## 4 Prevention Mechanisms of the Proposed Scheme
### Probability Analysis of Vehicles Based on Elliptical Segment Area Transmission Range
By referring to the efficient transmission range for NV, we chose a transmission range between 250 and 550 m. However, we consider the smaller transmission range of 250 m as effective. This is because of reduced CO, which can be utilized in the elliptical segment probability analysis of the NV/NODV. We consider \(X\) as the random variable, which represents the number of NV/NODV present and located in the ESATR, whereby each NV/NODV possesses the global key (\(Gk\)). After each NV/NODV is authenticated and shares the \(Gk\) securely, the probability \(P_{Sma}^{ENSE}(X=n)\) in the presence of \(n\) NV/NODV in the proposed ESATR, which utilizes encrypted SRSIE, in non-shadow environment (ENSE) can be obtained in the given Equation (4) as:  
\[P_{Sma}^{ENSE}(X=n)=\frac{(\lambda\times S_{ana})^{n}\times e^{-(\lambda\times S _{ana})}}{n!} \tag{4}\]  
Substituting the value of \(S_{area}\) from Equation (3), we obtain Equation (4) as:\[P_{S_{\textit{max}}}^{ENSE}(X=n) =\left[\frac{\left[\lambda\{(\frac{\phi}{2}(\left(\alpha-\beta\right)- \frac{b}{2}(\frac{2}{\tau}\sin(\alpha-\beta))\right)=\frac{\phi}{2}((\left( \alpha-\beta\right)-\sin(\alpha-\beta))\}\right]^{n}}{n!}\right] \tag{5}\] \[\times e^{-\lambda\{(\frac{\phi}{2}(\left(\alpha-\beta\right)- \frac{b}{2}(\frac{2}{\tau}\sin(\alpha-\beta))=\frac{\phi}{2}((\left(\alpha- \beta\right)-\sin(\alpha-\beta))\}\]  
\[P_{S_{\textit{max}}}^{ENSE}(X=0) =\left[\frac{\left[\lambda\{(\frac{\phi}{2}(\left(\alpha-\beta \right)-\frac{b}{2}(\frac{2}{\tau}\sin(\alpha-\beta))=\frac{\phi}{2}((\alpha- \beta)-\sin(\alpha-\beta))\}\right]^{0}}{0!}\right]\] \[\times e^{-\lambda\{(\frac{\phi}{2}(\left(\alpha-\beta\right)- \frac{b}{2}(\frac{2}{\tau}\sin(\alpha-\beta))=\frac{\phi}{2}((\left(\alpha- \beta\right)-\sin(\alpha-\beta))\}\]  
\[P_{S_{\textit{max}}}^{ENSE}(X=0) =e^{-\lambda\{(\frac{\phi}{2}(\left(\alpha-\beta\right)-\frac{b}{2 }(\frac{2}{\tau}\sin(\alpha-\beta))=\frac{\phi}{2}((\left(\alpha-\beta\right) -\sin(\alpha-\beta))\}} \tag{6}\]  
The probability of \(P_{S_{\textit{max}}}^{ENSE}(X\geq 1)\) in the presence of at least one vehicle in the segment area with encryptin and authentication and sharing of global key \(Gk\) in a non-shadowing environment can be expressed as given in Equation (7):  
\[P_{S_{\textit{max}}}^{ENSE}(X\geq 1)=1-e^{-\lambda\{(\frac{\phi}{2}(\left( \alpha-\beta\right)-\frac{b}{2}(\frac{2}{\tau}\sin(\alpha-\beta))=\frac{\phi}{ 2}((\left(\alpha-\beta\right)-\sin(\alpha-\beta))\}} \tag{7}\]  
The above PESATRM probability analysis model, which is integrated with the PSAM, is proposed in addition to the message broadcast algorithms that were investigated. These have been used to decrease the broadcasting storm in the network. Moreover, the models' integration reduces trustworthiness concerns in the network. The combined effect of the PESATRM and algorithms also increase established trust in the network. This was possible through achieving an efficient ESATR. In addition, the algorithms implemented in the proposed scheme models PESATRM and PSAM also lessen the iterated broadcasting to keep less overhead information and decrease the network load. The process of using the PESATRM and PSAM integration probability models and the broadcast/multicast and unicast algorithms to verify the network is secured from HDSAs, including DoSJA and other associated attacks. Even though the deployment of these models in the scheme were satisfactory, in order to make the model more efficient for selection of trustworthy vehicles or nodes in the network, the Cuckoo/CSA (ABC) optimization algorithm, which include swarm intelligence, is applied to select more trustworthy nodes. This is based upon the probability of legitimate selection of the nodes to be part of the network. Therefore, probability analysis specification selection using Cuckoo/CSA (ABC) for selecting the legitimate nodes to be part of the network communication process is determined as follows. Table 2 shows the Cuckoo/CSA (ABC) specification.