## 3 Road-Based Multi-Metric Forwarder Evaluation Scheme
### Information Collection Stage
#### 3.1.2 Vehicle Trajectory
\[P_{r}(STP_{C-NFV})=1-\left(\frac{1}{\sum_{i=1}^{n}\Delta(v_{i})}\right) \tag{6}\]  
For the purpose of clarity, \(\omega\) is substituted for \(P_{r}(STP_{C-NFV})\), \(\sigma_{0}\) is substituted for \(D_{(C-NFV)}(t_{0})\), \(\sigma_{i}\) is substituted for \(D_{(C-NFV)}(t_{i})\) and the distance between SVN and DVN \(D_{(SVN\leftrightarrow DVN)}\) is replaced with \(\tau\) in the following Equations (7)-(9). \[VTJ_{(C-NFV)}=\left\{ \begin{array}{ll}1,&\text{if }\sigma_{0}\times(\omega)<R\\ 1,&\text{if }\sigma_{0}\times(\omega)>\text{Rand}\sigma_{1}\times(\omega)<R\\ \text{f}(\sigma_{0},\sigma_{i}),\text{ if }\sigma_{0}\times(\omega),\sigma_{i} \times(\omega)>\text{Rand}\sigma_{0}\times(\omega)>\sigma_{i}\times(\omega)\\ \text{g}(\sigma_{0},\sigma_{i}),\text{ if }\sigma_{0}\times(\omega),\sigma_{i} \times(\omega)>\text{Rand}\sigma_{0}\times(\omega)<\sigma_{i}\times(\omega) \end{array} \right. \tag{7}\]  
where  
\[f(\sigma_{0},\sigma_{i})=\frac{\sigma_{i}-\tau}{R-\tau} \tag{8}\]  
\[g(\sigma_{0},\sigma_{i})=\frac{\sigma_{0}-\tau}{R-\tau} \tag{9}\]  
The evaluation of the VTJ is conducted at the two paths, which are computed at each vehicle of the multipath. The positions of C-NFV and DVN are represented as \(\overrightarrow{P}_{C-NFV}\) and \(\overrightarrow{P}_{DVN}\), respectively. The brackets \(\|.\|\) is the modulus function of a vector. The trajectory parameter value increases as the C-NFV navigates towards the DVN; it decreases as the C-NFV navigates away from the DVN, as shown in Equation (7). Considering the equation, four different situations of the tracking parameters are depicted. The first situation is when the C-NFV is within the transmission coverage R of the DVN with estimation of its probability of stoppage \(\sigma_{0}\times(\omega)<R\) thus, the \(VTJ_{(C-NFV)}\) is given the highest value, which is 1, in respective of the value of \(\sigma_{1}\times(\omega)\). The second situation is when the future distance C-NFV is within the transmission coverage of the DVN with the probability of its stoppage \(\sigma_{0}\times(\omega)>R\) and \(\sigma_{1}\times(\omega)<R\); hence, the \(VTJ_{(C-NFV)}\) is also given the highest value, that is 1. The third situation is when the present distance and future distance of C-NFV are both greater than the transmission coverage with a probability of stoppage \(\sigma_{0}\times(\omega),\ \sigma_{i}\times(\omega)>R\). At this point, the condition \(\sigma_{0}\times(\omega)>\sigma_{i}\times(\omega)\) with estimation of its probability of stoppage at the subcase is considered, which means that the future distance of C-NFV to the DVN is less than the present distance of C-NFV to DVN. It means that the C-NFV is getting nearer to the DVN. The forth, which is the last situation, only the sub-case \(\sigma_{0}\times(\omega)<\sigma_{i}\times(\omega)\) is considered, it means that the future distance of C-NFV to the DVN is greater than the present distance of the C-NFV to the DVN. This impliesthat, the C-NFV is getting far apart from the DVN. Therefore, two functions fandg are introduced in Equations (8) and (9), respectively. Thus, the vehicle tracking is an important parameter for vehicular communication that can assist in selection of the optimal NFV, which improves the quality of the video delivery. The hello message receive rate, which can be related to the playback freezes and startup delay of a video packet has been discussed in the next subsection.