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

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  • Bong Dae Choi
  • Yong Wan Lee
  • Yang Woo Shin

Abstract

We present a diffusion approximation of the first overflow time in the G I / 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 G I / G / m system with finite capacity. We use the first passage time of diffusion process as the first overflow time in the G I / 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 G I / 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.

Suggested Citation

  • Bong Dae Choi & Yong Wan Lee & Yang Woo Shin, 1995. "Diffusion approximation for first overflow time in G I / G / m system with finite capacity," International Journal of Stochastic Analysis, Hindawi, vol. 8, pages 1-18, January.
    • Handle: RePEc:hin:jnijsa:816350
    DOI: 10.1155/S1048953395000025
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