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Transient Analysis of Queueing-Based Congestion with Differentiated Vacations and Customer’s Impatience Attributes

  • Research Article-Systems Engineering
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Abstract

This research article studies the critical issue of the single-server congestion problem with prominent customer impatience attributes and server strategic differentiated vacation. Despite their apparent practical relevance, the proposed congestion problem has yet to be studied from a service/production perspective with transient analysis. The queue-theoretic approach is used for mathematical modeling. The transient queue-size distribution has been derived using a modified Bessel function and generating function technique. A time-dependent solution is advantageous for queueing systems’ dynamic behavior over a planning phase and is predominantly valuable within the real-time design process for the state-of-the-art strategic system. The time-dependent explicit expression of variance and mean for the number of waiting customers in the system is also derived for quick statistical insights. Finally, numerical results are also exhibited to study the system’s behavior in depth.

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Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

Authors acknowledge the sincere thanks to anonymous reviewer and member of editorial board for considering our manuscript for possible publication.

Funding

The third author (MD) extends his sincere thanks to funding agency CSIR-UGC, India, for the financial support SRF/NET (1081/(CSIR-UGC NET DEC. 2018)). There is no funding support for open access to any author from any funding agency to pursue this research work.

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Authors and Affiliations

  1. Department of Mathematics, Chandigarh University, Mohali, Punjab, 133301, India

    Amit Kumar

  2. Department of Mathematics, Birla Institute of Technology and Science Pilani, Pilani Campus, Pilani, Rajasthan, 333031, India

    Suman Kaswan, Mahendra Devanda & Chandra Shekhar

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  1. Amit Kumar
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  2. Suman Kaswan
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  3. Mahendra Devanda
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  4. Chandra Shekhar
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The author has read and approved this version of the article, and due care has been taken to ensure the integrity of the work. No part of this paper has been published or submitted elsewhere.

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Correspondence to Chandra Shekhar.

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Kumar, A., Kaswan, S., Devanda, M. et al. Transient Analysis of Queueing-Based Congestion with Differentiated Vacations and Customer’s Impatience Attributes. Arab J Sci Eng 48, 15655–15665 (2023). https://doi.org/10.1007/s13369-023-08020-3

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  • DOI: https://doi.org/10.1007/s13369-023-08020-3

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