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Transient analysis of a Markovian queuing model with multiple-heterogeneous servers, and customers’ impatience

Author

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  • Rakesh Kumar

    (Shri Mata Vaishno Devi University)

  • Sapana Sharma

    (Shri Mata Vaishno Devi University)

Abstract

A Markovian queuing system with multiple-heterogeneous servers, reneging and retention of reneging customers is studied. The transient analysis of the model is performed using probability generating function technique. Important measures of performance like expected system size, average reneging rate and average retention rate are presented. The transient behavior of state probabilities is studied numerically. The transient behavior of performance measures is also studied. Further, a comparative analysis is performed which shows that the multiple-heterogeneous servers queuing model performs better than the multiple-homogeneous servers queuing model. Finally, the steady-state solution of the model is also obtained.

Suggested Citation

  • Rakesh Kumar & Sapana Sharma, 2021. "Transient analysis of a Markovian queuing model with multiple-heterogeneous servers, and customers’ impatience," OPSEARCH, Springer;Operational Research Society of India, vol. 58(3), pages 540-556, September.
    • Handle: RePEc:spr:opsear:v:58:y:2021:i:3:d:10.1007_s12597-020-00495-0
    DOI: 10.1007/s12597-020-00495-0
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    References listed on IDEAS

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    1. R. Sudhesh & A. Azhagappan, 2020. "Transient solution of an M/M/∞ queue with system's additional tasks and impatient customers," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 16(1), pages 82-97.
    2. Frank Haight, 1959. "Queueing with reneging," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 2(1), pages 186-197, December.
    3. S. Subba Rao, 1965. "Queuing Models with Balking, Reneging, and Interruptions," Operations Research, INFORMS, vol. 13(4), pages 596-608, August.
    4. Vijendra P. Singh, 1970. "Two-Server Markovian Queues with Balking: Heterogeneous vs. Homogeneous Servers," Operations Research, INFORMS, vol. 18(1), pages 145-159, February.
    5. Rakesh Kumar & Sapana Sharma, 2019. "Transient analysis of an M/M/c queuing system with retention of reneging customers," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 36(1), pages 78-91.
    6. B. Kumar & J Raja, 2006. "On multiserver feedback retrial queues with balking and control retrial rate," Annals of Operations Research, Springer, vol. 141(1), pages 211-232, January.
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    Cited by:

    1. Yacov Satin & Rostislav Razumchik & Ivan Kovalev & Alexander Zeifman, 2023. "Ergodicity and Related Bounds for One Particular Class of Markovian Time—Varying Queues with Heterogeneous Servers and Customer’s Impatience," Mathematics, MDPI, vol. 11(9), pages 1-15, April.

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