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.
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