## 2 Materials and Methods
### Carbon Emission Modeling of the Intelligent Vehicle Mixing Scenario
#### 2.2.2 Carbon Emission Calculation Model of Heterogeneous Traffic Flow  
The specific forms of carbon emission estimation models vary across different scenarios. This section primarily focuses on studying the intelligent vehicle dedicated lane scenario and the scenario based on the proportion of vehicles at off-ramps. 1. Carbon emission measurements of intelligent vehicle dedicated lane. Resistance will change, considering the car and vehicle position as follows: \[\text{Lead vehicle}:\ \mu\left\{ \begin{array}{ll}-0.7575x^{-1.5225}+1.0325&x \leq 7.91\\ 1&x>7.91\end{array} \right.\] (8) \[\text{Following vehicle}:\ \beta\left\{ \begin{array}{ll}-1.7834x^{-0.0672}&x \leq 55.58\\ 1&x>55.58\end{array} \right.\] (9) where \(\beta,\ \mu\) are the air resistance correction coefficients; \(x\) is the vehicle spacing in m. When the vehicle is the first car, \(x\) is the distance between the vehicle and the rear car; when the vehicle is the follower, \(x\) is the distance between the vehicle and the front car. The contrast movement rate of the vehicle queue and air resistance coefficient in the vehicle's instantaneous power consumption are modified as shown in (10) and (11). \[VSP=\frac{\frac{a(EK+EP)}{dt}+F_{w}v+F_{t}v+F_{f}v}{m}=v[a(1+\epsilon)+g\times \sin\theta+g\times C_{w}]\] (10) \[f_{e}(v,a)\left\{ \begin{array}{ll}\frac{1}{\eta}\left(\frac{Mg\mu v}{3600}+ \frac{\beta(\mu)C_{d}x^{3}}{76140}+\frac{\delta Mu}{3600}\right)&a\geq 0\\ 0&a<0\end{array} \right.\] (11)
2. Calculation of carbon emissions based on the proportion of vehicles at off-ramps The simulation explores the relationship between the exit ramp vehicle occupancy based on 1000 vehicles. The exit ramp occupancy range is set to 0 to 1, and vehicle carbon emissions are measured in hours, as shown in Table 3. The results obtained by data analysis and fitting show that there is a linear relationship between the off-ramp rate and the carbon emission in the off-ramp influence area, showing the form of quadratic function, which means that with the increase in the off-ramp rate, the carbon emission in the off-ramp influence area will also show a certain change law. This finding provides an important theoretical basis for further research and the optimization of vehicle carbon emissions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Vehicle Off-Ramp Occupancy** & **The Carbon Emissions Produced per Hour** \\ \hline
0.1 & \(7.20\times 10^{3}\) g \\ \hline
0.2 & \(7.13\times 10^{3}\) g \\ \hline
0.3 & \(7.12\times 10^{3}\) g \\ \hline
0.4 & \(7.11\times 10^{3}\) g \\ \hline
0.5 & \(7.10\times 10^{3}\) g \\ \hline
0.6 & \(7.09\times 10^{3}\) g \\ \hline
0.7 & \(7.12\times 10^{3}\) g \\ \hline
0.8 & \(7.15\times 10^{3}\) g \\ \hline
0.9 & \(7.17\times 10^{3}\) g \\ \hline
1 & \(7.20\times 10^{3}\) g \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Off-ramp vehicle share and CO\({}_{2}\) emissions in its affected area. According to existing data, the road carbon emissions calculation formula for the ramp vehicle ratio was obtained, as shown in Formula (12). \[y=ax^{2}+bx+c \tag{12}\]  
where \(y\) is the CO\({}_{2}\) emission in the off-ramp affected area affected by the proportion of vehicles at the off-ramp, \(x\) is the vehicle proportion at the off-ramp, and a, b, and c are all parameters. After substituting the specific parameters and data, two linear equations, (13) and (14), were obtained. \[y=0.21x^{2}-0.505x+7.3\quad 0\leq x\leq 0.7 \tag{13}\]  
\[y=-8.7x^{2}+15.8x\quad 0.7<x\leq 1 \tag{14}\]  
Based on Equation (12), a carbon emission calculation formula was established for the three lanes of the main expressway affected by the proportion of vehicles on the ramp:  
\[