Journal of Applied Mathematics and Stochastic Analysis 
Volume 8 (1995), Issue 1, Pages 11-28
doi:10.1155/S1048953395000025

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

Bong Dae Choi,1 Yong Wan Lee,1 and Yang Woo Shin2

 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

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.