## 3 Road-Based Multi-Metric Forwarder Evaluation Scheme
### Multi-Metric Video Streaming with Dynamic Self-Weightting Score
#### 3.2.2 Multi-Metric Video Streaming with Dynamic Self-Weighting Score
\begin{array}{l}\text{VR}_{\text{m}1}=\frac{ \big{(}\text{mt}_{1}[\text{t}_{1}]-\text{AV}_{\text{mt}_{1}}[\text{t}_{1}] \big{)}-\big{(}\text{mt}_{1}[\text{t}_{0}]-\text{AV}_{\text{mt}_{1}}[\text{t }_{0}]\big{)}}{2}\\ \text{VR}_{\text{m}2}=\frac{\big{(}\text{mt}_{2}[\text{t}_{1}]-\text{AV}_{\text {mt}_{2}}[\text{t}_{1}]\big{)}-\big{(}\text{mt}_{2}[\text{t}_{0}]-\text{AV}_{ \text{mt}_{2}}[\text{t}_{0}]\big{)}}{2}\\ \cdot\\ \cdot\\ \cdot\\ \cdot\\ \text{VR}_{\text{m}5}=\frac{\big{(}\text{mt}_{5}[\text{t}_{1}]-\text{AV}_{\text {mt}_{5}}[\text{t}_{1}]\big{)}-\big{(}\text{mt}_{5}[\text{t}_{0}]-\text{AV}_{ \text{mt}_{5}}[\text{t}_{0}]\big{)}}{2}\end{array} \right. \tag{17}\]  
where \(\ 0\leq\text{mt}_{n}[\text{t}_{0}]\), \(\text{mt}_{n}[\text{t}_{1}]\leq 1\) and \(0\leq\text{AV}_{\text{mt}_{n}}[\text{t}_{0}]\), \(\text{AV}_{\text{mt}_{n}}[\text{t}_{1}]\leq 1\), such that \(\text{n}\in(1,\ 5)\). The \(\text{mt}_{n}[\text{t}_{0}]\) and \(\text{mt}_{n}[\text{t}_{1}]\) are the initial score of individual metrics \(\text{mt}_{n}\) for period \(\text{t}_{0}\) and \(\text{t}_{1}\), respectively. The \(\text{AV}_{\text{mt}_{n}}[\text{t}_{0}]\) and \(\text{AV}_{\text{mt}_{n}}[\text{t}_{1}]\) are the mean score value of metrics \(\text{mt}_{n}\) computed for all the C-NFV. Thus, if \(\text{VR}_{\text{m}}\ \leq\ 0\), it depicts that the metrics \(\text{mt}_{n}\) is becoming worst at the period \((\text{t}_{1}-\text{t}_{0})\), as a result of this, the variation value tends to zero \(\text{VR}_{\text{m}}\to 0\). Consequently, a vector related to \(\text{VR}_{\text{m}}\) is derived as \(\text{VR}_{\text{m}}=(\text{VR}_{\text{m}1},\ \text{VR}_{\text{m}2},\ \ldots,\ \text{VR}_{\text{m}5})\). Assuming that the maximum score of a vector \(\text{VR}_{\text{m}}\) is \(\text{VR}_{\text{m}_{\text{max}(\text{x})}}\) such that \(\text{x}\in(1-\ 5)\). The highest vector variation value is termed as the \(\text{VR}_{\text{m}_{\text{max}(\text{x})}}\). Then, it follows the normalization of the vectors \(\text{VR}_{\text{m}}\) between 0 and 1, that is, \(\ 0\geq\text{VR}_{\text{m}}\leq 1\); the normalized vector is named \(\text{N}_{\text{v}}\), which is represented in Equation (18). In order to make sure that the total sum of weights of the metrics is equal to the maximum value of one. Hence, a parameter \(\tau\) value based on Equation (19) is formulated. \[N_{v}=\left\{ \begin{array}{c}N_{v1}=\frac{VR_{m\text{t}}}{VR_{m_{max}(x)}}\\.\\.\\.\\.\\ N_{v(x)}=\frac{VR_{m_{max}(x)}}{VR_{m_{max}(x)}}=1\\.\\.\\.\\ N_{v5}=\frac{VR_{m5}}{VR_{m_{max}(x)}}.\\ \end{array} \right. \tag{18}\]  
\[\tau=\frac{1}{\sum_{n=1}^{5}N_{v_{n}}} \tag{19}\]  
Further, vectors of weights \(\mathrm{Wt}\) are normalized as follows in Equation (20):  
\[\mathrm{Wt}=\left\{ \begin{array}{c}\mathrm{Wt}_{1}=\mathrm{N}_{v1}\times \tau\\.\\.\\.\\ \mathrm{Wt}_{\mathrm{x}}=\mathrm{N}_{v(x)}\times\tau=\tau\\.\\.\\.\\ \mathrm{Wt}_{5}=\mathrm{N}_{v5}\times\tau.\\ \end{array} \right. \tag{20}\]  
Therefore, the weight scores (\(\mathrm{Wt}_{1}\), \(\mathrm{Wt}_{2}\), \(\mathrm{Wt}_{3}\), \(\mathrm{Wt}_{4}\), \(\mathrm{Wt}_{5}\)) of all the metrics are dynamically computed instead of assigning equal or varied fixed weight to the multiple metrics. In the case that, all metrics are becoming worst, which is a very rare situation, then all metrics are giving equal weight scores \(\mathrm{Wt}_{n}=\frac{1}{5}\). However, this kind of situation is very difficult to occur. Thus, the dynamic self-weighting mechanism improves the optimality in the selection of NFV from the set of C-NFV. Thus, this leads to higher video packet delivery. Algorithm 2 computes the multi-metric dynamic self-weighting score for optimal NFV selection. In line 1, the weighting score is initiated by computing the metrics and their corresponding scores, which is in lines 2 and 3, respectively. Line 4 evaluates the variation value, which is based on the difference between the average metric value of a C-NFV and the initial metric value at initial time and at a different period of time, that is, line 5.