a sleep-mode with wake-up threshold in a cloud environment," Annals of Operations Research, Springer, vol. 293(1), pages 193-212, October.
    17. Ding, S. & Koole, G. & van der Mei, R.D., 2015. "On the estimation of the true demand in call centers with redials and reconnects," European Journal of Operational Research, Elsevier, vol. 246(1), pages 250-262.
    18. Amina Angelika Bouchentouf & Abdelhak Guendouzi, 2021. "Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers," SN Operations Research Forum, Springer, vol. 2(1), pages 1-23, March.
    19. F. P. Barbhuiya & U. C. Gupta, 2020. "A Discrete-Time GIX/Geo/1 Queue with Multiple Working Vacations Under Late and Early Arrival System," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 599-624, June.
    20. Alexander Dudin & Sergei Dudin & Valentina Klimenok & Yuliya Gaidamaka, 2021. "Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption," Mathematics, MDPI, vol. 9(13), pages 1-15, 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:eee:apmaco:v:250:y:2015:i:c:p:287-297. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.