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Analysis of a discrete-time working vacation queue with balking

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Abstract

This paper investigates a discrete-time single server finite buffer queue with single working vacation wherein the customers decide either to join the queue or balk. The inter-arrival times, service times and vacation times are assumed to be independent and geometrically distributed. Using matrix method, the steady-state probabilities are obtained. Various performance measures of the model and average sojourn time are presented. An optimization problem is considered using particle swarm optimization (PSO) through a cost function. Further, maximum likelihood estimate (MLE) for the balking parameter is obtained. Numerical results are presented in the form of tables and graphs to show the effect of parameters on the system performance.

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Acknowledgments

The authors would like to thank the anonymous referees for their valuable comments and suggestions which helped in improving the quality of the paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Andhra University, Visakhapatnam, 530003, India

    P. Vijaya Laxmi, K. Jyothsna & D. Seleshi

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  1. P. Vijaya Laxmi
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  2. K. Jyothsna
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  3. D. Seleshi
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Correspondence to P. Vijaya Laxmi.

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Laxmi, P.V., Jyothsna, K. & Seleshi, D. Analysis of a discrete-time working vacation queue with balking. OPSEARCH 52, 562–581 (2015). https://doi.org/10.1007/s12597-014-0191-4

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