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

The particular statistical properties found in network measurements, namely self-similarity and long-range dependence, cannot be ignored in modelling 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 the discrete-time heavy-tailed chains, a tractable approach to characterise 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 showing 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 characterise a number of discrete-time communication systems, for instance ATM and Optical Packet Switching, and further derive meaningful performance met- rics, such as the average burst duration and the number of active sources in a random instant.