IDEAS home Printed from https://ideas.repec.org/a/ibn/ijspjl/v13y2025i2p55.html
   My bibliography  Save this article

A Queueing Model With Servers Disguised as Customers

Author

Listed:
  • Janhavi Prabhu
  • Myron Hlynka

Abstract

Queueing theory has been used to model and optimize customer service in numerous real life applications. In this paper, we propose a new model, motivated by the phenomenon of pseudoprogression in cancer, in which the length of a queue appears to increase for a period of time, before reducing at a faster rate. We assume that servers arrive in the queue alongside the customers, that is, ’disguised’ as customers. We derive the general equations for this model using matrix analytic methods, and demonstrate its working with numerical simulations.

Suggested Citation

  • Janhavi Prabhu & Myron Hlynka, 2025. "A Queueing Model With Servers Disguised as Customers," International Journal of Statistics and Probability, Canadian Center of Science and Education, vol. 13(2), pages 1-55, January.
    • Handle: RePEc:ibn:ijspjl:v:13:y:2025:i:2:p:55
    as

    Download full text from publisher

    File URL: https://ccsenet.org/journal/index.php/ijsp/article/download/0/0/50268/54411
    Download Restriction: no
    File URL: https://ccsenet.org/journal/index.php/ijsp/article/view/0/50268
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Neuts, Marcel F., 1984. "Matrix-analytic methods in queuing theory," European Journal of Operational Research, Elsevier, vol. 15(1), pages 2-12, January.
    2. U. Yechiali & P. Naor, 1971. "Queuing Problems with Heterogeneous Arrivals and Service," Operations Research, INFORMS, vol. 19(3), pages 722-734, June.
    3. Valentina Klimenok & Alexander Dudin & Olga Dudina & Irina Kochetkova, 2020. "Queuing System with Two Types of Customers and Dynamic Change of a Priority," Mathematics, MDPI, vol. 8(5), pages 1-25, May.
    4. Li, Hui & Yang, Tao, 2000. "Queues with a variable number of servers," European Journal of Operational Research, Elsevier, vol. 124(3), pages 615-628, August.
    5. Valentina Klimenok & Alexander Dudin & Vladimir Vishnevsky, 2020. "Priority Multi-Server Queueing System with Heterogeneous Customers," Mathematics, MDPI, vol. 8(9), pages 1-16, September.
    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. Qiu, Qinjing & Kawai, Reiichiro, 2022. "A decoupling principle for Markov-modulated chains," Statistics & Probability Letters, Elsevier, vol. 182(C).
    2. Srinivas R. Chakravarthy & Alexander N. Dudin & Sergey A. Dudin & Olga S. Dudina, 2023. "Queueing System with Potential for Recruiting Secondary Servers," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    3. 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.
    4. Yacov Satin & Rostislav Razumchik & Ivan Kovalev & Alexander Zeifman, 2023. "Ergodicity and Related Bounds for One Particular Class of Markovian Time—Varying Queues with Heterogeneous Servers and Customer’s Impatience," Mathematics, MDPI, vol. 11(9), pages 1-15, April.
    5. Chakravarthy, Srinivas R. & Agnihothri, Saligrama R., 2008. "A server backup model with Markovian arrivals and phase type services," European Journal of Operational Research, Elsevier, vol. 184(2), pages 584-609, January.
    6. Refael Hassin & Ran I. Snitkovsky, 2017. "Strategic customer behavior in a queueing system with a loss subsystem," Queueing Systems: Theory and Applications, Springer, vol. 86(3), pages 361-387, August.
    7. D Worthington, 2009. "Reflections on queue modelling from the last 50 years," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 83-92, May.
    8. Kumar, Anshul & Jain, Madhu, 2023. "Cost Optimization of an Unreliable server queue with two stage service process under hybrid vacation policy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 259-281.
    9. V. Vinitha & N. Anbazhagan & S. Amutha & K. Jeganathan & Bhanu Shrestha & Hyoung-Kyu Song & Gyanendra Prasad Joshi & Hyeonjoon Moon, 2022. "Analysis of a Stochastic Inventory Model on Random Environment with Two Classes of Suppliers and Impulse Customers," Mathematics, MDPI, vol. 10(13), pages 1-18, June.
    10. De Angelis, Vanda & Felici, Giovanni & Impelluso, Paolo, 2003. "Integrating simulation and optimisation in health care centre management," European Journal of Operational Research, Elsevier, vol. 150(1), pages 101-114, October.
    11. Nimrod Dvir & Refael Hassin & Uri Yechiali, 2020. "Strategic behaviour in a tandem queue with alternating server," Queueing Systems: Theory and Applications, Springer, vol. 96(3), pages 205-244, December.
    12. K. Jeganathan & S. Selvakumar & S. Saravanan & N. Anbazhagan & S. Amutha & Woong Cho & Gyanendra Prasad Joshi & Joohan Ryoo, 2022. "Performance of Stochastic Inventory System with a Fresh Item, Returned Item, Refurbished Item, and Multi-Class Customers," Mathematics, MDPI, vol. 10(7), pages 1-37, April.
    13. Konstantin Samouylov & Olga Dudina & Alexander Dudin, 2023. "Analysis of Multi-Server Queueing System with Flexible Priorities," Mathematics, MDPI, vol. 11(4), pages 1-22, February.
    14. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Multi-Server Queue with Self-Sustained Servers," Mathematics, MDPI, vol. 9(17), pages 1-18, September.
    15. Vladimir Vishnevsky & Valentina Klimenok & Alexander Sokolov & Andrey Larionov, 2021. "Performance Evaluation of the Priority Multi-Server System MMAP/PH/M/N Using Machine Learning Methods," Mathematics, MDPI, vol. 9(24), pages 1-27, December.
    16. A. Oblakova & A. Al Hanbali & R. J. Boucherie & J. C. W. Ommeren & W. H. M. Zijm, 2019. "An exact root-free method for the expected queue length for a class of discrete-time queueing systems," Queueing Systems: Theory and Applications, Springer, vol. 92(3), pages 257-292, August.
    17. Anatoly Nazarov & Alexander Moiseev & Svetlana Moiseeva, 2021. "Mathematical Model of Call Center in the Form of Multi-Server Queueing System," Mathematics, MDPI, vol. 9(22), pages 1-13, November.
    18. 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.

    More about this item

    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

    Statistics

    Access and download statistics

    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:ibn:ijspjl:v:13:y:2025:i:2:p:55. 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: Canadian Center of Science and Education (email available below). General contact details of provider: https://edirc.repec.org/data/cepflch.html .

    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.