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Journal of Applied Mathematics and Stochastic Analysis
Volume 8, Issue 1, Pages 11-28
http://dx.doi.org/10.1155/S1048953395000025

Diffusion approximation for first overflow time in GI/G/m system with finite capacity

1Korea Advanced Institute of Science and Technology, Department of Mathematics, Gusong-dong, Yusong-gu, Taejon 305-701, Korea
2Changwon National University, Department of Statistics, 9 Sarimdong, Changwon 641-773, Korea

Received 1 February 1994; Revised 1 June 1994

Copyright © 1995 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present a diffusion approximation of the first overflow time in the GI/G/m system with finite capacity. We derive the Laplace Stieltjes transform of the first passage time of diffusion process which approximates the system size in the GI/G/m system with finite capacity. We use the first passage time of diffusion process as the first overflow time in the GI/G/m system with finite capacity. To check on accuracy of this approximation, the analytical results for the mean of the first overflow time in the GI/G/m system with finite capacity is numerically compared with the diffusion approximation results. Numerical results show that the diffusion approximation is a good approximation for heavy traffic systems.