Large deviations for small buffers: An insensitivity result

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