## 4 Numerical Analysis
### Travel Cost Function Analysis  
Similarly, to intuitively show the impacts of Q, L, and \(\mathrm{B_{E}}\)) on the travel cost (M), the drawing function in Python is used to produce a three-dimensional thermal map. The \(x\)-axis of the graph represents Q, the \(y\)-axis represents \(\mathrm{B_{EV}}\), the \(z\)-axis represents L, and the color of the data points represents M. As shown in Figure 6, the color shading indicates the total cost. 1. The impact of traffic flow Q on travel cost M  
To intuitively explain the impacts of Q and \(\mathrm{B_{EV}}\) on M, the following specific data points are selected for further analysis, as shown in Table 2.  
Figure 5: Time spent at recharge nodes in the queuing system \(\mathrm{T_{W}}\). Figure 6: Travel cost. \begin{table}
\begin{tabular}{c c} \hline \hline Q & M (B\({}_{\text{EV}}\) = 0.5, L = 500) \\ \hline
0 & 0 \\
200 & 35,500 \\
400 & 71,000 \\
600 & 106,500 \\
800 & 142,000 \\
1000 & 177,500 \\ \hline \end{tabular}
\end{table} 
Table 2: Changes in the travel cost M with the traffic flow Q.  
Figure 7: Influence of the traffic flow Q on travel cost M.  
total cost increases by 177.50 yuan. This shows that the total number of vehicles directly affects the total cost, and the more vehicles there are, the higher the total cost. Because each vehicle incurs a certain cost while driving, an increase in the total number of vehicles will increase the total cost. 2. Influence of the EV penetration rate BEV on the travel cost M As shown in Table 3 and Figure 8, in the cases of Q = 500 and L = 500, the total cost M gradually decreases as BEV increases from 0 to 1. Fitting function:  
\[\text{M}=-75,000.00\text{B}_{\text{EV}}+126,250.00\]  
The fitting function shows that the effect of BEV on M is linear, with a coefficient of \(-75,000.00\). This means that for every 1 unit increase in the proportion of electric vehicles, the total cost is reduced by 75,000.00 yuan. The energy consumption per mile by an EV DEV is lower than the energy consumption per mile of a GV DGV. As the proportion of electric vehicles increases, the total cost decreases. Therefore, increasing the proportion of electric vehicles will help reduce the overall cost of travel. 3. The influence of mileage L on travel cost M As shown in Table 4 and Figure 9, in the case of Q = 500 and BEV = 0.5, M increases linearly as L increases from 0 to 1000. Figure 8: Influence of the electric vehicle penetration rate BEV on the travel cost M. \begin{table}
\begin{tabular}{c c} \hline \hline
**BEV** & **M (Q = 500, L = 500)** \\ \hline
0 & 126,250 \\
0.2 & 111,250 \\
0.4 & 96,250 \\
0.6 & 81,250 \\
0.8 & 66,250 \\
1 & 51,250 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The change in the travel cost M with the penetration rate of EVs BEV. Fitting function:  
\[\text{M}=177.50\text{L}+0.00\]  
The fitting function shows that the influence of L on M is linear, and the coefficient is 177.50. This means that for each additional kilometer of driving, the total cost increases by 177.50 yuan. The greater the mileage is, the greater the energy consumption and usage costs of the vehicle, resulting in an increase in the total cost. This suggests that the distance traveled has a direct impact on the total cost; the longer the distance traveled is, the greater the total cost. At the same time, the impacts of the total number of vehicles and mileage on the total cost have the same slope and intercept, which is reasonable because the increase in cost is the same in both cases given the proportional relationships between these parameters. An increase in the proportion of EVs will significantly reduce the total cost, which is also expected. In summary, Q directly affects the total cost, and an increase in Q will linearly increase the total cost. Increasing the penetration rate of EVs can effectively reduce the total cost because the energy cost per unit of EV travel is lower than that for EVs. The total cost is proportional to the distance traveled, and the longer the distance is, the greater the total cost.