## 3 System Model and Problem Formulation
### NR-V2X-NOMA Communication Model  
In the NR-V2X vehicular networking system, we denote the transmitter as \(i\), receiver vehicle as \(j\), and the considered time slot as \(t\). SINR is represented as follows:  
\[\eta_{i\to j}^{t}=\frac{h_{s}^{t}h_{i\to j}^{t}p_{i}^{t}\Big{/}L_{d}(d_{i\to j})}{ I_{t\to j}^{t}+p_{n}}, \tag{3}\]  
where \(p_{i}^{t}\) is the transmission power by vehicle \(i\), \(h_{s}^{t}\) is the random small-scale fading gain, \(h_{i\to j}^{t}\) is the large-scale fading gain of the link from \(i\) to \(j\) in time slot \(t\), \(L(d_{i\to j})\) is the path loss as a function of the distance from \(i\) to \(j\), \(p_{n}\) is the noise power, and \(I_{i\to j}^{t}\) is the interference power. In Equation (3), the numerator represents the received power, while \begin{table}
\begin{tabular}{c l l l} \hline \hline
**Notation** & **Description** & **Notation** & **Description** \\ \hline \(N_{v}\) & Total number of vehicles. & \(D\) & Road length. \\ \hline \(D_{RSI}\) & RSU coverage range. & \(w\) & The maximum distance of the vehicle as the receiver. \\ \hline \(RC\) & The value of the resource counter. & \(\Gamma\) & The size of SW and RRI. \\ \hline \(\eta\) & SINR. & \(h_{s}\) & Small scale fading gain. \\ \hline \(h\) & Large scale fading gain. & \(p\) & Vehicle transmission power. \\ \hline \(L_{d}\) & Path loss. & \(d\) & Distance between communication vehicles. \\ \hline \(I\) & Interference signal power. & \(p_{n}\) & noise power. \\ \hline \(\sigma\) & Signal overlap degree. & \(C\) & Received signal power. \\ \hline \(u\) & Communication situation. & \(W\) & Resource channel bandwidth for vehicle selection. \\ \hline \(G\) & Message size. & \(\Phi\) & The AoI at the receivers. \\ \hline \(\varphi\) & The AoI of messages in the queue. & \(\beta\) & Has vehicle transmitted messages. \\ \hline \(q\) & Queue length. & \(L\) & Queue capacity. \\ \hline \(E\) & Energy consumption generated by vehicles in reserved resources. & \(l_{i}\) & Communication time of vehicle i. \\ \hline \(N\) & Number of receivers for a certain vehicle. & \(P^{l}(u^{t}=1)\) & The probability of the receiving end successfully receiving the message. \\ \hline \(\theta_{x}\) & The weights of the transition function strategy network between discrete and continuous actions. & \(\theta_{Q}\) & The weights of state action value function strategy networks. \\ \hline \(lr_{x}\) & Learning rate of transition function strategy networks between discrete and continuous actions. & \(lr_{Q}\) & Learning rate of state action value function strategy network. \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The summary for notations. the denominator is the sum of the noise power and interference, assumed to be Gaussian with zero mean. \(I_{i\to j}^{t}\) is defined as follows:  
\[I_{i\to j}^{t}=\sum_{k\in\mathcal{V}^{t},k\
eq i}\sigma_{k,i}^{t}\frac{h_{k}^{t }h_{k\to j}^{t}p_{k}^{t}}{L_{d}(d_{k\to j})}, \tag{4}\]  
where \(V^{t}\) is the set of nodes transmitting in time slot \(t\), \(\sigma_{k,i}^{t}\) is a multiplicative coefficient between 0 and 1 that quantifies the interference power of \(k\) in the subchannel used by \(i\), relative to the transmission power of \(k\). If \(k\) uses the exact same subchannel as \(i\), \(\sigma_{k,i}^{t}\) is 1; if its signal does not overlap or only partially overlaps, \(\sigma_{k,i}^{t}\) is less than 1. The calculation of \(\sigma_{k,i}^{t}\) takes into account the in-band emission, consistent with the specifications in [33]. The receiver \(j\) employs a serial interference cancellation mechanism in NOMA to decode multiple messages in different subchannels. The decoding process involves selecting the message with the maximum power as the desired signal, while treating the others as interference signals.