# A Sign of Things to Come: Predicting the Perception of Above-the-Fold Time in Web Browsing
## 4 Evaluation
### Impact of PCT on QoE Estimation  
To investigate how PCT impacts the robustness of QoE estimation models, we used IQX and WQL (Waiting time and its QoE evaluation on a linear ACR scale is _L_ogarithmic) web QoE models. The IQX and WQL are two parametric web QoE models which can be used to quantify the link between perceived user QoE and waiting time for a web page loading. The IQX model is a generic QoE model where QoE and technical QoS metrics are correlated through an exponential relationship [7]. The IQX model uses the following equation:  
\[\text{QoE}^{\text{IQX}}(t)=\alpha e^{-\beta t}+\gamma, \tag{3}\]  
where \(t\) is the waiting time measured by a time instant or time integral metric and \(\alpha\), and \(\beta\) and \(\gamma\) are empirically derived constants. The constants are tuned in accordance with the context (i.e., Web, VOIP, Video). The authors illustrate that when the current level of QoE is high, a small variation in the QoS is perceptually noticeable, thus yielding to an exponential relationship between QoE and waiting time.  
[PERSON] et al. [8] proposed a logarithmic web QoE estimation model in accordance with the Weber-Fechner law [21]. Their proposed web QoE model is derived from a hypothesis which assumes the relationship between _Wa_iting time and its QoE evaluation on a linear ACR scale is _L_ogarithmic (WQL). The authors used the following fitting function and validated the WQL hypothesis:  
\[\text{QoE}^{\text{WQL}}=a-b\text{ln}(t), \tag{4}\]  
where \(t\) refers to the waiting time measured by a time instant or time integral metric, and \(a\) and \(b\) are derived by minimizing the least square errors between the fitting function and the Mean Opinion Score (MOS) values.  
The constants from IQX and WQL models fitting curves (where MOS is estimated based on ATF time) were taken from a study by [PERSON] et al. [6]. The constants of the fitting curves are then used to compute corresponding MOS values for a given PCT time (a measure for ATF). Please note that we have assumed that the result of [PERSON] [6]'s study is generalizable and can be used to estimate QoE in this research.  
In our previous study [10], a similar analysis for both WQL and IQX using objective ATF metric illustrated that both models are generally underestimating the perceived quality using objective ATF with R-squared of 0.76 and 0.66, respectively. Using PCT as a measure for ATF in the QoE models reduces the underestimation of both IQX and WQL. In both cases, the estimated MOS using PCT is closer to the estimated MOS using perceived ATF. For example, in Figure 9, the majority of MOS estimations using PCT and perceived ATF are close to the diagonal line, which represents a tight positive correlation between them. Moreover, the MOS estimation using IQX shows a lower distance between the two estimations (using PCT and perceived ATF). The computed R-squared is for WQL and IQX are 0.79 and 0.76, respectively. It can be seen that, while the R-squared for WQL using PCT and objective ATF stayed the same (due to the logarithmic nature), the R-squared for IQX, which is an exponential model, is improved by 0.10.  
It is acknowledged that, in order to comprehensively demonstrate the influence of PCT on WQL/IQX, an end to end subjective test evaluation would be valuable. However, it is presented here with constants taken from another study [6] to illustrate how PCT can improve speed metrics, like SI, and as a component to improve QoE estimation models.