## 4 Joint Push-Pull Communication Mode  
In this section, we detail the process of information transfer in the joint push-pull communication mode and the selection of relay vehicles in a multi-hop communication routing. Real-time traffic conditions and charging infrastructure service status information are crucial for dynamic path optimization and charging selection of AEVs. We improve the traditional push-pull mode and propose a joint push-pull communication mode for AEVs to access real-time traffic conditions and charging infrastructures service status information from RSUs. Push communication mode is a passively accepted communication mode. The vehicle passively receives information from nearby RSUs. Pull communication mode is a request-based mode in which vehicles request specific information only when they need it [37]. The joint push-pull communication mode combines the strengths of these two modes to improve communication efficiency. It allows vehicles to request specific information as needed while actively sending their own information when appropriate, and passively receiving information from nearby RSUs. Therefore, the joint push-pull communication mode can provide a more efficient communication framework and contribute to the overall  
Figure 3: Illustration of intersection communication range between vehicle and RSU. Figure 2: Procedures of dynamic path-planning and charging selection system. performance of the VANET system. On the one hand, the RSU sends information to AEV in push mode. The analysis is as follows:  
**Case1:** The RSU periodically publishes charging infrastructure service status information to vehicles within the intersection communication range. **Case2:** When normal traffic is affected by a traffic accident, the RSU sends the accident message (road segment ID, estimated impact time) to the vehicles on the nearest road segment. On the other hand, the AEV requests information from the RSU in pull mode. When the SoC of the AEV is lower than threshold \(\Omega\) and cannot support it to reach the destination, the AEV implements V2G through one-hop V2R or multi-hop V2V and V2R to obtain charging infrastructures service status information, facilitating the identification of available charging infrastructure. For multi-hop communication routing, we mainly consider the stability, distance, and reputation values of adjacent vehicle nodes, and define a metric \(NR\) to select the best next-hop vehicle node with the smallest \(NR\). The expression of \(NR\) is as follows:  
\[NR=\xi_{1}LS_{kh}+\xi_{2}D_{kh}+\xi_{3}M_{kh}, \tag{1}\]  
here, \(0\leq\xi_{1}\leq 1,0\leq\xi_{2}\leq 1,0\leq\xi_{3}\leq 1\), and \(\xi_{1}+\xi_{2}+\xi_{3}=1\), \(LS_{kh},D_{kh}\) and \(M_{kh}\) are the link stability, distance between vehicle node \(h\) and last-hop vehicle node \(k\), and the reputation values of vehicle node \(k\), respectively. Link stability is an indicator to measure the lifetime of the wireless link between two vehicular nodes, which was proposed in [38]. Assuming that the positions of vehicle \(k\) and its neighbor node \(h\) at time \(t\) are \(\left(x_{k},y_{k}\right)\) and \(\left(x_{h},y_{h}\right)\), and the positions of them at time \(t+\Delta t\) are \(\left(x_{k}^{\prime},y_{k}^{\prime}\right)\) and \(\left(x_{h}^{\prime},y_{h}^{\prime}\right)\). The movement vectors of node \(k\) and \(h\) in time interval \(\Delta t\) are \(\left(m_{k}^{x},m_{k}^{y}\right)=\left(x_{k}-x_{k}^{\prime},y_{k}-y_{k}^{ \prime}\right)\) and \(\left(m_{h}^{x},m_{h}^{y}\right)=\left(x_{h}-x_{h}^{\prime},y_{h}-y_{h}^{ \prime}\right)\), respectively. Then, link stability is defined as:  
\[LS_{kh}=1-\frac{\min\left(\sqrt{\left(m_{k}^{x}-m_{h}^{x}\right)^{2}+\left(m_ {k}^{y}-m_{h}^{y}\right)^{2}},R\right)}{R}, \tag{2}\]  
where \(R\) is the communication range of vehicles. \(h\in N_{k}\), \(N_{k}\) is the set of neighbor nodes of the vehicle \(k\). Larger \(LS_{kh}\) denotes a lower variation in the position between two vehicles \(k\) and \(h\).