The authors present a diffusion approximation of the first overflow time in the G/G/m system with finite capacity. They 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. The authors use the first passage time of diffusion process as the first overflow time in the G/G/Gm 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/M/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.
