IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i23p3722-d1530910.html
   My bibliography  Save this article

An M/G/1 Queue with Repeated Orbit While in Service

Author

Listed:
  • Gabi Hanukov

    (Department of Industrial Engineering & Management, Ariel University, Ariel 40700, Israel)

  • Yonit Barron

    (Department of Industrial Engineering & Management, Ariel University, Ariel 40700, Israel)

  • Uri Yechiali

    (Department of Statistics and Operations Research, Tel Aviv University, Tel Aviv 69978, Israel)

Abstract

Orbit and retrial queues have been studied extensively in the literature. A key assumption in most of these works is that customers “go to orbit” when they are blocked upon arrival. However, real-life situations exist in which customers opt to go to orbit to efficiently use their orbit time rather than residing dormant at the service station while waiting for their service to be completed. This paper studies such a system, extending the scope of traditional orbit and retrial queues. We consider an M/G/1 queue where customers repeatedly go to orbit while their service remains in progress. That is, if a customer’s service is not completed by within a specified “patience time”, the customer goes to orbit for a random “orbit time”. When the customer orbits, the server continues rendering her/his service. If, on return, the service is already completed, the customer leaves the system. Otherwise, s/he waits for another patience time. This policy is repeated until service completion. We analyze such an intricate system by applying the supplementary variable technique and using Laplace–Stieltjes transforms. Performance measures are derived, and a comparison analysis is provided between various service time distributions.

Suggested Citation

  • Gabi Hanukov & Yonit Barron & Uri Yechiali, 2024. "An M/G/1 Queue with Repeated Orbit While in Service," Mathematics, MDPI, vol. 12(23), pages 1-22, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:23:p:3722-:d:1530910
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/23/3722/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/12/23/3722/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Sapana Sharma & Rakesh Kumar & Bhavneet Singh Soodan & Pradeep Singh, 2023. "Queuing models with customers' impatience: a survey," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 26(4), pages 523-547.
    2. Antonio Gómez-Corral & Tuan Phung-Duc, 2016. "Retrial queues and related models," Annals of Operations Research, Springer, vol. 247(1), pages 1-2, December.
    3. Dieter Fiems, 2023. "Retrial queues with constant retrial times," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 347-365, April.
    4. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, July-Dece.
    5. Gabi Hanukov & Shoshana Anily & Uri Yechiali, 2020. "Ticket queues with regular and strategic customers," Queueing Systems: Theory and Applications, Springer, vol. 95(1), pages 145-171, June.
    6. Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.
    7. C. Knessl & B. J. Matkowsky & Z. Schuss & C. Tier, 1990. "An Integral Equation Approach to the M/G/2 Queue," Operations Research, INFORMS, vol. 38(3), pages 506-518, June.
    8. Yu Zhang & Jinting Wang, 2023. "Managing retrial queueing systems with boundedly rational customers," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 74(3), pages 748-761, March.
    9. Kathirvel Jeganathan & Thanushkodi Harikrishnan & Kumarasankaralingam Lakshmanan & Agassi Melikov & Janos Sztrik, 2023. "Modeling of Junior Servers Approaching a Senior Server in the Retrial Queuing-Inventory System," Mathematics, MDPI, vol. 11(22), pages 1-31, November.
    Full references (including those not matched with items on IDEAS)

    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. Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.
    2. Wei Xu & Liwei Liu & Linhong Li & Zhen Wang & Sabine Wittevrongel, 2023. "Analysis of a Collision-Affected M/GI/1/ /N Retrial Queuing System Considering Negative Customers and Transmission Errors," Mathematics, MDPI, vol. 11(16), pages 1-23, August.
    3. KM Rashmi & S. K. Samanta, 2024. "Analysis of Two-Way Communication in $$M_1^X, M_2/G_1,G_2/1$$ M 1 X , M 2 / G 1 , G 2 / 1 Retrial Queue Under the Constant Retrial Policy," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-32, December.
    4. Sem Borst & Onno Boxma, 2018. "Polling: past, present, and perspective," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 335-369, October.
    5. 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.
    6. Manickam Vadivukarasi & Kaliappan Kalidass, 2021. "Discussion on the transient behavior of single server Markovian multiple variant vacation queues," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 31(1), pages 123-146.
    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. 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.
    9. Houyuan Jiang & Zhan Pang & Sergei Savin, 2012. "Performance-Based Contracts for Outpatient Medical Services," Manufacturing & Service Operations Management, INFORMS, vol. 14(4), pages 654-669, October.
    10. Shan Gao & Zaiming Liu & Qiwen Du, 2014. "Discrete-Time Gix/Geo/1/N Queue With Working Vacations And Vacation Interruption," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(01), pages 1-22.
    11. Wee Meng Yeo & Xue-Ming Yuan & Joyce Mei Wan Low, 2017. "On $$M^{X}/G(M/H)/1$$ M X / G ( M / H ) / 1 retrial system with vacation: service helpline performance measurement," Annals of Operations Research, Springer, vol. 248(1), pages 553-578, January.
    12. Anatoly Nazarov & János Sztrik & Anna Kvach & Ádám Tóth, 2020. "Asymptotic sojourn time analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs," Annals of Operations Research, Springer, vol. 288(1), pages 417-434, May.
    13. Müller, Reinhard & Talkner, Peter & Reimann, Peter, 1997. "Rates and mean first passage times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 247(1), pages 338-356.
    14. 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.
    15. Pengfei Guo & Zhe George Zhang, 2013. "Strategic Queueing Behavior and Its Impact on System Performance in Service Systems with the Congestion-Based Staffing Policy," Manufacturing & Service Operations Management, INFORMS, vol. 15(1), pages 118-131, September.
    16. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
    17. Ambika, K. & Vijayashree, K.V. & Janani, B., 2024. "Modelling and analysis of production management system using vacation queueing theoretic approach," Applied Mathematics and Computation, Elsevier, vol. 479(C).
    18. Achyutha Krishnamoorthy & Anu Nuthan Joshua & Dmitry Kozyrev, 2021. "Analysis of a Batch Arrival, Batch Service Queuing-Inventory System with Processing of Inventory While on Vacation," Mathematics, MDPI, vol. 9(4), pages 1-29, February.
    19. 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.
    20. 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.

    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:gam:jmathe:v:12:y:2024:i:23:p:3722-:d:1530910. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.