Discrete-time heavy-tailed chains, and their properties in modeling network traffic

The particular statistical properties found in network measurements, namely self-similarity and long-range dependence, cannot be ignored in modeling network and Internet traffic. Thus, despite their mathematical tractability, traditional Markov models are not appropriate for this purpose, since their memoryless nature contradicts the burstiness of transmitted packets. However, it is desirable to find a similarly tractable model which is, at the same time, rigorous at capturing the features of network traffic. This work presents discrete-time heavy-tailed chains, a tractable approach to characterize network traffic as a superposition of discrete-time "on/off" sources. This is a particular case of the generic "on/off" heavy-tailed model, thus shows the same statistical features as the former, particularly self-similarity and long-range dependence, when the number of aggregated sources approaches infinity. The model is then applicable to characterize a number of discrete-time communication systems, for instance, ATM and optical packet switching, to further derive meaningful performance metrics such as average burst duration and the number of active sources in a random instant.