## 4 Empirical Results
### Analytical Result  
In this section, analytical results have been obtained using MATLAB to analyze the impact of parameter changes on the mathematical formulations considered. The set of values of various parameters required to obtain the results have been mentioned in the individual plots themselves. The impact of parameter changes on \(P_{area}^{NSE}(X\geq 1)\) and \(P_{area}^{SE}(X\geq 1)\) is shown in Figure 8.  
Figure 8: Impact of parameters in \(P_{area}^{NSE}(X\geq 1)\) and \(P_{area}^{SE}(X\geq 1)\). From the results depicted in Figure 8a, it can be clearly observed that for the offset angle \(\alpha~{}=~{}50^{\circ}\), the probability \(P_{Sarea}^{NSE}(X\geq 1)\) of presence of at least one vehicle in the segment area in a non-shadowing environment is 0.7 for a vehicle density \(\lambda=0.0003\) vehicles/m\({}^{2}\). The value \(\alpha~{}=~{}50^{\circ}\) has been considered as a minimum threshold to analyze the performance of SLD-GEDIR. The results depicted in Figure 8b clearly indicate that for each of the vehicle densities considered, the probability \(P_{Sarea}^{NSE}(X\geq 1)\) of the presence of at least one vehicle in the segment area in a non-shadowing environment is equal to or greater than 0.7 for the transmission range of 500 m or above. This result has been used to analyze the performance of SLD-GEDIR. The results in Figure 8c show that for sector angle \(\alpha=50^{\circ}\), the probability \(P_{Sarea}^{NSE}(X\geq 1)\) of the presence of at least one vehicle in the segment area in a non-shadowing environment is about 0.7 for a vehicle density \(\lambda=0.0003\) vehicles/m\({}^{2}\). Moreover, for any particular value of the vehicle density considered, the probability \(P_{Sarea}^{NSE}(X\geq 1)\) increases with the increase in sector angle. For example, at \(\alpha=90^{\circ}\), the probability \(P_{Sarea}^{NSE}(X\geq 1)\) achieves the maximum value of approximately 1.0 for \(\lambda=0.0003\) vehicles/m\({}^{2}\). The impact of shadowing on the probability \(P_{Sarea}(X\geq 1)\) of the presence of at least one vehicle in the segment area has been shown in the results depicted in Figure 8d. It clearly reveals that the impact of shadowing is high for a smaller sector angle (\(\leq 40^{\circ}\)) but with the increase in sector angle (\(\geq 60^{\circ}\)) the impact is reduced drastically. The results depicted in Figure 9a show that \(PER_{link}^{N}\) is lowest with a link length of 200 m for each values of sector angle that has been considered. This observation has been used for the selection of NHVs with the best quality link. The results also reveal that the vehicles belonging to the border area are not the best NHV choice as considered in the state-of-the-art protocols since the probability of going out of transmission range is higher for border vehicles. This outcome has been further validated by the other results given in Figure 9b. The results shown in Figure 9b clearly convey that for a better quality one-hop link, the NHV must be a vehicle present well-inside the segment area but not at the border of the segment area. For example, when \(R=250~{}m\) is considered, the length of the best quality one-hop link is found to be approximately 200 \(m\). Figure 9: Impact of parameters on \(PER_{link}^{N}\) (**a**) and (**b**) in non-shadowing environment, (**c**) in shadowing environment and (**d**) impact of parameters on \(P_{NHV}\). The results in Figure 9c show the impact of shadowing on \(PER_{link}^{N}\). It can be clearly observed that the impact of shadowing increases drastically as soon as link length becomes larger than \(200\;m\). As soon as the length of one-hop link approaches towards \(R=250\;m\), \(PER_{link}^{N}\) increases faster due to higher probability of border vehicles going out of range. The results depicted in Figure 9d show that the probability of finding an NHV increases with the increase in degree of connectivity. Moreover, it also suggests that smaller sector angles give better performance with less number of next hop vehicles.