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Asymptotic Analysis for Systems with Deferred Abandonment

Author

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  • Katsunobu Sasanuma

    (College of Business, Stony Brook University, Stony Brook, NY 11794, USA)

Abstract

This short paper concerns the analysis of the M/M/k queueing system with customer abandonment. In this system, service managers provide a finite buffer space, which is a waiting area that prevents customers from abandoning the system. Abandonment of the system can occur from reneging (exiting from the queue while waiting), and/or balking (leaving the system without waiting). We derive an analytical expression to represent the impact of the buffer space capacity on the delay probability and the abandonment probability for a system with deferred abandonment. The result indicates the provision of the buffer space in a large system could only increase the delay probability while the abandonment probability remains unchanged. Despite the benevolent intentions of service managers, providing a buffer space may exacerbate the performance of larger systems.

Suggested Citation

  • Katsunobu Sasanuma, 2021. "Asymptotic Analysis for Systems with Deferred Abandonment," Mathematics, MDPI, vol. 9(18), pages 1-11, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2187-:d:630719
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    References listed on IDEAS

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    1. C. J. Ancker & A. V. Gafarian, 1963. "Some Queuing Problems with Balking and Reneging. I," Operations Research, INFORMS, vol. 11(1), pages 88-100, February.
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    3. Frank Haight, 1959. "Queueing with reneging," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 2(1), pages 186-197, December.
    4. Chenguang (Allen) Wu & Achal Bassamboo & Ohad Perry, 2019. "Service System with Dependent Service and Patience Times," Management Science, INFORMS, vol. 65(3), pages 1151-1172, March.
    5. David Azriel & Paul D. Feigin & Avishai Mandelbaum, 2019. "Erlang-S: A Data-Based Model of Servers in Queueing Networks," Management Science, INFORMS, vol. 65(10), pages 4607-4635, October.
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