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Impact of the degradation in service rate in MAP/PH/1 queueing system with phase type vacations, breakdowns, and repairs

Author

Listed:
  • Alka Choudhary

    (Central University of Rajasthan)

  • Srinivas R. Chakravarthy

    (Kettering University)

  • Dinesh C. Sharma

    (Central University of Rajasthan)

Abstract

In many service systems, the service rates of the servers or the machines degrade over time due to a variety of reasons like fatigue, deficiency (due to manufacturing defect or energy loss, deformation, or excessive heat), and lack of proper maintenance. To make a service system beneficial for both customers and management points of view, it is imperative that models are developed to understand the impact of degradation. In this paper, we study $$MAP/PH/1-$$ M A P / P H / 1 - type queueing models incorporating degradation, failures/breakdowns and repairs. The degradation and to restore to normalcy in the service rate we look at two scenarios. In the first one, the service is restored to normalcy immediately after the server becomes idle or a fixed number of services is offered. In the second one, the restoration takes a random time that is modeled using a phase type distribution. Also, there are a variety of reasons that lead to failures/breakdowns of the server. We model these using (possibly) different phase type distributions. Both the models are studied analytically using matrix-analytic methods and illustrative numerical examples bringing out the qualitative behavior of the impact of degrading services are discussed. Two cost optimization problems whose solutions are obtained using particle swarm optimization technique along with a few illustrative examples are presented.

Suggested Citation

  • Alka Choudhary & Srinivas R. Chakravarthy & Dinesh C. Sharma, 2023. "Impact of the degradation in service rate in MAP/PH/1 queueing system with phase type vacations, breakdowns, and repairs," Annals of Operations Research, Springer, vol. 331(2), pages 1207-1248, December.
    • Handle: RePEc:spr:annopr:v:331:y:2023:i:2:d:10.1007_s10479-023-05628-4
    DOI: 10.1007/s10479-023-05628-4
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    References listed on IDEAS

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    1. Harrison White & Lee S. Christie, 1958. "Queuing with Preemptive Priorities or with Breakdown," Operations Research, INFORMS, vol. 6(1), pages 79-95, February.
    2. 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.
    3. 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).
    4. Fiems, Dieter & Maertens, Tom & Bruneel, Herwig, 2008. "Queueing systems with different types of server interruptions," European Journal of Operational Research, Elsevier, vol. 188(3), pages 838-845, August.
    5. Madhu Jain & Sandeep Kaur & Parminder Singh, 2021. "Supplementary variable technique (SVT) for non-Markovian single server queue with service interruption (QSI)," Operational Research, Springer, vol. 21(4), pages 2203-2246, December.
    6. Amina Angelika Bouchentouf & Mouloud Cherfaoui & Mohamed Boualem, 2019. "Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers," OPSEARCH, Springer;Operational Research Society of India, vol. 56(1), pages 300-323, March.
    7. 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.
    8. Ke, Jau-Chuan & Liu, Tzu-Hsin & Yang, Dong-Yuh, 2018. "Modeling of machine interference problem with unreliable repairman and standbys imperfect switchover," Reliability Engineering and System Safety, Elsevier, vol. 174(C), pages 12-18.
    9. 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.
    10. 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, January.
    11. 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.
    12. Chakravarthy, Srinivas R., 2014. "A multi-server queueing model with server consultations," European Journal of Operational Research, Elsevier, vol. 233(3), pages 625-639.
    13. Kim, Chesoong & Klimenok, V.I. & Dudin, A.N., 2017. "Analysis of unreliable BMAP/PH/N type queue with Markovian flow of breakdowns," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 154-172.
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