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Analysis of MAP / PH /1 Queueing System with Degrading Service Rate and Phase Type Vacation

Author

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  • Alka Choudhary

    (Department of Mathematics, Central University of Rajasthan, Ajmer 305817, India)

  • Srinivas R. Chakravarthy

    (Departments of Industrial and Manufacturing Engineering and Mathematics, Kettering University, Flint, MI 48504, USA)

  • Dinesh C. Sharma

    (Department of Mathematics, Central University of Rajasthan, Ajmer 305817, India)

Abstract

Degradation of services arises in practice due to a variety of reasons including wear-and-tear of machinery and fatigue. In this paper, we look at M A P / P H / 1 -type queueing models in which degradation is introduced. There are several ways to incorporate degradation into a service system. Here, we model the degradation in the form of the service rate declining (i.e., the service rate decreases with the number of services offered) until the degradation is addressed. The service rate is reset to the original rate either after a fixed number of services is offered or when the server becomes idle. We look at two models. In the first, we assume that the degradation is instantaneously fixed, and in the second model, there is a random time that is needed to address the degradation issue. These models are analyzed in steady state using the classical matrix-analytic methods. Illustrative numerical examples are provided. Comparisons of both the models are drawn.

Suggested Citation

  • Alka Choudhary & Srinivas R. Chakravarthy & Dinesh C. Sharma, 2021. "Analysis of MAP / PH /1 Queueing System with Degrading Service Rate and Phase Type Vacation," Mathematics, MDPI, vol. 9(19), pages 1-17, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2387-:d:643107
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    References listed on IDEAS

    as
    1. Srinivas R. Chakravarthy, 2009. "Analysis Of A Multi-Server Queue With Markovian Arrivals And Synchronous Phase Type Vacations," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 26(01), pages 85-113.
    2. Gely Basharin & Valeriy Naumov & Konstantin Samouylov, 2018. "On Markovian modelling of arrival processes," Statistical Papers, Springer, vol. 59(4), pages 1533-1540, December.
    3. Naishuo Tian & Zhe George Zhang, 2006. "Vacation Queueing Models Theory and Applications," International Series in Operations Research and Management Science, Springer, number 978-0-387-33723-4, April.
    4. Chakravarthy, Srinivas R. & Shruti, & Kulshrestha, Rakhee, 2020. "A queueing model with server breakdowns, repairs, vacations, and backup server," Operations Research Perspectives, Elsevier, vol. 7(C).
    5. Chakravarthy, Srinivas R., 2007. "A multi-server synchronous vacation model with thresholds and a probabilistic decision rule," European Journal of Operational Research, Elsevier, vol. 182(1), pages 305-320, October.
    6. Naishuo Tian & Zhe George Zhang, 2006. "Applications of Vacation Models," International Series in Operations Research & Management Science, in: Vacation Queueing Models Theory and Applications, chapter 0, pages 343-358, Springer.
    Full references (including those not matched with items on IDEAS)

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