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Markovian queue optimisation analysis with an unreliable server subject to working breakdowns and impatient customers

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  • Cheng-Dar Liou

Abstract

This study investigates an infinite capacity Markovian queue with a single unreliable service station, in which the customers may balk (do not enter) and renege (leave the queue after entering). The unreliable service station can be working breakdowns even if no customers are in the system. The matrix-analytic method is used to compute the steady-state probabilities for the number of customers, rate matrix and stability condition in the system. The single-objective model for cost and bi-objective model for cost and expected waiting time are derived in the system to fit in with practical applications. The particle swarm optimisation algorithm is implemented to find the optimal combinations of parameters in the pursuit of minimum cost. Two different approaches are used to identify the Pareto optimal set and compared: the epsilon-constraint method and non-dominate sorting genetic algorithm. Compared results allow using the traditional optimisation approach epsilon-constraint method, which is computationally faster and permits a direct sensitivity analysis of the solution under constraint or parameter perturbation. The Pareto front and non-dominated solutions set are obtained and illustrated. The decision makers can use these to improve their decision-making quality.

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  • 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.
    • Handle: RePEc:taf:tsysxx:v:46:y:2015:i:12:p:2165-2182
    DOI: 10.1080/00207721.2013.859326
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    References listed on IDEAS

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    1. C. J. Ancker & A. V. Gafarian, 1963. "Some Queuing Problems with Balking and Reneging. I," Operations Research, INFORMS, vol. 11(1), pages 88-100, February.
    2. Y.C. Chang & W.L. Pearn, 2011. "Optimal management for infinite capacity -policy M/G/1 queue with a removable service station," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(7), pages 1075-1083.
    3. C. J. Ancker & A. V. Gafarian, 1963. "Some Queuing Problems with Balking and Reneging---II," Operations Research, INFORMS, vol. 11(6), pages 928-937, December.
    4. Saadatseresht, Mohammad & Mansourian, Ali & Taleai, Mohammad, 2009. "Evacuation planning using multiobjective evolutionary optimization approach," European Journal of Operational Research, Elsevier, vol. 198(1), pages 305-314, October.
    5. 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.
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    Cited by:

    1. Lan Shaojun & Tang Yinghui, 2017. "Performance Analysis of a Discrete-Time Queue with Working Breakdowns and Searching for the Optimum Service Rate in Working Breakdown Period," Journal of Systems Science and Information, De Gruyter, vol. 5(2), pages 176-192, April.
    2. Miaomiao Yu & Yinghui Tang, 2022. "Analysis of a renewal batch arrival queue with a fault-tolerant server using shift operator method," Operational Research, Springer, vol. 22(3), pages 2831-2858, July.
    3. 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.
    4. Yang, Dong-Yuh & Wu, Chia-Huang, 2021. "Evaluation of the availability and reliability of a standby repairable system incorporating imperfect switchovers and working breakdowns," Reliability Engineering and System Safety, Elsevier, vol. 207(C).

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