Self-Similar Traffic and Upper Bounds to Buffer-Overflow Probability in an ATM Queue

From real measurements in high-speed communications networks, it was recently shown 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. A 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 [TG] 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. ----This work was supported in part by a grant from Nortel (BNR), and in part by NSERC operating grant A-8450 and by NWO project 713-229. 1.INTRODUCTION SELF-SIMILAR TRAFFIC AND UPPER BOUNDS TO BUFFER-OVERFLOW PROBABILITY IN AN ATM QUEUE