Large Deviations for Small Buffers: An Insensitivity Result

This article focuses on a queue fed by a large number of "semi-Markov modulated fluid sources", e.g., on/off sources with on and off-times that have general distributions. The asymptotic regime is considered in which the number of sources grows large, and the buffer and link rate are scaled accordingly. We aim at characterizing the exponential decay rate of the buffer overflow probability for the regime of small buffers. An insensitivity result is proven: the decay rate depends on the distributions of the on and off-times only through their means. The efficiency gain to be achieved by using small buffers is significant, as the decay rate grows fast: proportionally to the square root of the buffer size.