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Analysis of queues in a random environment with impatient customers

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Abstract

We study M/M/c queues (c = 1, 1 < c < ∞ and c = ∞) in a Markovian environment with impatient customers. The arrivals and service rates are modulated by the underlying continuous-time Markov chain. When the external environment operates in phase 2, customers become impatient. We focus our attention on the explicit expressions of the performance measures. For each case of c, the corresponding probability generating function and mean queue size are obtained. Several special cases are studied and numerical experiments are presented.

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Authors and Affiliations

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

    Sen-lin Yu & Zai-ming Liu

Authors
  1. Sen-lin Yu
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  2. Zai-ming Liu
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Correspondence to Zai-ming Liu.

Additional information

Supported by the National Natural Science Foundation of China (No. 11671404) and the Fundamental Research Funds for the Central Universities of Central South University 2016zzts014.

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Yu, Sl., Liu, Zm. Analysis of queues in a random environment with impatient customers. Acta Math. Appl. Sin. Engl. Ser. 33, 837–850 (2017). https://doi.org/10.1007/s10255-017-0701-2

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  • DOI: https://doi.org/10.1007/s10255-017-0701-2

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