On the threshold for observing approximate invariance of effective bandwidth

Effective bandwidth is a descriptor in the context 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 called ldquoinvariance propertyrdquo of effective bandwidth. Numerical simulations have suggested that in some cases, the ldquoinvariance propertyrdquo 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. The advantage of predefining 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.