## 3 System Model
### Transportation Network Architecture  
As shown in Figure 1, the transportation network architecture includes a road network and communication network, which is composed of AEVs, charging infrastructures, and RSUs. The V2X topology is considered to be a combination of V2V, V2I, and V2G. In the V2X topology scenario, AEVs can communicate with each other and with RSUs via one-hop or multi-hop. AEVs can also communicate with charging infrastructures via one-hop and multi-hop V2V and V2R. RSUs can communicate with each other through wired connections. The V2X topology can help create a connected and efficient transportation system that allows for real-time information exchange, which can improve the efficiency and convenience of the overall transportation system. The details are as follows:  
The road network is described as \(\mathrm{G}(\mathrm{V},\Theta)\), where \(\mathrm{V}\) stands for the set of road nodes, and \(|\mathrm{V}|=\mathrm{N}\), \(\Theta\) represents the set of road segments, and \(|\Theta|=\mathrm{M}\). For \(\forall i,j\in\mathrm{V}\), if there is a direct road segment formed, we express it as \((i,j)\), and \((i,j)\in\Theta\). If the road segment \((i,j)\) is an ES, then \(r_{ij}=1\), otherwise \(r_{ij}=0\). \(\Theta_{r}\) represents the set of all ESs. We set \(O(i)=\{j\in\mathrm{V}|(\mathrm{i,j})\in\Theta\}\) as the adjacent node of road node \(i\). The length of section \((i,j)\) is expressed as \(L_{ij}\). Since all road segments in the road network have driving directions, to distinguish different lane directions, we define \((i,j)\) and \((j,i)\) as two different segments, i.e., \((i,j)\) is not equal to \((j,i)\), but \(L_{ij}=L_{ji}\). The starting node and destination node of AEV are denoted as \(s\) and \(d\), respectively. The time of AEV at the starting node is denoted as \(t_{s}\). AEVs are equipped with a global positioning system (GPS), sensing system, and computer system, which can detect its own travel information and can constantly update it. The travel information of an AEV includes the state of charge (SoC), speed, road segment ID, and time stamp. Each AEV is equipped with an on-board unit (OBU) to realize the communication between V2V, V2R, and V2G [35; 36]. An AEV obtains real-time traffic conditions and charging infrastructures service status information from the nearest RSU via the proposed joint push-pull communication mode to realize dynamic path optimization and charging selection. We assume that the time for AEV \(k\) to enter the intersection communication range at road node \(i\) is similar to the time for AEVs to arrive at road node \(i\), expressed as \(t_{i}^{k}\), and the time of AEV \(k\) leaving road node \(i\) is denoted as \(t_{i}^{k}\). \(t_{ij}^{k^{\prime}}(t_{s})\) represents the travel time of the AEV \(k\) on the road segment \((i,j)\) estimated by the starting node based on the traffic information at this time, and assume that the SoC of  
Figure 1: Illustration of the transportation network architecture. AEV \(k\) reaching the road node \(i\) and reaching the \(cs_{i}\) is the same, denoted as \(C_{i}^{k}\). \(E_{ij}^{k}(t)\) is the consumption of charge of AEV \(k\) on the road section \((i,j)\). Charging infrastructures includes CSs and ESs. CSs communicate service status information (e.g., the number of charging slots in service and the remaining time, the number of vehicles in the queue, number of vehicles leaving the queue) to the nearest RSU. In this paper, we discuss the uneven distribution of CSs in some intersections. We assume that CSs are only deployed at road nodes. For example, if a CS is deployed at road node \(i\), it is denoted as \(cs_{i}\), and \(V_{cs}\) is used to denote the set of CSs. ESs are formed by charging/discharging tracks, which are composed of coils buried under the road and connected to the energy-storage device by a common bus. When AEVs move on the charging/discharging track, the energy can be transmitted to the AEVs wirelessly and dynamically.