## 5 Capacity Evaluation Analysis
### Capacity Estimation under CAVs Environment  
The aforementioned section presents a capacity assessment method for traffic flow and validates it in an HV environment (Ra = 0%). This method allows for estimating the capacity of a bus stop using measured data of FD or FLR and actual traffic volume Q. However, as CAVs have not been widely deployed at this stage, there is a lack of measured data, making it currently impossible to utilize this method for estimating the capacity of bus stops under the CAVs environment. Therefore, this paper introduces a supplementary approach to predict the capacity of bus stops under the CAVs environment (referred to as C\({}_{\text{CAV}}\)) based on indicators derived from the conventional human-driven traffic flow.  
Initially, we investigated the relationship between capacity and penetration rates (0%, 50%, and 100%) for all scenarios. After comparing various common functional models, we found that a quadratic polynomial function could better describe the relationship between C\({}_{\text{CAV}}\) and C\({}_{\text{HV}}\). Thus, a fourth-degree polynomial function was chosen to fit the numerical relationship between FD/Q-C\({}_{\text{CAV}}\) and FLR/Q-C\({}_{\text{CAV}}\).  
Subsequently, simulation data of FD at a 0% penetration rate were selected to fit the relationship models between FD and C\({}_{\text{CAV}}\). However, since the method of capacity evaluation using FD is not applicable to single-berth curbside bus stops, data for this scenario were not included. The fitting results and goodness of fit are presented in Table 14, and the corresponding fitting graphs are shown in Figure 14.  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Bus Stop**} & \multicolumn{2}{c}{**R2**} \\ \cline{2-3}  & **FD—Capacity** & **FLR—Capacity** \\ \hline No. 1 & 0.9070 & 0.9101 \\ No. 2 & 0.9001 & 0.8879 \\ No. 3 & 0.8522 & 0.9253 \\ No. 4 & 0.9425 & 0.9230 \\ \hline \hline \end{tabular}
\end{table}
Table 13: The fitting function used and the R\({}^{2}\) of FLR/Q-Capacity.  
Lastly, the FLR data at a 0% penetration rate and the capacity at 50% and 100% penetration rates from all ten scenarios were selected to establish a functional relationship expression between FLR and C\({}_{\text{CAV}}\). The fitted functional expressions and goodness of fit are presented in Table 15, and the corresponding fitting graphs are displayed in Figure 15.  
The analysis of the fitting results reveals that using the FD indicator yields better fitting performance for C\({}_{\text{CAV}}\), with R2 values consistently exceeding 0.98. However, its applicability is limited to bus bay stops. Although the goodness of fit for FLR is relatively lower, it can provide estimations for C\({}_{\text{CAV}}\) across all types of bus stops mentioned in this paper. Therefore, when applying this relationship model, the selection can be made based on the type of bus stop. In summary, both FD and FLR indicators are capable of predicting the capacity of bus stops under the CAVs environment and exhibit satisfactory performances. However, it is important to note that the actual performance of this relationship model still requires validation due to the lack of real-world data at present.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Penetration Rate** & **Function Expression** & \(\mathbf{R^{2}}\) \\ \hline
50\% & \(y=-6.3185\times 10^{-9}x^{4}+5.1064\times 10^{-7}x^{3}+\) & 0.95952 \\
100\% & \(y=-2.4517\times 10^{-10}x^{4}+6.4746\times 10^{-8}x^{3}-\) & 0.95693 \\ \hline \hline \end{tabular}
\end{table}
Table 15: The fitting function and the R\({}^{2}\) of FLR/Q-C\({}_{\text{CAV}}\).  
Figure 14: The FD–C\({}_{\text{CAV}}\) relationship fitting curve under different Ra. (**a**) Ra = 50%; (**b**) Ra = 100%.  
Figure 15: The FLR-C\({}_{\text{CAV}}\) relationship fitting curve under different Ra. (**a**) Ra = 50%; (**b**) Ra = 100%.