# Bit Rate Adaptation Using Linear Quadratic Optimization for Mobile Video Streaming
## 5 Determining LQE Parameters  
In this section, we explore the effect of LQE parameters, which are knobs to control the behavior of a client player according to different user demands. To this end, we examine LQE with trace-driven simulations with several parameter settings (See Section 6 for the simulation setup).  
Figure 2(a) shows the CDFs of the number of bit rate changes in the 3570 scenarios according to different \(\sigma\) and \(m\) while we set \(q_{0}\) & \(\sigma\) to 70s and \(10^{4}\), respectively. In these simulations, we use one for \(m\), i.e., disable the count-based switching logic in LQE, so that we investigate the effect of the adjustment factor for reducing the number of bit rate changes. As shown in Figure 2(a), the number of bit rate changes decreases until \(\sigma=0.05\) and starts to increase after \(\sigma\) becomes larger than 0.05. In the experiments, we observe that \(\sigma\) does not notably affect streaming quality such as the total rebuffering duration. Therefore, we select \(\sigma=0.05\), which yields the fewest number of bit rate changes without increasing the rebuffering duration.  
Given \(\sigma=0.05\), we explore the effect of the counter-based switching logic. As shown in Figure 2(b), using \(m\geq 2\) successfully enables LQE to reduce the number of bit rate changes together with the adjustment factor: \(m=2\) reduces the number of bit rate changes by almost half. However, as \(m\) increases, LQE response more slowly to network dynamics, resulting in a longer rebuffering duration: \(m=2\) triggers rebufferings in 3% more scenarios than \(m=1\) in our simulations. We use the counter threshold of \(m=2\), which significantly reduces the number of bit rate changes with the smallest impact on the rebuffering behavior.  
Next, we investigate the effect of the control weight \(\rho\) on the number of bit rate changes and streaming quality. Figure 4 shows the CDFs of the number of bit rate changes of LQE with different values of \(\rho\) while we set \(\sigma\) & \(q_{0}\) to 0.05 and 70 s, respectively. We observe that the number of bit rate changes decreases as \(\rho\) becomes larger, while a larger \(\rho\) results in longer total rebuffering durations. We choose \(\rho=10^{4}\) which compromises between the number of bit rate changes and the total rebuffering duration.  
Figure 5 presents the CDFs of average bit rate and total rebuffering duration of LQE with different values of \(q_{0}\) while \(\sigma\) and \(\rho\) are set to 0.01 and \(10^{4}\), respectively. We observe that the average bit rate and total rebuffering duration become smaller and shorter as \(q_{0}\) increases, showing the trade-off between average bit rate and rebuffering. It is because a larger \(q_{0}\) is likely to incur more negative error, resulting in lower bit rate selections, which can shorten the duration of rebuffering. For the rest of the experiments, we choose \(q_{0}=70\)  
Figure 3: Effect of \(\sigma\) and \(m\) (LQE).  
that yields similar average bit rates compared to \(q_{0}=90\) while exhibiting moderately short rebuffering durations.