# Analysis and Prediction of the IPv6 Traffic over Campus Networks in Shanghai
## 3 Dataset and Traffic Usage Features
### Self-Similarity Analysis  
Since studies found that the self-similarity model can describe network traffic's characteristics more accurately than the traditional Poisson traffic model, it has been widely used in Internet-related studies [9; 42; 43]. The Hurst exponent (H) is a classic metric used to describe the self-similarity characteristic of the network traffic. To calculate the R/S statistic from a stationary process, it approximately satisfies  
\[E[R(n)/S(n)]=Cn^{H},n\rightarrow\infty \tag{1}\]  
where \(H\) is the Hurst exponent varying between 0 and 1, \(n\) is the number of data slots in a stationary process, \(R(n)\) is the range of the cumulative deviations from the mean in the first \(n\) data slots, \(S(n)\) is the standard deviation of the first \(n\) data slots, \(E(x)\) is the expected value, and \(C\) is a constant. Clearly, \(H>0.5\) is a necessary condition for the existence of self-similarity, and a time series with larger \(H\) has stronger self-similarity. A value of \(H=0.5\) indicates that the series is completely uncorrelated and can be described as a random walk, whereas \(H<0.5\) suggests that the series tends to switch between high and low values in the long term.  
We estimate the value of the Hurst exponent [44] using the aggregate variance method (A/V), the R/S method, and the periodogram method (P) and compare the Hurst exponents of IPv6 and IPv4 traffic volume.  
* The aggregate variance method plots the sample variance versus the block size of each aggregation level on a log-log plot. If the series is self-similar, the plot will be a line with slope \(\beta\) greater than -1. The H is estimated by \(H=1+\beta/2\).
* \(R/S\) method uses the rescaled range statistic (\(R/S\) statistic). The \(R/S\) statistic is the range of the cumulative deviations of a time series sequence from its mean, divided by its standard deviation. The method plots the R/S statistic versus the number of points of the aggregated series and the plot should be linear with a slope. The estimation of the Hurst exponent is the slope.
* Periodogram method plots the the spectral density of a time series versus the frequencies on a log-log plot. The slope of the plot is the estimate of \(H\).  
The results are summarized in Table 1. As it shows, in both universities, the IPv4 Hurst exponents of the upstream or downstream traffic are similar to the IPv6 Hurst exponents, while in a study on a campus network in 2012 [9], there was a big gap between the self-similarity of IPv4 traffic and that of IPv6 traffic. The results imply the difference between IPv6 and IPv4 traffic is much smaller than earlier results in [9].  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Traffic** & & **IPv4** & **IPv6** & **IPv4** & **IPv6** \\
**Category** & **Method** & **Downstream** & **Downstream** & **Upstream** & **Upstream** \\ \hline  & R/S & 0.6703 & 0.6609 & 0.6962 & 0.6957 \\ DHU & A/V & 0.6936 & 0.6671 & 0.6355 & 0.6984 \\  & P & 0.5936 & 0.6315 & 0.5503 & 0.6285 \\ \hline  & R/S & 0.7159 & 0.6990 & 0.8104 & 0.8090 \\ ECNU & A/V & 0.6652 & 0.6698 & 0.8253 & 0.7843 \\  & P & 0.5476 & 0.6740 & 0.6771 & 0.7349 \\ \hline \hline \end{tabular}
\end{table}
Table 1: The values of Hurst exponents of IPv4 and IPv6 traffic.