Testing the Gaussian approximation of aggregate traffic

We search for methods or tools to detect whether the 1-dimensional marginal distribution of traffic increments of aggregate TCP-traffic satisfy the hypothesis of approximate normality. Gaussian approximation requires a high level of aggregation in both "vertical" (source aggregation) and "horizontal" (time scale) directions. We discuss these different concepts of aggregation first separately, with an example from real data traffic, and show how to rule out cases where the level of aggregation will not be sufficient. Gaussian approximation is then quantified with the square of the linear correlation coefficient in normal-quantile plots. We propose an elementary method based on this correlation test, by looking at the behavior of the test statistic for different sample sizes, and show positive and negative examples from the example data. We use this method to look for the first time scale, where the Gaussian approximation is plausible with the example data, and then we look how much more vertical aggregation would be needed for smaller time scales in order to obtain a reasonable approximation by normal distribution.