## 3 System Model and Problem Formulation  
### Scenario Description  
This section describes the AoI and energy optimization model based on NR-V2X Internet of Vehicles (IoV) system as shown in Figure 1, focusing primarily on the NR-V2X resource selection method. In Mode 2, vehicles utilizing NR-V2X adopt a perception-based SPS scheme for dynamic and semi-persistent resource selection. In the dynamic scheme, resources can only be used once, while in the semi-persistent scheme, resources are reserved for RC times. Additionally, the re-evaluation mechanism in Mode 2 can detect and avoid potential conflicts in message propagation. For NR-V2X Side-Link communication, resources in the time domain are composed of frames and subframes. Each frame typically consists of 10 subframes, with each frame's duration usually being 10 ms The subframe is typically 1 ms. In the frequency domain, the smallest schedulable frequency unit is the Resource Block (RB). In the NR-V2X standard, RBs are sequentially combined to form subchannels, allowing vehicles to transmit messages on one or more subchannels [30]. Vehicles continuously monitor channels over a period of time by measuring the Reference Signal Received Power (RSRP) of all \(J\) subchannels, storing the latest information of \(N_{sense}\) time slots for use as a perception window when resource selection is required. RSRP represents the received power level of the reference signal in a mobile communication system, which is a key indicator for evaluating wireless signal quality and coverage. The higher the RSRP value, the stronger the received signal, and the better the signal quality. Then, vehicles initialize a selection window (SW) with a set of consecutive candidate time slots, namely RRI-sized slots. Each vehicle utilizes the information in the perception window to select available communication resources within the SW. Initially, \(Z_{A}\) is set to include all slots in the SW, and if \(z_{n}\) represents the time slot \(n\) following the perception window, then \(Z_{A}=[z_{n}+T_{1},z_{n}+T_{1}+1,\ldots,z_{n}+\Gamma]\). Then, vehicles exclude all resources corresponding to the subframe from the set \(Z_{A}\) based on certain conditions. Firstly, due to half-duplex communication, vehicles cannot perceive the resources used by other vehicles in the same slot in the perception window. Hence, all resources corresponding to the slot need to be excluded from the SW. Secondly, if the RSRP measurement corresponding to the candidate subframe exceeds RSRP\({}_{th}\), all resources corresponding to that candidate subframe are excluded from the SW. The exclusion criterion for the RSRP of the \(i\)-th subframe (the \(j\)-th subchannel) in the SW can be expressed as follows:  
\[RSRP\left(z_{{}_{th}+T1+i-\text{{Notens}}}^{j}\right)\geq RSRP_{th}. \tag{1}\]  
If the remaining number of resources in \(Z_{A}\) is less than X% of the total available resources, RSRP\({}_{th}\) is increased by 3 dB. In NR-V2X Mode 2, X can be set to 20, 35, or 50. Finally, vehicles randomly select a communication resource from the remaining resources in \(Z_{A}\) to reserve for subsequent transmission use, transmitting RC times at intervals of RRI. RC varies with RRI to ensure the time of the selected resource is between 0.5 and 1.5 s. Therefore, as shown in reference [31], the initial value of RC for a vehicle RC0 is represented as follows:  
\[RC_{i}^{0}=\left\{ \begin{array}{cc}\frac{1000}{\max(20,\Gamma)}&20\leq\Gamma \leq 100\\ 50&1\leq\Gamma\leq 19\end{array} \right.. \tag{2}\]  
After RC decreases to 0, vehicles have the option to either continue using the preselected resources with a probability of \(P_{rk}\) or reselect new resources for transmission with a probability of \(1-P_{rk}\). Before transmitting messages,vehicles that select communication resources in time slot \(z_{old}\) may check whether these resources are still available using a reassessment mechanism (i.e., not reserved by another vehicle) [32]. Vehicles will perform  
Figure 1: NR-V2X IoV system.