# Optimization Strategy for Electric Vehicle Routing under Traffic Impedance Guidance
## 2 Establishment of the Electric-Power-Traffic Network Model
### Dynamic Traffic Network Model
#### 2.2.2 Traffic Impedance Model  
In the quantitative analysis of road weights, traffic impedance is commonly used by transportation agencies to describe the cost of vehicle travel on a road segment, such as travel distance, speed, and time. In static road networks, road segment length is often used as the measure of traffic impedance. However, this approach cannot accurately capture the actual driving conditions of vehicles and cannot provide effective route guidance. In the dynamic road network model presented in this paper, the travel time cost has the most significant impact on user travel behavior. Therefore, a model is introduced where travel time is used as the measure of road impedance. Road impedance includes both road impedance and node impedance [24], as shown in Figure 3.  
The road impedance model can be represented as follows:  
\[w_{ij}(t)=C_{i}(t)+R_{ij}(t) \tag{5}\]  
Figure 3: Illustration of road impedance.  
where \(\rm w_{\bar{ij}}\) represents the road impedance, which is composed of node impedance \(\rm C_{i}\) and segment impedance \(\rm R_{ij}\). \(\rm R_{ij}\) and \(\rm C_{ij}\) are determined by the road traffic saturation level S, which is defined as the ratio of real-time traffic flow \(\rm q_{\bar{ij}}\) to the maximum capacity \(\rm M_{\bar{ij}}\) of the road, as shown below:  
\[S_{ij}(t)=\frac{q_{ij}(t)}{M_{ij}} \tag{6}\]  
According to the classification criteria for urban traffic conditions, road conditions can be divided into four levels based on the saturation level S: smooth flowing (0-S-0.6), slow moving (0.6-S-0.8), congested (0.8-S-1), and heavily congested (1-S-2). The impedance models for segment impedance and node impedance corresponding to different saturation levels are as follows:  
* Segment Impedance Model The segment impedance \(\rm R_{ij}\) for different saturation levels is represented as follows: \[R_{ij}(t)=\left\{\begin{array}{ll}R_{ij}^{1}(t):t_{0}(1+m\cdot S_{ij}^{n}),& 0\leq S\leq 1\\ R_{ij}^{2}(t):t_{0}(1+m\cdot(2-S_{ij})^{n}),&1\leq S\leq 2\end{array}\right.\] (7) where \(\rm t_{0}\) represents the zero-flow travel time on the road, m and n are the influencing factors of the segment impedance model. The segment impedance model shown in Equation (7) represents the delay in travel time for vehicles in a certain road segment based on the different saturation levels of the segment.
* Node Impedance Model The node impedance \(\rm C_{i}\) for different saturation levels is represented as follows: \[C_{i}(t)=\left\{\begin{array}{ll}C_{i}^{1}(t):\frac{9}{10}\left[\frac{g(1- \lambda)^{2}}{2(1-AS_{ij})}+\frac{S_{ij}^{2}}{2q(1-S_{ij})}\right],&0\leq S \leq 0.6\\ C_{i}^{2}(t):\frac{g(1-\lambda)^{2}}{2(1-AS_{ij})}+\frac{1.5(S_{ij}-0.6)}{1-S_ {ij}}\cdot S_{ij},&S>0.6\end{array}\right.\] (8)  
In the equation, g represents the signal cycle, \(\lambda\) represents the green ratio, and q represents the arrival rate of vehicles on the road segment. When vehicles pass through road intersections, they are restricted by traffic signals, resulting in travel time delay, which is known as node impedance, as shown in the above equation.
* Integrated Traffic Impedance Model Based on the real-time saturation level of the road, the segment impedance and node impedance corresponding to the respective conditions are combined to obtain the time-varying integrated traffic impedance model as shown in Equation (9):  
\[w_{ij}(t)=\left\{\begin{array}{ll}R_{ij}^{1}(t)+C_{i}^{1}(t),&0<S\leq 0.6\\ R_{ij}^{1}(t)+C_{i}^{2}(t),&0.6<S\leq 0.8\\ R_{ij}^{2}(t)+C_{i}^{1}(t),&0.8<S\leq 1\\ R_{ij}^{2}(t)+C_{i}^{2}(t),&1<S\leq 2\end{array}\right. \tag{9}\]