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Analysis of the waiting time distribution in M/G/1 retrial queues with two way communication

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Listed:
  • Se Won Lee

    (Pukyong National University)

  • Bara Kim

    (Korea University)

  • Jeongsim Kim

    (Chungbuk National University)

Abstract

We consider an M/G/1 retrial queue in which there are two types of calls: ingoing calls made by regular customers and outgoing calls made by the server in idle time. The service times of ingoing calls and outgoing calls have different arbitrary distributions. In this paper, we are interested in the analysis of the waiting time distribution. We obtain an equation for the joint transform of the number of ingoing calls in the orbit and the waiting time of an arbitrary ingoing call. Using this result, we can obtain the moments of the waiting time distribution of an arbitrary ingoing call.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:310:y:2022:i:2:d:10.1007_s10479-020-03717-2
    DOI: 10.1007/s10479-020-03717-2
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    References listed on IDEAS

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    1. Hiroyuki Sakurai & Tuan Phung-Duc, 2016. "Scaling limits for single server retrial queues with two-way communication," Annals of Operations Research, Springer, vol. 247(1), pages 229-256, December.
    2. J. Artalejo, 1999. "A classified bibliography of research on retrial queues: Progress in 1990–1999," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 7(2), pages 187-211, December.
    3. Jeongsim Kim & Bara Kim, 2016. "A survey of retrial queueing systems," Annals of Operations Research, Springer, vol. 247(1), pages 3-36, December.
    4. Hiroyuki Sakurai & Tuan Phung-Duc, 2015. "Two-way communication retrial queues with multiple types of outgoing calls," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(2), pages 466-492, July.
    5. J. R. Artalejo & J. A. C. Resing, 2010. "Mean Value Analysis Of Single Server Retrial Queues," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 27(03), pages 335-345.
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    Cited by:

    1. 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.
    2. Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.

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