IDEAS home Printed from https://ideas.repec.org/a/spr/operea/v24y2024i2d10.1007_s12351-024-00827-8.html
   My bibliography  Save this article

Orbit while in service

Author

Listed:
  • Gabi Hanukov

    (Ariel University)

  • Uri Yechiali

    (Tel Aviv University)

Abstract

In various real-life queueing systems, part of the service can be rendered without involvement or presence of the customers themselves. In those queues, customers whose service order is still in process may leave the service station, go to ‘orbit’ for a random length of time, and then return to find out if their order has been completed. Common examples are car’s annual maintenance works, food ordering, etc. In this paper, a thorough analysis of a single-server ‘orbit while in service’ queueing model with general service time is presented. Assuming an Exponentially distributed orbit time, we derive general formulae for the distributions of (i) a customer’s total residence time in the system; (ii) a customer’s net actual residence time in the system during service (not including orbit time); (iii) the time an orbiting customer is late to return, i.e., remains in orbit after his/her service has been completed; and (iv) the total number of customers in the system. Considering the family of Gamma-distributed service times (spanning the range of distributions between the Exponential and the Deterministic), as well as the Uniform distribution, we further derive explicit formulae for the distributions of the above variables. Under linear cost assumptions, the optimal mean orbit time is numerically calculated for each of the above service-time distributions. Figures depicting the behavior of the measures as functions of the parameters are presented.

Suggested Citation

  • Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.
    • Handle: RePEc:spr:operea:v:24:y:2024:i:2:d:10.1007_s12351-024-00827-8
    DOI: 10.1007/s12351-024-00827-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12351-024-00827-8
    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/s12351-024-00827-8?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. Muthukrishnan Senthil Kumar & Aresh Dadlani & Kiseon Kim, 2020. "Performance analysis of an unreliable M/G/1 retrial queue with two-way communication," Operational Research, Springer, vol. 20(4), pages 2267-2280, December.
    2. Hayriye Ayhan, 2022. "Server assignment policies in queues with customer abandonments," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 393-395, April.
    3. Anatoly Nazarov & Tuan Phung-Duc & Svetlana Paul & Olga Lizyura, 2022. "Diffusion Limit for Single-Server Retrial Queues with Renewal Input and Outgoing Calls," Mathematics, MDPI, vol. 10(6), pages 1-14, March.
    4. Shan Gao & Hua Dong & Xianchao Wang, 2021. "Correction to: Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation," Operational Research, Springer, vol. 21(1), pages 645-646, March.
    5. Jing Dong & Rouba Ibrahim, 2021. "SRPT Scheduling Discipline in Many-Server Queues with Impatient Customers," Management Science, INFORMS, vol. 67(12), pages 7708-7718, December.
    6. Mouloud Cherfaoui & Amina Angelika Bouchentouf & Mohamed Boualem, 2023. "Modelling and simulation of Bernoulli feedback queue with general customers' impatience under variant vacation policy," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 46(4), pages 451-480.
    7. Jie Liu & Jinting Wang, 2017. "Strategic joining rules in a single server Markovian queue with Bernoulli vacation," Operational Research, Springer, vol. 17(2), pages 413-434, July.
    8. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, July.
    9. S Sindhu & Achyutha Krishnamoorthy & Dmitry Kozyrev, 2023. "On Queues with Working Vacation and Interdependence in Arrival and Service Processes," Mathematics, MDPI, vol. 11(10), pages 1-16, May.
    10. 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.
    11. Mingang Yin & Ming Yan & Yu Guo & Minghe Liu, 2023. "Analysis of a Pre-Emptive Two-Priority Queuing System with Impatient Customers and Heterogeneous Servers," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    12. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.
    13. Offer Kella & Uri Yechiali, 1988. "Priorities in M/G/1 queue with server vacations," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 23-34, February.
    14. Yonatan Levy & Uri Yechiali, 1975. "Utilization of Idle Time in an M/G/1 Queueing System," Management Science, INFORMS, vol. 22(2), pages 202-211, October.
    15. Dieter Fiems, 2023. "Retrial queues with constant retrial times," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 347-365, April.
    16. 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, January.
    17. Shan Gao & Hua Dong & Xianchao Wang, 2021. "Equilibrium and pricing analysis for an unreliable retrial queue with limited idle period and single vacation," Operational Research, Springer, vol. 21(1), pages 621-643, March.
    18. Se Won Lee & Bara Kim & Jeongsim Kim, 2022. "Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication," Annals of Operations Research, Springer, vol. 310(2), pages 505-518, March.
    19. 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.
    20. Shuo Wang & Xiuli Xu, 2021. "Equilibrium strategies of the fluid queue with working vacation," Operational Research, Springer, vol. 21(2), pages 1211-1228, June.
    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. 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.

    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 & 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.
    2. V., Saravanan & V., Poongothai & P., Godhandaraman, 2023. "Performance analysis of a multi server retrial queueing system with unreliable server, discouragement and vacation model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 204-226.
    3. 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.
    4. 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).
    5. Janani, B., 2022. "Transient Analysis of Differentiated Breakdown Model," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    6. Geni Gupur, 2022. "On the asymptotic expression of the time-dependent solution of an M/G/1 queueing model," Partial Differential Equations and Applications, Springer, vol. 3(2), pages 1-16, April.
    7. 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.
    8. M. I. G. Suranga Sampath & K. Kalidass & Jicheng Liu, 2020. "Transient Analysis of an M/M/1 Queueing System Subjected to Multiple Differentiated Vacations, Impatient Customers and a Waiting Server with Application to IEEE 802.16E Power Saving Mechanism," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(1), pages 297-320, March.
    9. Qingqing Ma & Yiqiang Q. Zhao & Weiqi Liu & Jihong Li, 2019. "Customer Strategic Joining Behavior in Markovian Queues with Working Vacations and Vacation Interruptions Under Bernoulli Schedule," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 36(01), pages 1-26, February.
    10. G. K. Tamrakar & A. Banerjee, 2020. "On steady-state joint distribution of an infinite buffer batch service Poisson queue with single and multiple vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 57(4), pages 1337-1373, December.
    11. Tzu-Hsin Liu & Kuo-Ching Chiou & Chih-Ming Chen & Fu-Min Chang, 2024. "Multiserver Retrial Queue with Two-Way Communication and Synchronous Working Vacation," Mathematics, MDPI, vol. 12(8), pages 1-14, April.
    12. Hanukov, Gabi, 2022. "Improving efficiency of service systems by performing a part of the service without the customer's presence," European Journal of Operational Research, Elsevier, vol. 302(2), pages 606-620.
    13. Fan Xu & Ruiling Tian & Qi Shao, 2024. "Optimal Pricing Strategy in an Unreliable M/M/1 Retrial Queue with Delayed Repair and Breakdown Deterioration," Methodology and Computing in Applied Probability, Springer, vol. 26(2), pages 1-22, June.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.

    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:24:y:2024:i:2:d:10.1007_s12351-024-00827-8. 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.