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Fluid approximation and its convergence Rate for GI/G/1 queue with vacations

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Abstract

A GI/G/1 queue with vacations is considered in this paper. We develop an approximating technique on max function of independent and identically distributed (i.i.d.) random variables, that is max{η i , 1 ≤ i ≤ n}. The approximating technique is used to obtain the fluid approximation for the queue length, workload and busy time processes. Furthermore, under uniform topology, if the scaled arrival process and the scaled service process converge to the corresponding fluid processes with an exponential rate, we prove by the approximating technique that the scaled processes characterizing the queue converge to the corresponding fluid limits with the exponential rate only for large N. Here the scaled processes include the queue length process, workload process and busy time process.

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yong-jiang Guo

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  1. Yong-jiang Guo
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Correspondence to Yong-jiang Guo.

Additional information

Supported by the National Natural Science Foundation of China (No. 10826047 and No.10901023), and by the Fundamental Research Funds for the Central Universities under Contract BUPT2009RC0707.

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Guo, Yj. Fluid approximation and its convergence Rate for GI/G/1 queue with vacations. Acta Math. Appl. Sin. Engl. Ser. 27, 43–58 (2011). https://doi.org/10.1007/s10255-011-0038-1

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  • DOI: https://doi.org/10.1007/s10255-011-0038-1

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