Quality of service parameters and link operation point estimation based on effective bandwidth

PostprintThis work addresses the estimation and calculation of the operating point of a network's link in a digital traffic network. The notion of operating point comes from effective bandwidth (EB) theory. The results shown are valid for a wide range of traffic types. We show that, given a good EB estimator, the operating point, i.e. the values of time and space parameters in which the EB is related with the asymptotic overflow probability, can also be accurately estimated. This means that the operating point (and other parameters) inherits the statistical properties of the EB estimation. This affirmation is not an obvious one, because operating point parameters are related with the EB through an implicit function involving extremal conditions computations. Imposing some regularity conditions, a consistent estimator and confidence regions for the operating point and Quality of Service parameters are developed. These conditions are very general, and they are met by commonly used estimators as the averaging estimator presented in [C. Courcoubetis, R. Weber, Buffer overflow asymptotics for a switch handling many traffic sources, J. Appl. Probability 33 (1996)] or the Markov Fluid model estimator presented in [J. Pechiar, G. Perera, M. Simon, Effective bandwidth estimation and testing for Markov sources, Perform. Eval. 48 (2002) 157-175]. Using a software package developed by our group that estimates the EB and other relevant parameters from traffic traces, simulation results are compared with the analytical results, showing very good fitting