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A finite-source M/G/1 retrial queue with outgoing calls

Author

Listed:
  • Velika I. Dragieva

    (University of Forestry)

  • Tuan Phung-Duc

    (University of Tsukuba)

Abstract

In this paper we deal with a single-server, finite-source retrial queue where the server not only accepts incoming calls but after some exponentially distributed idle time makes outgoing calls. The service times of incoming and outgoing calls follow two distinct arbitrary distributions. The outgoing calls are directed not to the customers in the system but outside it, which implies that the model can be considered as a model with vacations or with customers of two types. Along with the standard retrial queue where all customers are allowed to join the orbit we consider also the corresponding queue with restriction on the orbit size. We derive formulas for computing the stationary system state distribution and investigate the influence of the system input parameters on the main macro characteristics of the system performance.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:293:y:2020:i:1:d:10.1007_s10479-019-03359-z
    DOI: 10.1007/s10479-019-03359-z
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    References listed on IDEAS

    as
    1. Jinting Wang & Fang Wang & Janos Sztrik & Attila Kuki, 2017. "Finite source retrial queues with two phase service," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 30(4), pages 421-440.
    2. Falin, G. I. & Artalejo, J. R., 1998. "A finite source retrial queue," European Journal of Operational Research, Elsevier, vol. 108(2), pages 409-424, July.
    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. Velika I. Dragieva, 2016. "Steady state analysis of the M/G/1//N queue with orbit of blocked customers," Annals of Operations Research, Springer, vol. 247(1), pages 121-140, December.
    6. Dieter Fiems & Tuan Phung-Duc, 2019. "Light-traffic analysis of random access systems without collisions," Annals of Operations Research, Springer, vol. 277(2), pages 311-327, June.
    7. Tien V. Do & Patrick Wüchner & Tamás Bérczes & János Sztrik & Hermann De Meer, 2014. "A New Finite-Source Queueing Model For Mobile Cellular Networks Applying Spectrum Renting," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 31(02), pages 1-19.
    8. Antonio Gómez-Corral & Tuan Phung-Duc, 2016. "Retrial queues and related models," Annals of Operations Research, Springer, vol. 247(1), pages 1-2, December.
    9. Jesus R. Artalejo & A. Gómez‐Corral, 2007. "Waiting time analysis of the M/G/1 queue with finite retrial group," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(5), pages 524-529, August.
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    Cited by:

    1. Wei Xu & Liwei Liu & Linhong Li & Zhen Wang & Sabine Wittevrongel, 2023. "Analysis of a Collision-Affected M/GI/1/ /N Retrial Queuing System Considering Negative Customers and Transmission Errors," Mathematics, MDPI, vol. 11(16), pages 1-23, August.

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