## 5 Forwarding Metric  
The mobility in the EMCR protocol considers the calculation of the curve-metric distance between the forwarder node and its neighbors with respect to their distance from the destination. In addition, the transmission range of sensors and vehicles is considered an essential factor in the forwarding decision, with the knowledge that the transmission range of vehicles (i.e., 500 m) is different from the transmission range of sensors (i.e., 150 m). The transmission range factor plays a role in improving the forwarding decision when this factor is used to normalize the distance between the forwarder and neighbor node in the weight function.  
A forwarding node \(i\) computes the weight of neighbor node \(j\) with respect to routing to destination node \(k\). If node \(j\) is in the transmission range of sensor node \(i\), then the distance will be normalized by the transmission range of the sensor. Otherwise, if node \(j\) is in the transmission range of vehicle node \(i\), the distance will be normalized by the transmission range of the vehicle. The neighbor closer to the destination is the most suitable forwarder node. Therefore, the weight is inversely proportional to the distance between the forwarder and the neighbor. Hence \(Weight_{i,j}^{(k)}\propto(Dist_{i,k}-Dist_{j,k})^{-1}\). The equation for the normalized distance is  
\[NDisti_{i,j}^{(k)}=\frac{Dist_{j,k}-Dist_{i,k}}{R_{i}} \tag{2}\]  
where \(NDisti_{i,j}^{(k)}\) is the normalized curve-metric distance between forwarder \(i\) and neighbor \(j\) from destination node \(k\). \(Dist_{j,k}\) is the curve-metric distance of neighbor \(j\) from destination \(nodek\), and \(Dist_{i,k}\) is the curve-metric distance of forwarder \(i\) from destination node \(k\). \(R_{i}\) is the transmission range of forwarder node \(i\).  
\(Angle_{j,k}\) is the normalized weight for the angle parameter. \(Angle_{j,k}\) gives more weight to the nodes that are moving toward the destination compared to those that are moving away.  
\[Angle_{j,k}=\begin{cases}-0.5&\text{if VN are moving closer}\\ +0.5&\text{if VN are moving away.}\end{cases} \tag{3}\]  
\(Road_{j,k}\) is the normalized weight for the road parameter in order to give more weight to nodes that are along the same road compared to those that are on a different road,\[Road_{j,k}=\begin{cases}0.0&\text{if VN are on same road}\\ +0.5&\text{if VN are on different road}\end{cases} \tag{4}\]  
The residual energy ratio metric is an essential component of the protocol for WSN. The algorithm routes a packet from one sensor to another by computing the residual energy ratio for each neighboring node.  
\[RER=\frac{E_{rem}}{E_{init}}, \tag{5}\]  
where \(RER\) is the residual energy ratio that is calculated using the remaining energy, \(E_{rem}\), and the initial energy, \(E_{init}\), which is the capacity stored in the energy source.  
The node with the minimum weight value will be selected as a forwarder node. The weight calculation for vehicle nodes with mobility consideration is  
\[\begin{split} Weight^{(k)}_{i,j}(VN)=(\alpha_{1}\times NDist^{(k) }_{i,j})+(\alpha_{2}\times Angle_{j,k})\\ +(\alpha_{3}\times Road_{j,k}).\end{split} \tag{6}\]  
In order to get the minimum weight for sensor nodes, since the weight is inversely proportional to the distance between the forwarder and neighbor node, then the weight has to be directly proportional to the residual energy ratio as \(Weight^{(k)}_{i,j}\propto RER_{j}\). The weight calculation for sensor nodes with residual energy consideration is  
\[Weight^{(k)}_{i,j}(SN)=(\alpha_{4}\times NDist^{(k)}_{i,j})\times(\alpha_{5} \times RER_{j}), \tag{7}\]  
where \(\alpha_{i}\) is the weighting factor for each parameter that indicates the relative importance of the parameter in making forwarding decisions. The weighting factors in Equations (6) and (7) are set to \(\alpha_{1}=\alpha_{2}=\alpha_{3}=\alpha_{4}=\alpha_{5}=1\), to have equal importance to all factors. The results of our performance analysis are provided in the following section.