Parametric Resampling Analysis of Traffic Measurements

Our aim in this paper is to apply the technique of parametric ‘bootstrapping’ (or ‘resampling’) to determine what sampling frequency of traffic measurements is necessary for the proper engineering of high-speed data networks. Recent studies have shown that Fractional Brownian Motion (FBM) is a good model for the traffic observed in high-speed data networks, capturing both self-similarity and long-range dependence. We investigate the effect of the frequency of collection of traffic measurements on the estimation of FBM traffic parameters and, in turn, on the accuracy of link engineering. We go beyond earlier studies to obtain the statistical properties of link engineering that is based on traffic estimation from sampled measurements. The key idea is to ‘resample’ by creating replicate data sets with the same parametric model as the original data set, from which the variability of the quantities of interest can be assessed with reference to the time-resolution of the traffic measurements, which is our basic control variable. We find that link engineering based on traffic measurements sampled at one-minute intervals produces significant error, in the range 7-26%, while engineering based on measurements sampled at one-second intervals results in an error in the range 2-4%. Hence, we conclude that for acceptable accuracy in capacity engineering for IP traffic, traffic measurements should be collected at a finer time-resolution than one-minute intervals, and that measurements at one-second intervals lead to acceptable accuracy.