## 5 Sensitivity Analysis
### Sensitivity Analysis Results  
In the sensitivity analysis, some indexes do not change significantly or have the same trend of change, so this section selects representative indexes for comparison. In terms of traffic efficiency, the number of stops value is very small, even 0 when the traffic volume is small; in terms of environmental indexes, CO and fuel consumption have the same trend; and in terms of safety, the comparison of the number of conflicts between the schemes is the most significant. Therefore, four indexes, delay, travel time, CO emissions, and number of conflicts, were chosen to perform a comparative analysis of the schemes. * Comparison of Scheme 2 and Scheme 1  
Using Scheme 1 as the comparator, we calculated the improvement ratio of the four indexes in Scheme 2 relative to Scheme 1 and plotted the improvement ratio in Figure 5.  
From Figure 5a, it can be seen that there is no significant change in delay between Scheme 2 and Scheme 1 for several traffic volumes at the diverging ratio of 10%. However, as the diverging ratio and traffic volume increased, the delays of Scheme 2 improved significantly, with a maximum improvement of 37.13% when the traffic volume exceeded 4620 veh/h and the diverging ratio surpassed 10%. \begin{table}
\begin{tabular}{c c} \hline
**Item** & **Value** \\ \hline Traffic volume (veh/h) & 1320/1980/2640/3300/3960/4620/5280/5940/6600 \\ Diverging and emerging ratio (\%) & 10/20/30/40/50 \\ \hline \end{tabular}
\end{table} 
Table 9: Sensitivity analysis results on traffic volume. The design purpose of the auxiliary lane is to reduce the impact on straight traffic. Therefore, Figure 5b represents the travel time in the straight direction. It can be seen from Figure 5 that Scheme 2 has varying degrees of improvement in travel times under various traffic combinations. The most significant improvement was observed when the diverging ratio exceeded 20%, and the traffic volume was greater than 4620 veh/h. Figure 5c shows the improvement in CO emissions of Scheme 2. It is evident that Scheme 2 exhibits lower CO emissions compared to Scheme 1 under all traffic combinations. Additionally, the improvement ratio shows a positive correlation with increasing traffic volumes. Figure 5d shows a negative improvement in the number of conflicts for Scheme 2 compared to Scheme 1 at the diverging ratio of 10%. However, as the diverging ratio increased, the negative improvement in the number of conflicts in Scheme 2 decreased with the increase in traffic volume, eventually transforming into a positive improvement. There is no notable disparity in traffic efficiency between Schemes 1 and 2 when the traffic volume remains below 4620 veh/h. Both schemes can effectively accommodate the freeway's capacity at this lower traffic volume range. When the traffic volume is low, the number of conflicts is small for both schemes. It is at higher traffic volumes that a significant difference in the number of conflicts became apparent between the two schemes. Therefore, although there is a negative improvement in the number of conflicts for Scheme 2 at low traffic levels, overall, Scheme 2 is better than Scheme 1 in terms of safety. In summary, Scheme 2 is superior to Scheme 1 regarding efficiency, safety, and environmental protection. * Comparison of Scheme 3 and Scheme 1  
From Figure 6a, it is evident that Scheme 3 significantly reduces delays across all traffic conditions. The improvement ratio reaches the maximum at 30%, 5280 veh/h, and the maximum value is 89.62%. After that, the improvement ratio decreases as the traffic volume and diverging ratio increase. Based on Figure 6b, it can be seen that Scheme 3 has a positive improvement in travel time in all cases. However, the improvement ratio is small within the traffic volume of 1320-3960 veh/h. Remarkably, the improvement ratio increases rapidly when the traffic volume exceeds 3960 veh/h and reaches a maximum of 66.45% at 30%, 5280 veh/h. Figure 6c shows that Scheme 3 demonstrates a substantial improvement in CO emissions compared to Scheme 1.