Overflow probability in an ATM queue with self-similar input traffic

Real measurements in high-speed communications networks have recently shown that traffic may demonstrate properties of long-range dependency peculiar to self-similar stochastic processes. Measurements have also shown that, with increasing buffer capacity, the resulting cell loss is not reduced exponentially fast as it is predicted by Markov-model-based queueing theory but, in contrast, decreases very slowly. Presenting a theoretical understanding to those experimental results is still a problem. The paper presents mathematical models for self-similar cell traffic and analyzes the overflow behavior of a finite-size ATM buffer fed by such a traffic. An asymptotical upper bound to the overflow probability, which decreases hyperbolically, h^-a, with buffer-size-h is obtained. A lower bound is also described, which demonstrates the same h^-a asymptotical behavior, thus showing an actual hyperbolical decay of overflow probability for a self-similar-traffic model