IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v17y2017i2d10.1007_s12351-016-0248-7.html
   My bibliography  Save this article

Performance analysis of an M/G/1 retrial queue with general retrial time, modified M-vacations and collision

Author

Listed:
  • V. Jailaxmi

    (PSG Institute of Technology and Applied Research)

  • R. Arumuganathan

    (PSG College of Technology)

  • M. Senthil Kumar

    (PSG College of Technology)

Abstract

In this paper, a single server retrial queue with general retrial time and collisions of customers with modified M-vacations is studied. The primary calls arrive according to Poisson process with rate λ. If the server is free, the arriving customer/the customer from orbit gets served completely and leaves the system. If the server is busy, arriving customer collides with the customer in service resulting in both being shifted to the orbit. After the collision the server becomes idle. If the orbit is empty the server takes at most M vacations until at least one customer is recorded in the orbit when the server returns from a vacation. Whenever the orbit is empty the server leaves for a vacation of random length V. If no customers appear in the orbit when the server returns from vacation he again leaves for another vacation with the same length. This pattern continues until he returns from a vacation to find at least one customer recorded in the orbit or he has already taken M vacations. If the orbit is empty by the end of the Mth vacation, the server remains idle for customers in the system. The time between two successive retrials from the orbit is assumed to be general with arbitrary distribution R(t). By applying the supplementary variables method, the probability generating function of number of customers in the orbit is derived. Some special cases are also discussed. A numerical illustration is also presented.

Suggested Citation

  • V. Jailaxmi & R. Arumuganathan & M. Senthil Kumar, 2017. "Performance analysis of an M/G/1 retrial queue with general retrial time, modified M-vacations and collision," Operational Research, Springer, vol. 17(2), pages 649-667, July.
    • Handle: RePEc:spr:operea:v:17:y:2017:i:2:d:10.1007_s12351-016-0248-7
    DOI: 10.1007/s12351-016-0248-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-016-0248-7
    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/s12351-016-0248-7?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. Li, Hui & Yang, Tao, 1995. "A single-server retrial queue with server vacations and a finite number of input sources," European Journal of Operational Research, Elsevier, vol. 85(1), pages 149-160, August.
    2. A. G. Pakes, 1969. "Some Conditions for Ergodicity and Recurrence of Markov Chains," Operations Research, INFORMS, vol. 17(6), pages 1058-1061, December.
    3. J. Artalejo, 1999. "A classified bibliography of research on retrial queues: Progress in 1990–1999," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 187-211, December.
    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. Sanga, Sudeep Singh & Jain, Madhu, 2019. "Cost optimization and ANFIS computing for admission control of M/M/1/K queue with general retrial times and discouragement," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    2. Lamia Lakaour & Djamil Aïssani & Karima Adel-Aissanou & Kamel Barkaoui, 2019. "M/M/1 Retrial Queue with Collisions and Transmission Errors," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1395-1406, December.

    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. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    2. T. Deepak, 2015. "On a retrial queueing model with single/batch service and search of customers from the orbit," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 493-520, July.
    3. Ioannis Dimitriou, 2013. "A preemptive resume priority retrial queue with state dependent arrivals, unreliable server and negative customers," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(3), pages 542-571, October.
    4. I. Atencia & G. Bouza & P. Moreno, 2008. "An M [X] /G/1 retrial queue with server breakdowns and constant rate of repeated attempts," Annals of Operations Research, Springer, vol. 157(1), pages 225-243, January.
    5. Sanga, Sudeep Singh & Jain, Madhu, 2019. "Cost optimization and ANFIS computing for admission control of M/M/1/K queue with general retrial times and discouragement," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    6. 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.
    7. 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.
    8. Haque, Lani & Armstrong, Michael J., 2007. "A survey of the machine interference problem," European Journal of Operational Research, Elsevier, vol. 179(2), pages 469-482, June.
    9. Bin Liu & Jie Min & Yiqiang Q. Zhao, 2023. "Refined tail asymptotic properties for the $$M^X/G/1$$ M X / G / 1 retrial queue," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 65-105, June.
    10. Gao, Shan & Wang, Jinting, 2014. "Performance and reliability analysis of an M/G/1-G retrial queue with orbital search and non-persistent customers," European Journal of Operational Research, Elsevier, vol. 236(2), pages 561-572.
    11. Wang, Jinting & Liu, Bin & Li, Jianghua, 2008. "Transient analysis of an M/G/1 retrial queue subject to disasters and server failures," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1118-1132, September.
    12. Baumann, Hendrik & Sandmann, Werner, 2014. "On finite long run costs and rewards in infinite Markov chains," Statistics & Probability Letters, Elsevier, vol. 91(C), pages 41-46.
    13. 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.
    14. Falin, G.I., 2010. "A single-server batch arrival queue with returning customers," European Journal of Operational Research, Elsevier, vol. 201(3), pages 786-790, March.
    15. 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.
    16. Li, Hui & Yang, Tao, 1998. "Geo/G/1 discrete time retrial queue with Bernoulli schedule," European Journal of Operational Research, Elsevier, vol. 111(3), pages 629-649, December.
    17. Shweta Upadhyaya, 2020. "Investigating a general service retrial queue with damaging and licensed units: an application in local area networks," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 716-745, September.
    18. Rami Atar & Anat Lev-Ari, 2018. "Optimizing buffer size for the retrial queue: two state space collapse results in heavy traffic," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 225-255, December.
    19. 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.
    20. R. Harini & K. Indhira, 2024. "Dynamical modelling and cost optimization of a 5G base station for energy conservation using feedback retrial queue with sleeping strategy," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 86(4), pages 661-690, August.

    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:operea:v:17:y:2017:i:2:d:10.1007_s12351-016-0248-7. 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.