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Equilibrium in a Queueing System with Retrials

Author

Listed:
  • Julia Chirkova

    (Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
    Current address: IAMR KarRC RAS, 11, Pushkinskaya Str., 185910 Petrozavodsk, Russia.
    These authors contributed equally to this work.)

  • Vladimir Mazalov

    (Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
    Institute of Mathematics and Information Technologies, Petrozavodsk State University, 185035 Petrozavodsk, Russia
    Current address: IAMR KarRC RAS, 11, Pushkinskaya Str., 185910 Petrozavodsk, Russia.
    These authors contributed equally to this work.)

  • Evsey Morozov

    (Institute of Applied Mathematical Research, Karelian Research Centre, Russian Academy of Sciences, 185910 Petrozavodsk, Russia
    Institute of Mathematics and Information Technologies, Petrozavodsk State University, 185035 Petrozavodsk, Russia
    Moscow Center for Fundamental and Applied Mathematics, Moscow State University, 119991 Moscow, Russia
    Current address: IAMR KarRC RAS, 11, Pushkinskaya Str., 185910 Petrozavodsk, Russia.)

Abstract

We find an equilibrium in a single-server queueing system with retrials and strategic timing of the customers. We consider a set of customers, each of which must decide when to arrive to a queueing system during a fixed period of time. In this system, after completion of service, the server seeks a customer blocked in a virtual orbit (orbital customer) to be served next, unless a new customer captures the server. We develop, in detail, a setting with two and three customers in the set, and formulate and discuss the problem for the general case with an arbitrary number of customers. The numerical examples for the system with two and three customers included as well.

Suggested Citation

  • Julia Chirkova & Vladimir Mazalov & Evsey Morozov, 2022. "Equilibrium in a Queueing System with Retrials," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:428-:d:737455
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    References listed on IDEAS

    as
    1. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
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    Cited by:

    1. Alexandra Borodina & Vladimir Mazalov, 2023. "On the Equilibrium in a Queuing System with Retrials and Strategic Arrivals," Mathematics, MDPI, vol. 11(16), pages 1-15, August.

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