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Stationary analysis of the infinite-server queue modulated by a multi-phase Markovian environment

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Abstract

We consider an infinite-server queue, where the arrival and service rates are both governed by a continuous-time Markov chain that is independent of all other aspects of the queue. Through constructing a pretty Markov process, several performance measures are derived by using the supplementary variable technique. In addition, special cases and numerical examples are studied in detail.

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Acknowledgements

The authors would like to sincerely thank the anonymous referees and the Editor for their valuable comments and suggestions, which help to improve the quality of this paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, Hunan, People’s Republic of China

    Senlin Yu & Zaiming Liu

Authors
  1. Senlin Yu
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  2. Zaiming Liu
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Correspondence to Zaiming Liu.

Additional information

This research is supported by the National Natural Science Foundation of China 11671404.

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Yu, S., Liu, Z. Stationary analysis of the infinite-server queue modulated by a multi-phase Markovian environment. J. Appl. Math. Comput. 58, 33–46 (2018). https://doi.org/10.1007/s12190-017-1132-1

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  • DOI: https://doi.org/10.1007/s12190-017-1132-1

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