## 3 Proposed Model and Problem Formulation
### Vehicle Communication Scenario
Thus, Equations (9) and (10) can be rewritten as:  
\[SINR_{AVV1}=\frac{P_{AV}|h_{AVV1}o|^{2}}{PL_{AVV1}(I_{V1}+N_{0}B)} \tag{14}\]  
\[SINR_{AVX,V1X}=\frac{P_{AV}|h_{AVXo}|^{2}}{PL_{AVX}(I_{1X}+N_{0}B)}+\frac{P_{ V}|h_{V1 Xo}|^{2}}{PL_{V1X}(I_{2X}+N_{0}B)} \tag{15}\]  
where \(PL_{AVV1}\), \(PL_{AVX}\) and \(PL_{V1X}\) are the path loss between autonomous vehicle and relay-vehicle, autonomous vehicle and any destination, and relay-vehicle and any destination, respectively, which can be modelled as \(PL_{AVV1}=PLo\ d_{AVV1}\)\({}^{\alpha}\), \(PL_{AVX}=PLo\ d_{AVX}\)\({}^{\alpha}\) and \(PL_{V1X}=PLo\ d_{V1X}\)\({}^{\alpha}\). Here, the parameters \(PLo\), \(d_{AVV1}\), \(d_{AVX}\) and \(d_{V1X}\) are the path loss constant, the distance between autonomous vehicle and relay-vehicle, autonomous vehicle and any destination, and relay-vehicle and any destination, respectively. The factor \(\alpha\) is the path loss exponent. Based on the assumption given in Equations (5) and (6), Equation (15) can be rewritten as:  
\[SINR_{AVX,V1X}=\frac{P_{AV}|h_{AVXo}|^{2}}{PL_{o}\ d_{AVX}\)\({}^  
\[0=\frac{\partial\mathrm{q}}{\partial I_{1X}}-\frac{\partial\lambda \bigg{(}\frac{P_{V}|h_{AVX}|^{2}}{SINR_{AVXmax}}-N_{o}B-I_{1X}\bigg{)}}{\partial I _{1X}}-\frac{\partial\zeta(P_{Vmax}-P_{V})}{\partial I_{1X}}-\frac{\partial\mu( SINR_{AVX,V1X}-SINR_{th})}{\partial I_{1X}} \tag{20}\]  
\[R_{AVX\to V1X}=B_{V1X}\,log_{2}(1+SINR_{AVX,V1X}) \tag{8}\]0  
\[R_{AVX\to V1X}=B_{V1X}\,log_{2}(1+SINR_{AVX,V1X}) \tag{8}\]1  
\[R_{AVX\to V1X}=B_{V1X}\,log_{2}(1+SINR_{AVX,V1X}) \tag{8}\]2  
\[R_{AVX\to V1X}=B_{V1X}\,log_{2}(1+SINR_{AVX,V1X}) \tag{8}\]3  
\[R_{AVX\to V1X}=B_{V1X}\,log_{2}(1+SINR_{AVX,V1X}) \tag{8}\]4  
\[R_{AVX\to V1X}=B_{V1X}\,log_{2}(1+SINR_{AVX,V1X}) \tag{8}\]5  
\[R_{AVX\to V1X}=B_{V1X}\,log_{2}(1+SINR_{AVX,V1X}) \tag{8}\]6  
\[R_{AVX\to V1X}=B_{V1X}\,log_{2}(1+SINR_{AVX,V1X}) \tag{8}\]7  
By taking the derivative of (18) with respect to \(\lambda\), \(\zeta\) and \(P_{V}\), respectively, the optimal solution to (1) can be found as:  
\[R_{AVX\to V1X}=B_{V1X}\,log_{2}(1+SINR_{AVX,V1X}) \tag{8}\]8  
\[R_{AVX\to V1X}=B_{V1X}\,log_{2}(1+SINR_{AVX,V1X}) \tag{8}\]9  
\[SINR_{AVV1}=\frac{P_{AV}|h_{AVV1}|^{2}}{I_{V1}+N_{o}B} \tag{9}\]0  
\[SINR_{AVV1}=\frac{P_{AV}|h_{AVV1}|^{2}}{I_{V1}+N_{o}B} \tag{9}\]1  
\[SINR_{AVV1}=\frac{P_{AV}|h_{AVV1}|^{2}}{I_{V1}+N_{o}B} \tag{9}\]2  
\[SINR_{AVV1}=\frac{P_{AV}|h_{AVV1}|^{2}}{I_{V1}+N_{o}B} \tag{9}\]3\[SINR_{AVV1}=\frac{P_{AV}|h_{AVV1}|^{2}}{I_{V1}+N_{o}B} \tag{9}\]4 \[SINR_{AVV1}=\frac{P_{AV}|h_{AVV1}|^{2}}{I_{V1}+N_{o}B} \tag{9}\]5 (35) \[SINR_{AVV1}=\frac{P_{AV}|h_{AVV1}|^{2}}{I_{V1}+N_{o}B} \tag{9}\]6  
\[SINR_{AVV1}=\frac{P_{AV}|h_{AVV1}|^{2}}{I_{V1}+N_{o}B} \tag{9}\]7  
The expressions obtained from Equations (21), (24), (27), (31), (34) and (37) play a significant role in enhancing the system performance, since they find the optimum required distance between AV2X, which give the user the required enhanced system performance and the required user satisfaction. Additionally, controlling the transmission power leads to the decrease of total power consumption and also the cost, as well as decreasing the interference among other existing devices. Four different metrics have been considered to evaluate the system performance of the proposed model, which are:  
1. [label=1.] 2. Throughput (\(S\)): the number of the successful received packets from any source to any destination in a unit time. Throughput is usually represented in bit per second (bit/s or bps). For the proposed model, the throughput can be expressed by the following formula [34]: \[SINR_{AVV1}=\frac{P_{AV}|h_{AVV1}|^{2}}{I_{V1}+N_{o}B} \tag{9}\]8 (38)
3. Packet delivery ratio (\(PDR\)): the ratio of the number of successfully received packets by the destinations to those generated by the sources. The increment of successful packet received by the destination nodes relative to the number of packets sent by the source nodes reflects how reliable and efficient the network is.