## 2 Material and Methods
### Proposed Analytical Model  
A V2X communication system is considered, where information about traffic transfers from any moving vehicle to improve road safety and enhance traffic efficiency. The system, for any vehicle-to-everything pair (V, X), consists of several vehicles (V), where V \(\varepsilon\left\{1,\ldots,n\right\}\), infrastructure, and interfering devices (I), where I \(\varepsilon\left\{1,\ldots,K\right\}\), as shown in Figure 1. The proposed model aims to find the interference transmission power (\(P_{I}\)) with a given outage probability (\(p_{outV2X}\)) target to enhance the system quality of service (QoS) by increasing the system overall system data rate (\(R_{bV2X}\)), which in return increases packet delivery ratio and minimizes packet loss rate and average end-to-end delay, i.e.,  
\[\begin{array}{l} \begin{array}{l}\begin{array}{l}Max\sum R_{bV2X}\\ s.t.\ \ \ C1:\{p_{outV2X}\leq 1-U\}\\ \ \ C2:\{P_{V}\leq P_{Vmax}\}\end{array}\end{array}  \tag{1}\]  
where \(C1\) and \(C2\) are the constraints of the optimization formulation problem. \(C1\) is considered that the V2X outage probability (\(p_{outV2X}\)) must satisfy the required QoS (\(U\)). \(C2\) articulates the fact that the vehicle transmission power (\(P_{V}\)) should not exceed the maximum vehicle transmission power (\(P_{Vmax}\)). \(U\) is the QoS of any V2X link, which can be expressed as:  
\[U=1-p_{outV2X} \tag{2}\]The probability that the receiver has a signal-to-interference-plus-noise-ratio (\(SINR\)) less than the required signal-to-interference-plus-noise-ratio threshold (\(SINR_{th}\)) is known as system outage probability, let \(SINR_{th}\) refers to \(\xi\). Therefore, \(p_{outV2X}\) can be formulated as [29]:  
\[p_{outV2X}=p(SINR\leq\xi)=1-\frac{P_{V}|h_{V2X}|^{2}}{\xi\sum_{i=1}^{K}P_{I}|h_{ I2X}|^{2}+P_{V}|h_{V2X}|^{2}}\,e^{-\frac{\xi\,N}{P_{V}|h_{V2X}|^{2}}} \tag{3}\]  
Assuming that \(N\ll P_{V}|h_{V2X}|^{2}\), then Equation (3) can be rewritten as:  
\[p_{outV2X}=1-\frac{P_{V}|h_{V2X}|^{2}}{\xi\sum_{i=1}^{K}P_{I}|h_{I2X}|^{2}+P_{V }|h_{V2X}|^{2}} \tag{4}\]  
where \(|h_{V2X}|^{2}\) and \(|h_{I2X}|^{2}\) are the channel gain coefficients between V and X and between any interfere device and X, which can be modeled as [30]:  
\[|h_{V2X}|^{2}=\frac{|h_{V2X}|^{2}}{PL_{V2X}} \tag{5}\]  
\[|h_{I2X}|^{2}=\frac{|h_{I0I2X}|^{2}}{PL_{I2X}} \tag{6}\]  
Here, the noise power spectral density is denoted by \(N\) is which is represented as \(N=N_{o}B\), and the system bandwidth in Hertz is denoted by \(B\). Moreover, \(P_{I}\) represents the interference transmission power between any interference device and X. The parameters \(|h_{oV2X}|^{2}\) and \(|h_{oI2X}|^{2}\) follow a complex normal distribution \(\mathcal{CN}\sim(0,1)\). \(PL_{V2X}\) and \(PL_{I12X}\) are the path loss between V and X and between any interference device and X, respectively. where \(PL_{V2X}\) and \(PL_{I12X}\) can be expressed as [30]:  
\[PL_{V2X}=\frac{1}{PL_{V2X}\,d_{V2X}^{\alpha}} \tag{7}\]  
Figure 1: V2X communication. \[PL_{II2X}=\frac{1}{PL_{0I2X}\,d_{II2X}{}^{\alpha}} \tag{8}\]  
where \(PL_{0V2X}\) and \(PL_{0I2X}\) are the path loss constant between V2X and between any interfere transmitting and X, respectively. \(d_{V2X}\) and \(d_{II2X}\) are the transmission distance between V2X and the distance between any interfere transmitting and X, respectively. \(\alpha\) is the path loss exponent. In this work, the main objectives are to evaluate the efficiency and reliability of the proposed model in terms of achievable data rate, packet delivery ratio, packet loss rate, average end-to-end delay, and to optimize it under vibrant network conditions. A vehicle network is considered where the transmission paths between any pair V-X are subjected to propagation path loss and narrowband Rayleigh fading with additive white Gaussian noise (AWGN) [31]. Moreover, the considered fading channel for different paths is assumed to be statistically mutually independent.