## Investigation of cell scale and burst scale effects on the
cell loss probability using large deviations

### C. Courcoubetis, V. A. Siris, and R. Weber. In *Proceedings
of 15th U.K. Workshop on Performance Engineering of Computer and
Telecommunication Systems (UKPEW'97) *, Ilkley, U.K., July 24,
1997.

Abstract

Considerable research activity has been directed towards estimating the Cell Loss
Probability (CLP) at the buffer of an ATM switch and understanding the ways in which it can
occur. Much of this activity has been conducted by modeling the cells which enter the buffer
as a continuous fluid. This model can capture the variability of a source at a burst level,
but it ignores the fact that the workload actually arrives in discrete cells. Nonetheless
the fluid model can give accurate estimates of the cell loss probability when the buffer
size is not very small. If the switch hasa very small amount of buffer per source then
cell level effects cannot be ignored. We consider both Constant Bit Rate (CBR) and
periodic on/off Variable Bit Rate (VBR) sources, and apply large asymptotic techniques
to a cell level model of an ATM output link. Our analysis simultaneously captures both
the cell scale and burst scale effects, enabling us to study the boundary between regions
in the parameter space where cell level effects are or are not signicant. In addition
to accurately computing the CLP, we are able to give an insightful qualitative description
of how cell loss occurs in very small buffers.}

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