## 3 Road-Based Multi-Metric Forwarder Evaluation Scheme
### Information Collection Stage
#### 3.1.2 Vehicle Trajectory  
The Vehicle Trajectory (VTJ), which is based on future position and distance between the PFV to C-NFV and to the DVN have been considered as an important parameter that can influence positively on the selection of the NFV that navigates towards the DVN. This can improve on the delivery time of the video streaming, hence improving the quality of the video streaming. The VTJ of the C-NFV is considered to complement the VDR metric because the VDR does not guarantee the successful delivery of video streaming in case of congestion; hence, there is a need for consideration of the future position of vehicles and their distance from the destination. The VTJ of a C-NFV is estimated as a function of present and the future distance of a C-NFV to the DVN from the PFV by employing the velocities \(\text{v}_{\text{p}_{\text{i}}}\) and \(\text{v}_{\text{p}_{\text{i}}}\). It is employed to determine the track of the C-NFV, which in turn provides the navigation nearness of the C-NFV to the targeted DVN. It also estimate if the C-NFV is navigating away from the DVN based on the distance calculation and direction. The VTJ helps the PFV not to perform incorrect forwarding decision based on density and SINR without considering if the C-NFV is navigating towards the DVN, which can result to loss of video packet. Therefore, the trajectory of the C-NFV is essential and benefiting parameter for vehicular communication. The \(\text{VTJ}_{\text{(C-NFV)}}\) of a C-NFV using the Future Distance \(\text{FD}_{\text{(C-NFV\leftrightarrow DVN)}}(\text{t}_{\text{i}})\) to the DVN at time t and the Present Distance to the DVN is \(\text{PD}_{\text{(C-NFV\leftrightarrow DVN)}}(\text{t}_{0})\), here \(\text{t}_{0}\) is assumed as zero \((0)\) since it is the initial time. The \(\text{FD}_{\text{(C-NFV\leftrightarrow DVN)}}(\text{t}_{\text{i}})\) is estimated by computing the future position of the C-NFV based on its speed considering Equation (3). First, the distance between the C-NFV and the DVN needs to be estimated; it is estimated based on the position of both C-NFV and the DVN. The Euclidean distance is calculated for each of the C-NFV to the DVN as expressed in Equation (4). The speed of the C-NFV and DVN are considered as \(\text{D}_{\text{(C-NFV\leftrightarrow DVN)}}=\|\overrightarrow{\text{P}}_{ \text{C-NFV}}-\overrightarrow{\text{P}}_{\text{DVN}}\|\) in relation to the condition given in Equation (7) [11]. The distance can be expressed as follows. \[\text{D}_{\text{(C-NFV)}}(\text{t}_{0})=\ \|\overrightarrow{\text{P}}_{ \text{C-NFV}}-\overrightarrow{\text{P}}_{\text{DVN}}\| \tag{3}\]Thus, Equations (4) and (5) are derived by considering the present distance of C-NFV at \(t_{0}=0\) and the future distance of C-NFV \(t=t_{i}\), respectively. \[D_{(C-NFV\leftrightarrow DVN)}=\sqrt{\left(P_{i(C-NFV)}-P_{i(DVN)}\right)^{2}+ \left(P_{j(C-NFV)}-P_{j(DVN)}\right)^{2}} \tag{4}\]  
\[D_{(C-NFV)}(t_{i})=\|\overrightarrow{P}_{C-NFV}+\left(v_{C-NFV}\times t\right) -\overrightarrow{P}_{DVN}\| \tag{5}\]  
The probability of stoppage of a speeding C-NFV \(P_{r}(STP_{C-NFV})\) has not been considered in the trajectory or vehicle tracking estimation. This is important because the behavior and decision of driver cannot be ascertained at any given time. Hence, the probability of stoppage of a speeding C-NFV has been introduced based on the number of changes in velocity \(\Delta(v_{i})\). The number of changes in velocity is based on the variation of different speed received within the different time of the hello message exchange including stopping at the traffic lights. Therefore, the C-NFV with lower variation in speed and closer to the DVN has been considered as one of the requirements for the NFV selection. The probability of C-NFV stoppage is estimated as in Equation (6). The C-NFV with a smaller value of \(P_{r}(STP_{C-NFV})\) and a smaller value of \(VTJ_{(C-NFV)}\) distance to the DVN is considered as one of the parameter for selecting NFV.