Self-similar traffic and upper bounds to buffer-overflow probability in an ATM queue

It was recently shown, from real measurements in high-speed communications networks, that network traffic may demonstrate properties of long-range dependency peculiar to the self-similar stochastic process. It was also shown by measurements that with increasing buffer capacity, the resulting cell loss is not reduced exponentially fast, as it is predicted by queueing theory applied to traditional telecommunication Markovian models, but in contrast, decreases very slowly. The problem is how to present a theoretical understanding to those experimental phenomena. 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 hyperbollically, h−a, with buffer size h is obtained. The lower bound given in Tsybakov and Georganas (1997) and the upper bound obtained here demonstrate the same h−a asymptotical behavior, thus showing the actual hyperbolical decay of overflow probability for a self-similar-traffic model.