Towards a statistical network calculus - Dealing with uncertainty in arrivals

The stochastic network calculus (SNC) has become an attractive methodology to derive probabilistic performance bounds. So far the SNC is based on (tacitly assumed) exact probabilistic assumptions about the arrival processes. Yet, in practice, these are only true approximately–at best. In many situations it is hard, if possible at all, to make such assumptions a priori. A more practical approach would be to base the SNC operations on measurements of the arrival processes (preferably even on-line). In this paper, we develop this idea and incorporate measurements into the framework of SNC taking the further uncertainty resulting from estimation errors into account. This is a crucial step towards a statistical network calculus (StatNC) eventually lending itself to a self-modelling operation of networks with a minimum of a priori assumptions. In numerical experiments, we are able to substantiate the novel opportunities by StatNC.