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A Queueing Model With Servers Disguised as Customers

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  • 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
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    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)

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    JEL classification:

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

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