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A queueing model with server breakdowns, repairs, vacations, and backup server

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  • Chakravarthy, Srinivas R.
  • Shruti,
  • Kulshrestha, Rakhee

Abstract

Queueing models wherein having a backup server during the absences (caused by vacations and breakdowns) of the main server have found many applications in practice. Such services offered by a backup server can be viewed as the (main) server working during a vacation or during a breakdown period. A backup server offering services can be thought of as the main server working (at a reduced rate) on vacations/repairs. Using Neuts’ versatile point process for the arrivals and modeling the service times with phase type distributions, we propose a model that generalizes some of the previously published ones on working-vacation-breakdown-repair queues. We carry out the steady-state analysis and report interesting illustrative numerical examples. We also prove decomposition results for the rate matrix and the mean number in the system under some special cases.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:oprepe:v:7:y:2020:i:c:s2214716019302076
    DOI: 10.1016/j.orp.2019.100131
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    References listed on IDEAS

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    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. 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, December.
    3. 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.
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    7. 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.
    8. Wojciech M. Kempa, 2016. "Transient workload distribution in the $$M/G/1$$ M / G / 1 finite-buffer queue with single and multiple vacations," Annals of Operations Research, Springer, vol. 239(2), pages 381-400, April.
    9. 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.
    10. Cosmika Goswami & N. Selvaraju, 2016. "Phase-Type Arrivals and Impatient Customers in Multiserver Queue with Multiple Working Vacations," Advances in Operations Research, Hindawi, vol. 2016, pages 1-17, March.
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    Cited by:

    1. Azizi, Fariba & Salari, Nooshin, 2023. "A novel condition-based maintenance framework for parallel manufacturing systems based on bivariate birth/birth–death processes," Reliability Engineering and System Safety, Elsevier, vol. 229(C).
    2. Alexander Dudin & Olga Dudina & Sergei Dudin & Konstantin Samouylov, 2021. "Analysis of Multi-Server Queue with Self-Sustained Servers," Mathematics, MDPI, vol. 9(17), pages 1-18, September.
    3. 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.
    4. Srinivas R. Chakravarthy & Alexander N. Dudin & Sergey A. Dudin & Olga S. Dudina, 2023. "Queueing System with Potential for Recruiting Secondary Servers," Mathematics, MDPI, vol. 11(3), pages 1-24, January.
    5. Gabi Hanukov & Shraga Shoval, 2023. "A Model for a Vacation Queuing Policy Considering Server’s Deterioration and Recovery," Mathematics, MDPI, vol. 11(12), pages 1-21, June.
    6. Mridula Jain & Anamika Jain, 2022. "Genetic algorithm in retrial queueing system with server breakdown and caller intolerance with voluntary service," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(2), pages 582-598, April.

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