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A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods

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Abstract

This paper presents an in-depth analysis of an infinite-space single-server Markovian queueing model for a customer support center that incorporates working breakdowns, repairs, balking, and reneging, along with both single and multiple vacation policies. Additionally, we consider the scenario where the server must wait for a random period before going on vacation. By employing the matrix-geometric method, we determine the steady-state probabilities of the system and derive essential performance measures. We construct an expected cost function and formulate an optimization problem to minimize the cost, using the direct search method to find the optimal service rates during working breakdown and busy periods. To demonstrate the model’s usefulness, the results are complemented with numerical illustrations and sensitivity analysis. This work thus enables improved decision-making and resource management in customer support centers by deepening our understanding of their dynamics.

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References

  1. Doshi BT (1986) Queueing systems with vacations-a survey. Queueing Syst 1(1):29–66

    Article  Google Scholar 

  2. Takagi H (1991) Queueing analysis: a foundation of performance analysis, vol 1: Vacation and priority systems, Part 1. Elsevier Science Publishers B.V., Amsterdam

    Google Scholar 

  3. Tian N, Zhang ZG (2006) Vacation queueing models theory and applications. Springer, New York

    Book  Google Scholar 

  4. Afroun F, Aissani D, Hamadouche D, Boualem M (2018) Q-matrix method for the analysis and performance evaluation of unreliable \({M/M/1/N}\) queueing model. Math Methods Appl Sci 41(18):9152–9163. https://doi.org/10.1002/mma.5119

    Article  Google Scholar 

  5. Begum A, Choudhury G (2023) Analysis of an \(M/\begin{pmatrix}G_1\ G_2\end{pmatrix}/1\) Queue with Bernoulli Vacation and Server Breakdown. Int J Appl Comput Math 9(1):9. https://doi.org/10.1007/s40819-022-01481-4

    Article  Google Scholar 

  6. Jain M, Meena RK (2017) Markovian analysis of unreliable multi-components redundant fault tolerant system with working vacation and F-policy. Cogent Math 4(1). https://doi.org/10.1080/23311835.2017.1306961

  7. Jain M, Sharma GC, Sharma S (2008) Performance modeling of state dependent system with mixed standbys and two modes of failure. Appl Math Model 32:712–724

    Article  Google Scholar 

  8. Laxmi PV, Rajesh P, Kassahun TW (2019) Performance measures of variant working vacations on batch arrival queue with server breakdowns. Int J Manag Sci Eng Manag 14(1):53–63

    Google Scholar 

  9. Nakdimon O, Yechiali U (2003) Polling systems with breakdowns and repairs. Eur J Oper Res 149:588–613

    Article  Google Scholar 

  10. Yang DY, Wu ZR, Tsou CS (2015) Reliability analysis of a repairable system with geometric reneging and threshold-based recovery policy. Proc Inst Mech Eng B J Eng Manuf 229(11):2047–2062

    Article  Google Scholar 

  11. Zirem D, Boualem M, Adel-Aissanou K, Aissani D (2019) Analysis of a single server batch arrival unreliable queue with balking and general retrial time. Qual Technol Quant Manag 16(6):672–695

    Article  Google Scholar 

  12. Yue D, Zhang Y, Yue W (2006) Optimal performance analysis of an \({M/M/1/N}\) queue system with balking, reneging and server vacation. Int J Pure Appl Math 28(1):101–115

    Google Scholar 

  13. Yechiali U (2007) Queues with system disasters and impatient customers when system is down. Queueing Syst 56:195–202

    Article  Google Scholar 

  14. Wang K-H, Ke J-B, Ke J-C (2007) Profit analysis of the \({M/M/R}\) machine repair problem with balking, reneging, and standby switching failures. Comput Oper Res 34(3):835–847

    Article  Google Scholar 

  15. Yue D, Yue W (2009) Analysis of an \({M/M/c/N}\) queueing system with balking, reneging, and synchronous vacations. In: Yue W, Takahashi Y, Takagi H (eds) Advances in Queueing Theory and Network Applications. Springer, New York

    Chapter  Google Scholar 

  16. Baruah M, Kailash C, Madan T (2013) Eldabi: a two stage batch arrival queue with reneging during vacation and breakdown periods. Am J Oper Res 3(6):11. https://doi.org/10.4236/ajor.2013.36054

    Article  Google Scholar 

  17. Li X, Wang J, Zhang F (2014) New results on equilibrium balking strategies in the single-server queue with breakdowns and repairs. Appl Math Comput 241:380–388. https://doi.org/10.1016/j.amc.2014.05.025

    Article  Google Scholar 

  18. Rao SH, Vasanta Kumar V, Srinivasa Kumar B, Srinivasa Rao T (2017) Analysis of two-phase queuing system with impatient customers, server breakdowns and delayed repair. Int J Pure Appl Math 115(4):651–663

    Article  Google Scholar 

  19. Bouchentouf AA, Guendouzi A (2018) Sensitivity analysis of multiple vacation feedback queuing system with differentiated vacations, vacation interruptions and impatient customers. Int J Appl Math Stat 57(6):104–121

    Google Scholar 

  20. Bouchentouf AA, Cherfaoui M, Boualem M (2019) Performance and economic analysis of a single server feedback queueing model with vacation and impatient customers. Opsearch 56(1):300–320

    Article  Google Scholar 

  21. Cherfaoui M, Bouchentouf AA, Boualem M (2023) Modelling and simulation of Bernoulli feedback queue with general customers’ impatience under variant vacation policy. Int J Oper Res 46(4):451–480

    Article  Google Scholar 

  22. Bouchentouf AA, Boualem M, Yahiaoui L, Ahmad H (2022) A multi-station unreliable machine model with working vacation policy and customers impatience. Qual Technol Quant Manag 19(6):766–796

    Article  Google Scholar 

  23. Majid S (2023) Performance analysis of a Markovian queue with impatient customers and working vacation. J Oper Res Soc China 11:133–156. https://doi.org/10.1007/s40305-021-00361-w

    Article  Google Scholar 

  24. Neuts MF (1981) Matrix-geometric solutions in stochastic models: an algorithmic approach. The John Hopkins University Press, Baltimore

    Google Scholar 

  25. Liou C-D (2015) Markovian queue optimisation analysis with an unreliable server subject to working breakdowns and impatient customers. Int J Syst Sci 46(12):2165–2182

    Article  Google Scholar 

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  1. The authors contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Applied Mathematics Laboratory (LMA), University of Bejaia, 06000, Bejaia, Algeria

    Anis Chettouf

  2. Laboratory of Mathematics, Djillali Liabes University of Sidi Bel Abbes, 22000, Sidi Bel Abbes, Algeria

    Amina Angelika Bouchentouf

  3. Research Unit LaMOS (Modeling and Optimization of Systems), Faculty of Technology, University of Bejaia, 06000, Bejaia, Algeria

    Mohamed Boualem

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  1. Anis Chettouf
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  2. Amina Angelika Bouchentouf
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  3. Mohamed Boualem
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Correspondence to Mohamed Boualem.

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Chettouf, A., Bouchentouf, A.A. & Boualem, M. A Markovian Queueing Model for Telecommunications Support Center with Breakdowns and Vacation Periods. Oper. Res. Forum 5, 22 (2024). https://doi.org/10.1007/s43069-024-00295-y

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