## 4 Results
### Statistical Error Propagation in QoE considering Correlation between PLR and Jitter
For instance, for sample size 800 the propagated CI width is 3 MOS units at PLR = 0.0035. This means that if we sequentially evaluate MOS at PLR = 0.0035 we know that 95% of these evaluated MOS values will lie between MOS = 4 and MOS = 1. This is significant uncertainty in the evaluated QoE. This signifies that it is very important to consider the sampling errors to evaluate QoE more accurately. Moreover, at relatively low and high PLR values the CI width was found to be significantly lower when compared to PLR > 0.001 and PLR < 0.01. This is because at very low PLR levels (PLR \(\approx\) 0) perceived quality is consistently high (MOS = 5) and critically the value of \(\partial QoE/\partial PLR\) is very small. The same holds true for high PLR levels (PLR > 0.05) where the QoE is consistently low (MOS = 1) and again \(\partial QoE/\partial PLR\) is very small; hence, in both cases the propagated statistical errors are very small. Whereas in the region between PLR > 0.001 and PLR < 0.01, \(\partial QoE/\partial PLR\) is large and hence the propagated errors in QoE are significantly larger. A very similar observation was reported in [36] where authors showed that the QoE varies mostly in the middle of the scale. Additionally, this is attributed to the use of an exponential function to model QoE, as exponential functions inherently have more variations at low PLR and are consistently low at high PLR levels. Figures 2 and 3 support our preliminary analysis, and it can be seen that with such a large increase in jitter values from 10 ms to 80 ms there is no significant change in the QoE confidence interval width. This does not mean that jitter does not affect the QoE of VoD applications, as increase in jitter magnitude results in degradation of QoE for VoD as demonstrated in Figure 1. Moreover, the slope of the QoE (jitter) function is significantly steeper at jitter = 10 ms as compared to the slope at jitter = 80 ms. Even then \(\partial QoE/\partial PLR\)\(\gg\partial QoE/\partial jitter\) at all jitter magnitudes. It means that the propagated statistical errors in QoE depends almost entirely upon the variations in QoE with PLR (which is large) while the statistical error in QoE with jitter is relatively small and can be considered to be insignificant for the models used in this paper. We extended this error propagation analysis further and considered a more sensitive QoE (jitter) model of VoD. This published model presented in Equation (7) shows a greater \(\partial QoE/\partial jitter\) value for increasing jitter values, such that for jitter = 1 ms the MOS = 5 and it rapidly degrades to MOS = 1 when the jitter increases to 5 ms [14]. Another reason for choosing this model is that it is also an exponential function, similar to the QoE (jitter) function used in this investigation. \[QoE=11.62*exp^{(-3.386*jitter)}+4.408*exp^{(-0.3477*jitter)} \tag{7}\]  
We evaluated this model using the same methodology and used Equation (5) to work out the asymptotic standard error and then confidence interval width of QoE for different operating points of PLR and jitter. Similarly, we used the lower and upper limiting two values of jitter (1 ms and 5 ms) in our results for this model. The results were plotted against PLR and presented in Figures 4 and 5. It is important that, the results from using this new jitter model (shown in Figures 4 and 5) show insignificant variations from the results in Figures 2 and 4. It is evident from Figures 2-5 that even using the more sensitive exponential function of QoE (w.r.t. jitter), the CI width of QoE of VoD application is not significantly affected. We examined this by using two different QoE (jitter) models: one (Equation (4)) in which QoE degrades gradually with increasing jitter and second (Equation (7)) in which QoE degrades sharply with increasing jitter. For instance, \(\partial QoE/\partial jitter\) of Equation (4) at jitter = 10 ms is \(-\)0.06 whereas, \(\partial QoE/\partial jitter\) of Equation (7) at jitter = 1 ms is \(-\)2.42.