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Performance analysis of an unreliable M/G/1 retrial queue with two-way communication

Author

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  • Muthukrishnan Senthil Kumar

    (PSG College of Technology)

  • Aresh Dadlani

    (Nazarbayev University)

  • Kiseon Kim

    (Gwangju Institute of Science and Technology)

Abstract

Efficient use of call center operators through technological innovations more often come at the expense of added operation management issues. In this paper, the stationary characteristics of an M/G/1 retrial queue is investigated where the single server, subject to active failures, primarily attends incoming calls and directs outgoing calls only when idle. The incoming calls arriving at the server follow a Poisson arrival process, while outgoing calls are made in an exponentially distributed time. On finding the server unavailable (either busy or temporarily broken down), incoming calls intrinsically join the virtual orbit from which they re-attempt for service at exponentially distributed time intervals. The system stability condition along with probability generating functions for the joint queue length distribution of the number of calls in the orbit and the state of the server are derived and evaluated numerically in the context of mean system size, server availability, failure frequency and orbit waiting time.

Suggested Citation

  • Muthukrishnan Senthil Kumar & Aresh Dadlani & Kiseon Kim, 2020. "Performance analysis of an unreliable M/G/1 retrial queue with two-way communication," Operational Research, Springer, vol. 20(4), pages 2267-2280, December.
    • Handle: RePEc:spr:operea:v:20:y:2020:i:4:d:10.1007_s12351-018-0417-y
    DOI: 10.1007/s12351-018-0417-y
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    References listed on IDEAS

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    1. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    2. M. Senthil Kumar & R. Arumuganathan, 2010. "An M X /G/1 retrial queue with two-phase service subject to active server breakdowns and two types of repair," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 8(3), pages 261-291.
    3. 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.
    4. Sofiane Ouazine & Karim Abbas, 2016. "A functional approximation for retrial queues with two way communication," Annals of Operations Research, Springer, vol. 247(1), pages 211-227, December.
    5. 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.
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    Cited by:

    1. Geni Gupur, 2022. "On the asymptotic expression of the time-dependent solution of an M/G/1 queueing model," Partial Differential Equations and Applications, Springer, vol. 3(2), pages 1-16, April.
    2. 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.
    3. 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).
    4. Gabi Hanukov & Uri Yechiali, 2024. "Orbit while in service," Operational Research, Springer, vol. 24(2), pages 1-32, June.
    5. Miaomiao Yu & Yinghui Tang, 2022. "Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method," Operational Research, Springer, vol. 22(3), pages 2831-2858, July.

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