Stochastic bounds and histograms for active queues management and networks analysis

Abstract

We present an extension of a methodology based on monotonicity of various networking elements and measurements performed on real networks. Assuming the stationarity of flows, we obtain histograms (distributions) for the arrivals. Unfortunately, these distributions have a large number of values and the numerical analysis is extremely time-consuming. Using the stochastic bounds and the monotonicity of the networking elements, we show how we can obtain, in a very efficient manner, guarantees on performance measures. Here, we present two extensions: the merge element which combine several flows into one, and some Active Queue Management (AQM) mechanisms. This extension allows to study networks with a feed-forward topology.