In this paper, we consider parsimonious Gaussian and Stable (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.

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Conference 2003 International Conference on Communications (ICC 2003)
Harmantzis, F.C. (Fotios C.), Hatzinakos, D. (Dimitrios), & Lambadaris, I. (2003). Effective bandwidths and tail probabilities for Gaussian and stable self-similar traffic. In IEEE International Conference on Communications (pp. 1515–1520).