Statistical modeling of the Internet traffic dynamics: To which extent do we need long-term correlations?

Recently we have suggested a universal superstatistical model of user access patterns and aggregated network traffic. The model takes into account the irregular character of end user access patterns on the web via the non-exponential distributions of the local access rates, but neglects the long-term correlations between these rates. While the model is accurate for quasi-stationary traffic records, its performance under highly variable and especially non-stationary access dynamics remains questionable. In this paper, using an example of the traffic patterns from a highly loaded network cluster hosting the website of the 1998 FIFA World Cup, we suggest a generalization of the previously suggested superstatistical model by introducing long-term correlations between access rates. Using queueing system simulations, we show explicitly that this generalization is essential for modeling network nodes with highly non-stationary access patterns, where neglecting long-term correlations leads to the underestimation of the empirical average sojourn time by several decades under high throughput utilization.