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Cost analysis of a finite M/M/R queueing system with balking, reneging, and server breakdowns

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  • Kuo-Hsiung Wang
  • Ying-Chung Chang

Abstract

We study an M/M/R queueing system with finite capacity plus balking, reneging, and server breakdowns. Arriving customers balk (do not enter) with a probability (1 − b n ) and renege (leave the queue after entering) according to a negative exponential distribution. The server can break down at any time even if no customers are in the system. Arrival and service times of the customers, and breakdown times and repair times of the servers are assumed to follow a negative exponential distribution. We use a matrix geometric method to derive the steady-state probabilities, using which various system performance measures that can be obtained. A cost model is developed to determine the optimum number of servers. Under the optimal operating conditions, numerical results are presented in which several system performance measures are evaluated based on assumed numerical values given to the system parameters. Sensitivity analysis is also investigated. Copyright Springer-Verlag Berlin Heidelberg 2002

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:56:y:2002:i:2:p:169-180
    DOI: 10.1007/s001860200206
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    Citations

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    Cited by:

    1. Vijay Rajan Lumb & Indra Rani, 2022. "Analytically simple solution to discrete-time queue with catastrophes, balking and state-dependent 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 783-817, April.
    2. 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.
    3. Cheng-Dar Liou, 2015. "Markovian queue optimisation analysis with an unreliable server subject to working breakdowns and impatient customers," International Journal of Systems Science, Taylor & Francis Journals, vol. 46(12), pages 2165-2182, September.
    4. Mingang Yin & Ming Yan & Yu Guo & Minghe Liu, 2023. "Analysis of a Pre-Emptive Two-Priority Queuing System with Impatient Customers and Heterogeneous Servers," Mathematics, MDPI, vol. 11(18), pages 1-16, September.
    5. Mohammad Firouz & Linda Li & Burcu B. Keskin, 2022. "Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity," Production and Operations Management, Production and Operations Management Society, vol. 31(11), pages 3963-3981, November.
    6. 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.
    7. Macarena Lozano & Pilar Moreno, 2008. "A discrete time single-server queue with balking: economic applications," Applied Economics, Taylor & Francis Journals, vol. 40(6), pages 735-748.

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