## 4 Experimental Setup
### Trace Analysis and Modeling  
The next challenge is to analyze the trace and to create a driving video traffic model for traffic generation later. To verify the correlation of video frame and to obtain the modeling parameter, we obtain the frame-to-frame correlation of the video traffic. Figure 9 is an example using our video trace, which shows correlation is present up to 20 seconds apart. We have used the Pareto distribution to characterize the general correlation of \"action\" video frame duration in wireless video streaming as well as the strong correlation between a cluster of byte loss and/or duplication caused by the air interface. The Pareto distribution is a long-tailed distribution with the following pdf (probability density function) \(g(x)\) for the consecutive I-frame duration, where the edge activity level is high. Note that \(x\) here is not the frame size but the group length rather. \[g(x)=c\alpha^{c}\ \ /\ x^{c\ +1}\ \ \ \ \ \alpha\ \leq x<\infty \tag{1}\]  
where \(\alpha>0\) is the location parameter and \(c>0\) is the shape parameter. The location parameter value can be obtained from the mean correlation length E(x) of the trace where E(x) = c\(\alpha/(\alpha-1)\). On the other hand, the shape parameter has to be obtained via the Hurst parameter. That is,  
\[H=\frac{1}{2}\big{(}3-c\big{)}\ \ \Rightarrow\ \ c=3\text{-}2H \tag{2}\]  
Note that the Hurst parameter is a useful parameter to reflect the invariance according to the entropy conservation property [26]. Since our video is highly compressed with little loss of information, the entropy/uncertainty remains the same. Therefore, we can determine c from Equation (2). An indirect but easy way to obtain the Hurst parameter value is via the _slope_ of the IDC (Index of Dispersion for Count) curve as a function of the level of aggregation. Here IDC is defined to be  
Figure 9: Correlation length of driving video. normalized variance of aggregated variables [26], and the level of aggregation refers the logarithm of the number of variables base-10 (therefore level-0 has 1 variable, level-1 has 10 variables, level-2 has 100 variables and so on). Mathematically, the relationship is given by [26]  
\[H=\frac{1}{2}\big{(}1+slope\big{)} \tag{3}\]  
The slope of the curve is usually measured from the first point to the last point on the graph. For example, Figure 10 gives the IDC of the video trace we use. From this figure, the slope is measured to be 0.33. Hence the Hurst parameter H is 0.67, and the shape parameter is \(c=1.66\). Once we obtain the pdf \(g(x)\) to characterize the activity duration (via the correlation of I-frames), we shall next determine the packet (frame) size distribution \(f(x)\), which is not Pareto in general. Furthermore, unlike the traditional video (e.g., video conference) with the moving part in the middle, our driving video has the moving part on the edge. Whereas the traditional video has a normal distribution in the middle for its packet size after 2D-DCT (Discrete Cosine Transform), the distribution for driving video is at the edge, which becomes very hard to model analytically to match the measured curve. After many trials, we have determined that an empirical model using nine mini-sources laid out in a grid can capture the distribution properly. The surrounding sources will capture the distribution of packets further away from the middle (edges and corners) which are usually moving and which produce large packets. The mini-sources closer to the center will capture the scenes in the middle which are relatively still and that produce smaller packets. Figure 11 demonstrates the empirical analysis we performed on frame size (horizontal axis) of our traffic trace. For simplicity, here we are using the basic camera configuration, which produces one packet per frame. We use a tool called EasyFitTM[55] to obtain the pdf of the \(n=9\) video traces. The orange curve in the figure shows that the lognormal distribution is the best distribution to fit the given histogram data. Figure 10: Entire trace IDC curve.