IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v204y2023icp259-281.html
   My bibliography  Save this article

Cost Optimization of an Unreliable server queue with two stage service process under hybrid vacation policy

Author

Listed:
  • Kumar, Anshul
  • Jain, Madhu

Abstract

In this investigation, an unreliable server Markovian queueing model is developed for a service system by considering two stage service process and hybrid vacation policy. By including the features of combination of working vacation (WV) and complete vacation (CV), the steady state probability distribution of the queue size of two stage service model via matrix geometric approach has been established. The cost function has been formulated to evaluate the optimal values of the decision variables of the service system. Particle swarm optimization (PSO) and Artificial bee colony (ABC) optimization algorithms are employed to compute the optimal service rates at optimum cost. To validate the model, numerical illustrations along with sensitivity analysis have been provided.

Suggested Citation

  • Kumar, Anshul & Jain, Madhu, 2023. "Cost Optimization of an Unreliable server queue with two stage service process under hybrid vacation policy," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 204(C), pages 259-281.
    • Handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:259-281
    DOI: 10.1016/j.matcom.2022.08.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475422003391
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2022.08.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chia-Jung Chang & Jau-Chuan Ke & Fu-Min Chang, 2018. "Unreliable retrial queue with loss and feedback under threshold-based policy," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 30(1), pages 1-20.
    2. Meena, Rakesh Kumar & Jain, Madhu & Assad, Assif & Sethi, Rachita & Garg, Deepika, 2022. "Performance and cost comparative analysis for M/G/1 repairable machining system with N-policy vacation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 315-328.
    3. Neuts, Marcel F., 1984. "Matrix-analytic methods in queuing theory," European Journal of Operational Research, Elsevier, vol. 15(1), pages 2-12, January.
    4. 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, July-Dece.
    5. Qingqing Ye, 2019. "The analysis of MX/M/1 queue with two-stage vacations policy," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(18), pages 4492-4510, September.
    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.
    7. Ahuja, Anjali & Jain, Anamika & Jain, Madhu, 2022. "Transient analysis and ANFIS computing of unreliable single server queueing model with multiple stage service and functioning vacation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 464-490.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Gorbunova, A.V. & Lebedev, A.V., 2023. "Nonlinear approximation of characteristics of a fork–join queueing system with Pareto service as a model of parallel structure of data processing," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 409-428.
    2. R. Harini & K. Indhira, 2024. "Meta heuristic optimization of a batch arrival retrial queue with optional re-service and M-optional vacations," 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. 15(9), pages 4252-4282, September.
    3. Chahal, Parmeet Kaur & Kumar, Kamlesh & Soodan, Bhavneet Singh, 2024. "Grey wolf algorithm for cost optimization of cloud computing repairable system with N-policy, discouragement and two-level Bernoulli feedback," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 545-569.
    4. R. Harini & K. Indhira, 2024. "Dynamical modelling and cost optimization of a 5G base station for energy conservation using feedback retrial queue with sleeping strategy," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 86(4), pages 661-690, August.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Priyanka Kalita & Gautam Choudhury & Dharmaraja Selvamuthu, 2020. "Analysis of Single Server Queue with Modified Vacation Policy," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 511-553, June.
    2. 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.
    3. Yuying Zhang & Dequan Yue & Wuyi Yue, 2022. "A queueing-inventory system with random order size policy and server vacations," Annals of Operations Research, Springer, vol. 310(2), pages 595-620, March.
    4. Yi Peng & Jinbiao Wu, 2020. "A Lévy-Driven Stochastic Queueing System with Server Breakdowns and Vacations," Mathematics, MDPI, vol. 8(8), pages 1-12, July.
    5. Srinivas R. Chakravarthy & Serife Ozkar, 2016. "Crowdsourcing and Stochastic Modeling," Business and Management Research, Business and Management Research, Sciedu Press, vol. 5(2), pages 19-30, June.
    6. Zsolt Saffer & Sergey Andreev & Yevgeni Koucheryavy, 2016. "$$M/D^{[y]}/1$$ M / D [ y ] / 1 Periodically gated vacation model and its application to IEEE 802.16 network," Annals of Operations Research, Springer, vol. 239(2), pages 497-520, April.
    7. Shunfu Jin & Xiuchen Qie & Wenjuan Zhao & Wuyi Yue & Yutaka Takahashi, 2020. "A clustered virtual machine allocation strategy based on a sleep-mode with wake-up threshold in a cloud environment," Annals of Operations Research, Springer, vol. 293(1), pages 193-212, October.
    8. Amina Angelika Bouchentouf & Abdelhak Guendouzi, 2021. "Single Server Batch Arrival Bernoulli Feedback Queueing System with Waiting Server, K-Variant Vacations and Impatient Customers," SN Operations Research Forum, Springer, vol. 2(1), pages 1-23, March.
    9. F. P. Barbhuiya & U. C. Gupta, 2020. "A Discrete-Time GIX/Geo/1 Queue with Multiple Working Vacations Under Late and Early Arrival System," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 599-624, June.
    10. Alexander Dudin & Sergei Dudin & Valentina Klimenok & Yuliya Gaidamaka, 2021. "Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption," Mathematics, MDPI, vol. 9(13), pages 1-15, June.
    11. 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).
    12. Igor Kleiner & Esther Frostig & David Perry, 2023. "Busy Periods for Queues Alternating Between Two Modes," Methodology and Computing in Applied Probability, Springer, vol. 25(2), pages 1-16, June.
    13. Tuan Phung-Duc, 2017. "Exact solutions for M/M/c/Setup queues," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 64(2), pages 309-324, February.
    14. Oz, Binyamin & Adan, Ivo & Haviv, Moshe, 2019. "The Mn/Gn/1 queue with vacations and exhaustive service," European Journal of Operational Research, Elsevier, vol. 277(3), pages 945-952.
    15. Meena, Rakesh Kumar & Jain, Madhu & Sanga, Sudeep Singh & Assad, Assif, 2019. "Fuzzy modeling and harmony search optimization for machining system with general repair, standby support and vacation," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 858-873.
    16. B. Krishna Kumar & R. Rukmani & A. Thanikachalam & V. Kanakasabapathi, 2018. "Performance analysis of retrial queue with server subject to two types of breakdowns and repairs," Operational Research, Springer, vol. 18(2), pages 521-559, July.
    17. Janani, B., 2022. "Transient Analysis of Differentiated Breakdown Model," Applied Mathematics and Computation, Elsevier, vol. 417(C).
    18. Zhongbin Wang & Yunan Liu & Lei Fang, 2022. "Pay to activate service in vacation queues," Production and Operations Management, Production and Operations Management Society, vol. 31(6), pages 2609-2627, June.
    19. Zhang, Zhe George & Tadj, Lotfi & Bounkhel, Messaoud, 2011. "Cost evaluation in M/G/1 queue with T-policy revisited, technical note," European Journal of Operational Research, Elsevier, vol. 214(3), pages 814-817, November.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:204:y:2023:i:c:p:259-281. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.