caa a22 4500 445830549 CHVBK 20180317145313.0 cr unu---uuuuu 170323e20110101xx s 000 0 eng 10.1007/s10255-011-0038-1 doi (NATIONALLICENCE)springer-10.1007/s10255-011-0038-1 Guo Yong-jiang School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut Fluid approximation and its convergence Rate for GI/G/1 queue with vacations [Elektronische Daten] [Yong-jiang Guo] 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. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 GI/G/1 queue with vacations nationallicence fluid approximation nationallicence exponential rate of convergence nationallicence Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/1(2011-01-01), 43-58 0168-9673 27:1<43 2011 27 10255 https://doi.org/10.1007/s10255-011-0038-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0038-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Guo Yong-jiang School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/1(2011-01-01), 43-58 0168-9673 27:1<43 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer