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Scaling limits for single server retrial queues with two-way communication

Author

Listed:
  • Hiroyuki Sakurai

    (Tokyo Institute of Technology)

  • Tuan Phung-Duc

    (Tokyo Institute of Technology)

Abstract

This paper studies M/G/1 retrial queues in which there are two arrival flows, i.e., incoming calls made by regular customers and outgoing calls made by the server in idle time. The stationary analysis of this system has been carried out in a recent paper by Artalejo and Phung-Duc (Appl Math Model 37(4):1811–1822, 2013). In this paper, we obtain a decomposition property where we prove that the queue length is decomposed into the sum of three independent random variables with clear physical meaning. We then derive scaling limits for the queue length distribution under some extreme conditions (i) heavy traffic, (ii) slow retrials and (iii) instantaneous connection to outgoing calls. Furthermore, we also investigate the convergence of our model to that without outgoing calls.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:247:y:2016:i:1:d:10.1007_s10479-015-1874-9
    DOI: 10.1007/s10479-015-1874-9
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    References listed on IDEAS

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    1. Tuan Phung-Duc & Ken'Ichi Kawanishi, 2014. "An Efficient Method For Performance Analysis Of Blended Call Centers With Redial," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-33.
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    Cited by:

    1. KM Rashmi & S. K. Samanta, 2024. "Analysis of Two-Way Communication in $$M_1^X, M_2/G_1,G_2/1$$ M 1 X , M 2 / G 1 , G 2 / 1 Retrial Queue Under the Constant Retrial Policy," Methodology and Computing in Applied Probability, Springer, vol. 26(4), pages 1-32, December.
    2. 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.
    3. Anatoly Nazarov & Tuan Phung-Duc & Svetlana Paul & Olga Lizyura, 2022. "Diffusion Limit for Single-Server Retrial Queues with Renewal Input and Outgoing Calls," Mathematics, MDPI, vol. 10(6), pages 1-14, March.

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