Diffusion approximation for first overflow time in \(GI/G/m\) system with finite capacity (Q1890817)

Summary: 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 \(GI/M/m\) 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.