## 2 Materials and Methods
### Carbon Emission Modeling of the Vehicle Queue Driving Scenario
#### 2.3.1 Carbon Emissions of Traffic Flow under Electric Vehicle Queue  
During the travel of an electric vehicle queue, the carbon emissions of the queue are influenced not only by the queue size but also significantly by the desired headway of intelligent vehicles within the queue.  
1. Carbon emissions based on the size of the electric fleet  
Consider a situation in which the number of electric vehicles mixed in can form a fleet. Assuming that the total number of vehicles in the road section is N; then, all the following vehicles in the fleet will maintain an equilibrium speed when driving. At the same time, the maximum scale of the fleet is \(n\), and the wind resistance correction coefficient is \(\beta,\ \mu\).  
\[\begin{array}{c} EC_{d}=\sum\limits_{t=1}^{T}\sum\limits_{i=1}^{n_{i}}f_{i}(p_{ t})\times ER_{i}(p_{t},co_{2})+\sum\limits_{t=1}^{T}\sum\limits_{j=1}^{n_{j}} \frac{1}{\eta}(\frac{Mg\mu\
u_{j}}{3600}+\frac{\mu C_{d}A\
u_{j}^{3}}{76140}+ \frac{\delta M\
u_{j}\mu_{j}}{3600})\times 697.5\\ \hskip 142.26378 pt+\sum\limits_{t=1}^{T}\frac{1}{\eta}(\frac{Mg\mu\
u_{c}}{3600 }+\frac{\delta C_{d}A\
u_{c}^{3}}{76140}+\frac{\delta M\
u_{c}\mu_{c}}{3600} )\times n_{ci}\times n\times 697.5\end{array} \tag{16}\]  
where \(EC_{d}\) is the CO\({}_{2}\) emission when the EV queue is not degraded in the heterogeneous traffic flow, \(v_{e}\) is the equilibrium speed when the vehicle travels in a queue, \(n_{i}\) is the human-driven fuel vehicle in the heterogeneous traffic flow, \(n_{ci}\) is the number of follower vehicles in queue \(i\), \(n_{j}\) is the first vehicle in all queues, and n is the fleet size.  
The carbon emissions based on the expected front time distance of the intelligent vehicle  
The following models of ACC and CACC vehicles reflect the relationship of front-time distance in heterogeneous traffic flows and were verified by the PATH laboratory at the University of California, Berkeley.  
Suppose that the total number of vehicles in the off-ramp-affected area is sufficiently large, N, where the intelligent vehicle mixing rate is \(p\) (\(p=1\)). When \(p=1\), the degradation of the cruise system is divided into three situations: front of the intelligent vehicle, largest intelligent fleet in front of the intelligent vehicle, and degradation mechanism of the two cruise systems. To facilitate this study, carbon measurement modeling was conducted when the front of the intelligent vehicle reached the largest intelligent fleet.  
Assuming that there are i intelligent fleet that have reached the largest n in front, the queue head is artificial following vehicles, the CACC vehicle mixing rate is \(p\) (\(p=1\)), the number of CACC vehicles is \(Np\), and the number of ACC vehicles is \(N*\frac{(1-p)p^{p+1}}{1-p^{2}}\). Then, the following carbon emission model is:  
\[\begin{array}{c}EC_{n}^{m}=\sum_{l}^{T}\sum\limits_{k=1}^{n_{k}}f_{k}(p_{t}) \times ER_{k}(p_{t},co_{2})+\sum\limits_{t}^{T}\sum\limits_{i=1}^{N*P}\frac{ 1}{\eta}(\frac{Mg\mu v_{i}(t)}{3600}+\frac{\beta C_{d}Av_{i}^{3}(t)}{76140}+ \frac{\delta Mv_{i}(t)a_{i}(t)}{3600})\\ \times 697.5+\sum\limits_{l}^{T}\sum\limits_{j=1}^{N*\frac{(1-p)p^{p+1}}{1-p^{ 2}}}\frac{1}{\eta}(\frac{Mg\mu v_{i}(t)}{3600}+\frac{\beta C_{d}Av_{i}^{3}(t)} {76140}+\frac{\delta Mv_{j}(t)a_{j}(t)}{3600})\times 697.5\end{array} \tag{17}\]  
where \(EC_{n}^{m}\) considers the CO\({}_{2}\) emissions generated in the case of CACC degradation caused by the largest intelligent fleet in front of the intelligent vehicle. Here, \(k\) is the vehicle queue; \(i\) is the vehicle queue CACC follower; \(j\) is the vehicle queue ACC follower; the \(v_{i}(t)\) is the speed of the CACC vehicle at time \(t\); and \(\alpha,\beta\) is the air resistance correction coefficient of the vehicle leader and the following vehicle respectively.