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MX/M/c Queue with catastrophes and state-dependent control at idle time

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Abstract

We consider an MX/M/c queue with catastrophes and state-dependent control at idle time. Properties of the queues which terminate when the servers become idle are first studied. Recurrence, equilibrium distribution, and equilibrium queue-size structure are studied for the case of resurrection and no catastrophes. All of these properties and the first effective catastrophe occurrence time are then investigated for the case of resurrection and catastrophes. In particular, we obtain the Laplace transform of the transition probability for the absorbing MX/M/c queue.

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Acknowledgements

This work was substantially supported by the National Natural Sciences Foundations of China (Grant Nos. 11371374, 11771452, 11701489, 11571372), the National Natural Science Foundation of China-Tian Yuan (Grant No. 11626203), and the Natural Sciences Foundations of Hunan Province (No. 2017JJ2328).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Central South University, Changsha, 410083, China

    Junping Li

  2. School of Mathematics and Computational Science, Xiangtan University, Xiangtan, 411105, China

    Lina Zhang

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  1. Junping Li
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  2. Lina Zhang
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Correspondence to Junping Li.

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Li, J., Zhang, L. MX/M/c Queue with catastrophes and state-dependent control at idle time. Front. Math. China 12, 1427–1439 (2017). https://doi.org/10.1007/s11464-017-0674-8

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  • DOI: https://doi.org/10.1007/s11464-017-0674-8

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