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

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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.

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Authors and Affiliations

  1. Department of Mathematics, College of Engineering, Anna University, Chennai, 600 025, India

    B. Krishna Kumar, A. Thanikachalam & V. Kanakasabapathi

  2. Department of Mathematics, Pachaiyappa’s College, Chennai, 600 030, India

    R. Rukmani

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  1. B. Krishna Kumar
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  2. R. Rukmani
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  3. A. Thanikachalam
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  4. V. Kanakasabapathi
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Correspondence to B. Krishna Kumar.

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Krishna Kumar, B., Rukmani, R., Thanikachalam, A. et al. Performance analysis of retrial queue with server subject to two types of breakdowns and repairs. Oper Res Int J 18, 521–559 (2018). https://doi.org/10.1007/s12351-016-0275-4

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  • DOI: https://doi.org/10.1007/s12351-016-0275-4

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