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A survey of retrial queueing systems

Author

Listed:
  • Jeongsim Kim

    (Chungbuk National University)

  • Bara Kim

    (Korea University)

Abstract

Retrial queueing systems have been extensively studied because of their applications in telephone systems, call centers, telecommunication networks, computer systems, and in daily life. This survey deals with various retrial queueing models. The main focus of this survey is to show analytic results for queue length distributions, waiting time distributions, and tail asymptotics for the queue length and waiting time distributions. This survey also considers the stability analysis of retrial queueing models.

Suggested Citation

  • Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    • Handle: RePEc:spr:annopr:v:247:y:2016:i:1:d:10.1007_s10479-015-2038-7
    DOI: 10.1007/s10479-015-2038-7
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    References listed on IDEAS

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    Cited by:

    1. Faruk Akın & E. Lerzan Örmeci, 2022. "Optimal control of a loss system with feedback," Queueing Systems: Theory and Applications, Springer, vol. 100(3), pages 381-383, April.
    2. Yang, Dong-Yuh & Tsao, Chih-Lung, 2019. "Reliability and availability analysis of standby systems with working vacations and retrial of failed components," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 46-55.
    3. Anatoly Nazarov & János Sztrik & Anna Kvach & Tamás Bérczes, 2019. "Asymptotic 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. 277(2), pages 213-229, June.
    4. Bin Liu & Yiqiang Q. Zhao, 2020. "Tail asymptotics for the $$M_1,M_2/G_1,G_2/1$$ M 1 , M 2 / G 1 , G 2 / 1 retrial queue with non-preemptive priority," Queueing Systems: Theory and Applications, Springer, vol. 96(1), pages 169-199, October.
    5. Bin Liu & Yiqiang Q. Zhao, 2022. "Tail Asymptotics for a Retrial Queue with Bernoulli Schedule," Mathematics, MDPI, vol. 10(15), pages 1-13, August.
    6. 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.
    7. Wang, Kuo-Hsiung & Wu, Chia-Huang & Yen, Tseng-Chang, 2022. "Comparative cost-benefit analysis of four retrial systems with preventive maintenance and unreliable service station," Reliability Engineering and System Safety, Elsevier, vol. 221(C).
    8. Alexander N. Dudin & Sergey A. Dudin & Valentina I. Klimenok & Olga S. Dudina, 2024. "Stability of Queueing Systems with Impatience, Balking and Non-Persistence of Customers," Mathematics, MDPI, vol. 12(14), pages 1-17, July.
    9. Wu, Chia-Huang & Yen, Tseng-Chang & Wang, Kuo-Hsiung, 2021. "Availability and Comparison of Four Retrial Systems with Imperfect Coverage and General Repair Times," Reliability Engineering and System Safety, Elsevier, vol. 212(C).
    10. Dieter Fiems, 2023. "Retrial queues with constant retrial times," Queueing Systems: Theory and Applications, Springer, vol. 103(3), pages 347-365, April.
    11. 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.
    12. 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.
    13. 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.
    14. Bin Liu & Jie Min & Yiqiang Q. Zhao, 2023. "Refined tail asymptotic properties for the $$M^X/G/1$$ M X / G / 1 retrial queue," Queueing Systems: Theory and Applications, Springer, vol. 104(1), pages 65-105, June.
    15. Julia Chirkova & Vladimir Mazalov & Evsey Morozov, 2022. "Equilibrium in a Queueing System with Retrials," Mathematics, MDPI, vol. 10(3), pages 1-15, January.
    16. 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.
    17. Lamia Lakaour & Djamil Aïssani & Karima Adel-Aissanou & Kamel Barkaoui, 2019. "M/M/1 Retrial Queue with Collisions and Transmission Errors," Methodology and Computing in Applied Probability, Springer, vol. 21(4), pages 1395-1406, December.
    18. Bara Kim & Jeongsim Kim, 2020. "Stability of a multi-class multi-server retrial queueing system with service times depending on classes and servers," Queueing Systems: Theory and Applications, Springer, vol. 94(1), pages 129-146, February.
    19. Anatoly Nazarov & János Sztrik & Anna Kvach & Ádám Tóth, 2022. "Asymptotic Analysis of Finite-Source M/GI/1 Retrial Queueing Systems with Collisions and Server Subject to Breakdowns and Repairs," Methodology and Computing in Applied Probability, Springer, vol. 24(3), pages 1503-1518, September.
    20. Velika I. Dragieva & Tuan Phung-Duc, 2020. "A finite-source M/G/1 retrial queue with outgoing calls," Annals of Operations Research, Springer, vol. 293(1), pages 101-121, October.

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