Diffusion approximation for first overflow time inGI/G/msystem with finite capacity

[摘要] We present a diffusion approximation of the first overflow time in theGI/G/msystem with finite capacity. We derive the Laplace Stieltjes transform of the first passage time of diffusion process which approximates the system size in theGI/G/msystem with finite capacity. We use the first passage time of diffusion process as the first overflow time in theGI/G/msystem with finite capacity. To check on accuracy of this approximation, the analytical results for the mean of the first overflow time in theGI/G/msystem 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.

[学科分类] 应用数学