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Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers

Author

Listed:
  • Amina Angelika Bouchentouf

    (Djillali Liabes University of Sidi Bel Abbes)

  • Mouloud Cherfaoui

    (University of Bejaia
    University of Biskra)

  • Mohamed Boualem

    (University of Bejaia)

Abstract

In this investigation, a single server M/M/1/N feedback queueing system with vacation, balking, reneging and retention of reneged customers is analyzed. By considering the mathematical modeling, we derive the steady state probabilities of the number of customers in the system. We obtain important measures of effectiveness of the model by using the stationary distribution, and develop a cost model of the queueing system. Further, a numerical study and a cost profit analysis are carried out.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:opsear:v:56:y:2019:i:1:d:10.1007_s12597-019-00357-4
    DOI: 10.1007/s12597-019-00357-4
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    References listed on IDEAS

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    1. Gautam Choudhury & Mitali Deka, 2015. "A batch arrival unreliable Bernoulli vacation model with two phases of service and general retrial times," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 7(3), pages 318-347.
    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, September.
    3. Rakesh Kumar & Sumeet Kumar Sharma, 2014. "A Markovian multi-server queuing model with retention of reneged customers and balking," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 20(4), pages 427-438.
    4. P. Vijaya Laxmi & V. Goswami & K. Jyothsna, 2013. "Analysis of Finite Buffer Markovian Queue with Balking, Reneging and Working Vacations," International Journal of Strategic Decision Sciences (IJSDS), IGI Global, vol. 4(1), pages 1-24, January.
    5. Veena Goswami, 2014. "A Discrete-Time Queue with Balking, Reneging, and Working Vacations," International Journal of Stochastic Analysis, Hindawi, vol. 2014, pages 1-8, October.
    6. Kuo-Hsiung Wang & Ying-Chung Chang, 2002. "Cost analysis of a finite M/M/R queueing system with balking, reneging, and server breakdowns," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 56(2), pages 169-180, November.
    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. Rakesh Kumar & Narendra Kumar Jain & Bhupernder Kumar Som, 2014. "Optimization of an M/M/1/N feedback queue with retention of reneged customers," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 24(3), pages 45-58.
    9. Amina Angelika Bouchentouf & Aicha Messabihi, 2018. "Heterogeneous two-server queueing system with reverse balking and reneging," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 251-267, June.
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    Cited by:

    1. Amina Angelika Bouchentouf & Lahcene Yahiaoui & Mokhtar Kadi & Shakir Majid, 2020. "Impatient customers in Markovian queue with Bernoulli feedback and waiting server under variant working vacation policy," Operations Research and Decisions, Wroclaw University of Science Technology, Faculty of Management, vol. 30(4), pages 5-28.
    2. Divya Velayudhan Nair & Achyutha Krishnamoorthy & Agassi Melikov & Sevinj Aliyeva, 2021. "MMAP/(PH,PH)/1 Queue with Priority Loss through Feedback," Mathematics, MDPI, vol. 9(15), pages 1-26, July.
    3. Amita Bhagat & Madhu Jain, 2020. "Retrial queue with multiple repairs, multiple services and non preemptive priority," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 787-814, September.
    4. 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.

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