Effective bandwidths and tail probabilities for Gaussian and stable self-similar traffic

In this paper, we consider parsimonious Gauusian and table (heavy-tailed) models, which best capture the self-similarity of aggregate packet traffic in broadband networks. Using the effective bandwidths theory, we extend the recent results on stable self-similar-driven queues with infinite buffer to the finite buffer case that model routers/switches more accurately. Large deviations results are extended from the large buffer regime to the many sources limiting regime. Unfortunately, in the stable case, traditional large-deviations formulae degenerate into not very helpful asymptotic results, unlike the Gaussian case. This has a negative impact in engineering considerations (e.g., connection admission control, buffer management, statistical multiplexing gains), with respect to those results, and leads to alternative solutions, e.g. empirical/numerical and simulation techniques.