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For Internet traffic engineering purposes, it is important to characterize traffic volumes typically over 5-minute intervals. Based on measurements made in a local network at Lucent in winter 1999, Cao et al., (2000) proposed a moving IID Gaussian model for the characterization of 5-minute traffic volumes, with a power-law relationship between the mean and the variance. In this paper we analyze novel measurements gathered from a 2.5 Gbps link in the Finnish university network (Funet) in summer 2004. We investigate the validity of the moving IID Gaussian model and the proposed mean-variance relationship when the measurement interval is varying from 1 second to 5 minutes. As a result, we find that the Gaussian assumption is much more justified with current core link rates. The mean-variance relationship seems, indeed, to follow a power-law with exponent approximately equal to 1.3 in our data set. However, the IID assumption concerning the standardized residual is not verified, but we find a clear positive correlation between adjacent 5-minute volumes, and only slightly weaker negative correlation for traffic volumes with distance 20-30 minutes. In addition, we demonstrate that the same phenomenon is already prevailing in the Lucent data set.