# A Novel Proprietary Internet Video Traffic Dataset Generation Algorithm
## 4 Analysis of Proprietary Internet Video Traffic Datasets
### Video Traffic Histogram Density  
In this section, we analyze the video traffic histogram density and distribution across three key features, bidirectional flow duration, bidirectional packets, and bidirectional bytes, for all video quality category proprietary datasets. To analyze the probability density function (PDF) and cumulative density function (CDF) of a specific video traffic feature vector, a histogram is used as an approximation of the PDF. Each bin represents an interval of the variable, with the normalized height approximating the probability density in that range. Increasing the number of bins while reducing bin width enhances the histogram's accuracy, allowing it to converge to the true PDF. To normalize the histogram, frequencies are scaled so the total area under the histogram equals 1, as defined in Equation (6). \[p_{i}=\frac{f_{i}}{mh} \tag{6}\]  
where  
* \(f_{i}\) is the frequency of points in the \(i\)-th bin of the histogram;
* \(p_{i}\) is the height of the \(i\)-th bin of the histogram;
* \(m\) is the total number of data points;
* \(h\) is the bin width. In practice, bin width is determined using the Sturges and Freedman-Diaconis rules, selecting the strategy that minimizes bin width. The cumulative density function (CDF) is derived from the PDF. The CDF can be estimated from a histogram-based PDF by summing the normalized heights of all bins up to and including the bin corresponding to a given value. For the bin containing the value, a proportional contribution is added based on the position of the value within the bin. This cumulative sum provides an estimate of the cumulative probability distribution. Figure 4 shows the traffic flow duration histogram \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Dataset** & _cvq_ & _cv_ & **Dataset** & _cvq_ & _cv_ & **Dataset** & _cvq_ & _cv_ \\ \hline nILAD & 0.9620 & 2.9209 & YVAIL & 0.4127 & 0.3996 & TVAL & 0.0719 & 0.1585 \\ nTLAD & 0.9620 & 2.9209 & YVAIL & 0.4127 & 0.3996 & TVAL & 0.0719 & 0.1585 \\ nPAD & 0.9620 & 2.9209 & YVAIL & 0.4127 & 0.3996 & TVAL & 0.0719 & 0.1585 \\ nILAD & 0.9620 & 2.9209 & YVAP & 0.4127 & 0.3996 & TVAP & 0.0719 & 0.1585 \\ nILPD & 0.9713 & 2.9478 & FVAL & 0.4983 & 0.8448 & TVQC & 0.7896 & 0.8538 \\ nTLPD & 0.9713 & 2.9478 & FVAL & 0.4983 & 0.8448 & YVQC & 0.4738 & 0.5037 \\ nLPD & 0.9713 & 2.9478 & FVAL & 0.4983 & 0.8448 & FVQC & 0.5639 & 0.6094 \\ nPPD & 0.9713 & 2.9478 & FVAD & 0.4983 & 0.8448 & & & \\ \hline Reference & _cvq_ & _cv_ & Reference & _cvq_ & _cv_ & Reference & _cvq_ & _cv_ \\ \hline
[10] & 0.3522 & 0.3881 & [11] & 0.8321 & 1.0149 & [12] & 0.0 & 0.0 \\
[13] & 0.5534 & 0.9055 & [14] & 0.3740 & 1.2235 & [16] & 0.0 & 0.0 \\
[20] & 0.4365 & 1.2184 & [21] & 0.5 & 0.4082 & [25] & 0.9669 & 2.3018 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measurement of the categories’ imbalance rate in the proprietary Internet video traffic datasets. density and cumulative distribution for proprietary datasets across all video quality categories. It reveals that for most nDPI datasets from all three platforms, the majority of flow durations concentrate in the first 25 s, while the CICFlowmeter datasets exhibit the opposite trend, with most flow durations concentrated in the range of 125-180 s. We set the flow metering timer to 180 s, which means the maximum flow duration in the samples will be capped at 180 s. The two DFI tools employ different flow metering strategies. Figure 5 displays the traffic flow bidirectional packet accumulation histogram density and cumulative distribution for all datasets. It shows that most bidirectional packet accumulations fall within the 0-1500 range. However, the nDPI Twitch dataset stands out with a significant concentration of flow samples having very large bidirectional packet accumulations, particularly in the range of 120,000-150,000. Figure 6 presents the traffic flow bidirectional byte accumulation histogram density and cumulative distribution for all datasets.