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M/M/1 queue with m kinds of differentiated working vacations

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Abstract

In this paper, we consider an M/M/1 vacation queueing system in which m different kinds of working vacations may be taken as soon as the system is empty. When parameters take proper different values, our model reduces to several classical models already studied in references. By quasi birth and death process and generalized eigenvalues method, we give the distributions for the number of customers and sojourn time in the system. Furthermore, we also give the stochastic decomposition results of such stationary indices.

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Acknowledgments

The authors wish to thank the anonymous referees and the editor for their valuable comments and suggestions, which are helpful to improve the paper. This research was supported by the foundation for university key teacher of Henan province (2014GGJS-136) and the foundation for university key research project of Henan province (16A110002).

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Authors and Affiliations

  1. School of Arts and Science, Sias International University, Zhengzhou, 451150, China

    Hongbo Zhang

  2. School of Mathematics and Statistics, Henan Institute of Education, Zhengzhou, 450046, China

    Hongbo Zhang & Gaojun Zhou

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  1. Hongbo Zhang
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  2. Gaojun Zhou
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Correspondence to Hongbo Zhang.

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Zhang, H., Zhou, G. M/M/1 queue with m kinds of differentiated working vacations. J. Appl. Math. Comput. 54, 213–227 (2017). https://doi.org/10.1007/s12190-016-1005-z

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  • DOI: https://doi.org/10.1007/s12190-016-1005-z

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