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Performance analysis of retrial queue with server subject to two types of breakdowns and repairs

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  • B. Krishna Kumar

    (Anna University)

  • R. Rukmani

    (Pachaiyappa’s College)

  • A. Thanikachalam

    (Anna University)

  • V. Kanakasabapathi

    (Anna University)

Abstract

This paper analyses a Markovian retrial queue where the server is subject to breakdowns and repairs. It is assumed that the breakdowns/repairs behaviour when the server is idle is different from the one when it is busy. Under the steady-state condition, explicit expressions for the partial probability generating functions of the server status and the number of customers in the orbit are obtained along with some key performance measures of the system. In addition, we study two new orbit characteristics, namely, the orbit idle period and the orbit busy period by using the first principle arguments. An approximate method of analysis for the system with losses is also suggested. The stochastic decomposition property is shown to hold good for the underlying retrial queueing system. Besides, we study the asymptotic behaviour of the system size under extreme conditions. Finally, some numerical results are illustrated.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:operea:v:18:y:2018:i:2:d:10.1007_s12351-016-0275-4
    DOI: 10.1007/s12351-016-0275-4
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    References listed on IDEAS

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    2. V., Saravanan & V., Poongothai & P., Godhandaraman, 2023. "Performance analysis of a multi server retrial queueing system with unreliable server, discouragement and vacation model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 204-226.
    3. Limin Rong & Feng Dong & Qiguo Gong, 2021. "Work Interruption: The Moderate Effect of Workload and Queue Length in the Manufacturing Industry," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 11(8), pages 618-631, August.
    4. Ahmadi-Javid, Amir & Hoseinpour, Pooya, 2019. "Service system design for managing interruption risks: A backup-service risk-mitigation strategy," European Journal of Operational Research, Elsevier, vol. 274(2), pages 417-431.

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