On the Observance of Approximate Invariance of Effective Bandwidth with Finite Number of Sources

Abstract — The effective bandwidth is a descriptor in the con-text of stochastic models for statistical sharing of resources. One of the most interesting properties of effective bandwidth is that it does not change when passing a network node under many sources limiting regime (infinitely many sources). This is referred as the “invariance property ” of effective band-width. Numerical simulations have suggested that in some cases, the “invariance property ” of effective bandwidths holds already for a surprisingly small number of competing flows even in the presence of aggressive TCP traffic. The real question, though, is: how many input processes are needed for reasonable convergence over the scale of interest? This work addresses this question using recent results from the large deviations theory under many sources limiting regime and the theory of statistical network calculus. We also show that as the number of arrival flows increases, the bound on the departure process ’ effective bandwidth converges exponentially fast to that of the effective bandwidth of the arrival. The advantage of identifying the minimum number of independent multiplexing flows at each network node to observe approximate invariance of effective bandwidth is that the task of network resources dimensioning can be greatly simplified. Index Terms — effective bandwidth, invariance property, many sources asymptotic, statistical network calculus, over-flow probability. I